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Review Article Volume 6 Issue 1

Checking the absolute value of the speed of light in 1D

David Marqués Villarroya

Department of Physics and Chemistry, IES Vilaplana (Vinaròs), Spain

Correspondence: David Marqués Villarroya, Department of Physics and Chemistry, IES Vilaplana, Spain, Tel 687813228

Received: January 31, 2023 | Published: February 10, 2023

Citation: Villarroya DM. Checking the absolute value of the speed of light in 1D. Open Access J Sci. 2023;6(1):5-7. DOI: 10.15406/oajs.2023.06.00185

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Abstract

Einstein's theory of relativity establishes that the measurement of the speed of light is constant and invariant in any frame of reference. In this article, we will review that this postulate is fulfilled by applying the Einstein’s velocity addition for the case of one spatial dimension (1D). This work may be of special usefulness for physics students and teachers of pre-university and first-year university levels to introduce relativistic theory.

Keywords: speed of light, velocity addition, relativity, Einstein, Galileo

Introduction

At the beginning of the 20th century there were some experiments that could not be explained by the classical mechanics of Newton and Galileo,1 for example, the experiments of Michelson-Morley2 and Bertozzi,3 which are well known by scientific community.2,3 In order to explain these experiments, after the attempt of some scientist like Lorentz and Minkowsky, Einstein developed the special theory of relativity,4–7 which is based on solely two postulates.8 The first postulate states that the laws of physics are the same in any inertial frame of reference.8 The second postulate states that the speed of light is the same as measured from any frame of reference, regardless of the relative speed between the observer and the source.8 Moreover, the speed of light in the vacuum is the highest possible in the universe and it cannot be surpassed.9 In this article, we will focus on the second postulate and verify that it holds in one dimension (1D) using Einstein's relativistic velocity addition law, which contrasts with Galileo's classic velocity addition theory and contradicts human common sense, as we will see in the following sections. Therefore, the main objective of this article consists of providing some interesting ideas and developments in order to improve the pedagogical field of secondary and higher education about the second postulate of Einstein following the same line of recent works about teaching relativity.10–12

Relativistic addition of velocities

The velocity addition theory in relativistic terms developed by Einstein is well known to the scientific community. This theory establishes the velocity perceived by two systems moving with relative velocities between them considering that none of these systems can surpass the speed of light. This theory is a generalization of Galileo's velocity addition rule that is used in classical physics when velocities are much less than the speed of light. Consider an inertial frame of reference O and two systems A and B that move along the X axis according to O Figure 1.

Figure 1 Addition of velocities scheme.

The velocity addition theory in relativity establishes that:5

u x ' = u x v 1 v c 2 u x MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjYdH8pE0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=x b9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaDaaale aacaWG4baabaGaai4jaaaakiabg2da9maalaaabaGaamyDamaaBaaa leaacaWG4baabeaakiabgkHiTiaadAhaaeaacaaIXaGaeyOeI0YaaS aaaeaacaWG2baabaGaam4yamaaCaaaleqabaGaaGOmaaaaaaGccaWG 1bWaaSbaaSqaaiaadIhaaeqaaaaaaaa@45A3@          (1)

in which u x MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjYdH8pE0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=x b9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaBaaale aacaWG4baabeaaaaa@3911@ is the speed at which the inertial frame of reference O observes system B is moving; v MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjYdH8pE0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=x b9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamODaaaa@37E9@ is the speed at which the inertial frame of reference O observes system A is moving; c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjYdH8pE0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=x b9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4yaaaa@37D6@ is the speed of light; and u x ' MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjYdH8pE0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=x b9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaDaaale aacaWG4baabaGaai4jaaaaaaa@39BD@ ;is the speed at which A observes B is moving.

From this point on, we consider that system B is a photon that moves at the speed of light ( c ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjYdH8pE0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=x b9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacaWGJb aacaGLOaGaayzkaaaaaa@395F@ according to the inertial frame of reference O in the positive direction of the x axis. Therefore, u x =c, MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjYdH8pE0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=x b9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaBaaale aacaWG4baabeaakiabg2da9iaadogacaGGSaaaaa@3BB9@ and the expression (1) can be rewritten as:

u x ' = cv 1 v c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjYdH8pE0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=x b9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaDaaale aacaWG4baabaGaai4jaaaakiabg2da9maalaaabaGaam4yaiabgkHi TiaadAhaaeaacaaIXaGaeyOeI0YaaSaaaeaacaWG2baabaGaam4yaa aaaaaaaa@4148@          (2)

In the following sections we will study the speed of B (a photon) perceived by the observer A ( u x ' ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjYdH8pE0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=x b9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacaWG1b Waa0baaSqaaiaadIhaaeaacaGGNaaaaaGccaGLOaGaayzkaaaaaa@3B50@ according to the relative movement that these two systems maintain. We will also compare and discuss the results with the classical Galileo velocity addition.

Speed of light with observer moving at vx

Consider that the observer A is moving in the positive X axis with velocity v x <c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjYdH8pE0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=x b9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamODamaaBaaale aacaWG4baabeaakiabgYda8iaadogaaaa@3B08@ according to the inertial frame of reference O in such a way that A is going after B Figure 2.

Figure 2 System A going after system B at speed  according to the inertial frame O.

Then, the system B is moving according to the observer A with this velocity:

u x ' = c v x 1 v x c = c v x c v x .c=c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjYdH8pE0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=x b9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaDaaale aacaWG4baabaGaai4jaaaakiabg2da9maalaaabaGaam4yaiabgkHi TiaadAhadaWgaaWcbaGaamiEaaqabaaakeaacaaIXaGaeyOeI0YaaS aaaeaacaWG2bWaaSbaaSqaaiaadIhaaeqaaaGcbaGaam4yaaaaaaGa eyypa0ZaaSaaaeaacaWGJbGaeyOeI0IaamODamaaBaaaleaacaWG4b aabeaaaOqaaiaadogacqGHsislcaWG2bWaaSbaaSqaaiaadIhaaeqa aaaakiaac6cacaWGJbGaeyypa0Jaam4yaaaa@5052@           (3)

Therefore, B is moving away from A at the speed of light  and the second postulate of Einstein’s theory is satisfied in this case. This result is incongruent with the classical conception of Galileo’s addition of velocities because this velocity should be u x ' =c v x MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjYdH8pE0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=x b9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaDaaale aacaWG4baabaGaai4jaaaakiabg2da9iaadogacqGHsislcaWG2bWa aSbaaSqaaiaadIhaaeqaaaaa@3EC6@ as we were taught in the school and our common sense dictates (because if, for example, I am the system A moving at 6 km/h and I am going after system B, which is moving at 10 km/h, my perception should be that the system B is moving away from me at 4 km/h).

Speed of light with observer moving at -vx

Consider now that the observer A is moving in the negative X axis with velocity v x <c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjYdH8pE0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=x b9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamODamaaBaaale aacaWG4baabeaakiabgYda8iaadogaaaa@3B08@ according to the inertial frame of reference O in such a way that A is moving away from B Figure 3.

Figure 3 System A moving away from system B at speed  according to the inertial frame O

.

Then, the system B is moving according to the observer A with this velocity:

u x ' = c( v x ) 1 ( v x ) c = c+ v x c+ v x .c=c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjYdH8pE0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=x b9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaDaaale aacaWG4baabaGaai4jaaaakiabg2da9maalaaabaGaam4yaiabgkHi TmaabmaabaGaeyOeI0IaamODamaaBaaaleaacaWG4baabeaaaOGaay jkaiaawMcaaaqaaiaaigdacqGHsisldaWcaaqaamaabmaabaGaeyOe I0IaamODamaaBaaaleaacaWG4baabeaaaOGaayjkaiaawMcaaaqaai aadogaaaaaaiabg2da9maalaaabaGaam4yaiabgUcaRiaadAhadaWg aaWcbaGaamiEaaqabaaakeaacaWGJbGaey4kaSIaamODamaaBaaale aacaWG4baabeaaaaGccaGGUaGaam4yaiabg2da9iaadogaaaa@5528@         (4)

So, as the previous case, B is moving away from A at the speed of light  and the second postulate of Einstein theory is satisfied too. This result is incongruent with the classical conception of Galileo’s addition of velocities because this velocity should be u x ' =c+ v x , MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjYdH8pE0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=x b9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaDaaale aacaWG4baabaGaai4jaaaakiabg2da9iaadogacqGHRaWkcaWG2bWa aSbaaSqaaiaadIhaaeqaaOGaaiilaaaa@3F75@ i.e. this velocity should be higher than speed of light (which is absolutely logical for us because if, for example, I am the system A moving at 6 km/h and I am moving away from system B, which is moving at 10 km/h, my perception should be that the system B is moving away from me at 16 km/h).

Speed of light with observer moving at c

Consider that the observer A is moving in the positive X axis with the higher possible velocity, the speed of light c, MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjYdH8pE0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=x b9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4yaiaacYcaaa a@3886@ according to the inertial frame of reference O in such a way that A is going after B with the same velocity that B Figure 4.

Figure 4 System A going after system B at speed  according to the inertial frame O

.

Then, the system B is moving according to the observer A with this velocity:

u x ' = cc 1 c c = cc cc .  c= 0 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjYdH8pE0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=x b9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaDaaale aacaWG4baabaGaai4jaaaakiabg2da9maalaaabaGaam4yaiabgkHi TiaadogaaeaacaaIXaGaeyOeI0YaaSaaaeaacaWGJbaabaGaam4yaa aaaaGaeyypa0ZaaSaaaeaacaWGJbGaeyOeI0Iaam4yaaqaaiaadoga cqGHsislcaWGJbaaaiaac6caqaaaaaaaaaWdbiaacckacaGGGcWdai aadogacqGH9aqpdaWcaaqaaiaaicdaaeaacaaIWaaaaaaa@4E4D@          (5)

In this case we obtain and indetermination that can be solved applying limits when v x c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjYdH8pE0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=x b9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamODamaaBaaale aacaWG4baabeaakiabgkziUkaadogaaaa@3BF1@ and using the L’Hôpital’s rule:

u x ' = lim v x c ( c v x 1 v x c )=c   lim v x c ( c v x c v x )c   1 1 =c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjYdH8pE0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=x b9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaDaaale aacaWG4baabaGaai4jaaaakiabg2da9maaxababaGaciiBaiaacMga caGGTbaaleaacaWG2bWaaSbaaWqaaiaadIhaaeqaaSGaeyOKH4Qaam 4yaaqabaGcdaqadaqaamaalaaabaGaam4yaiabgkHiTiaadAhadaWg aaWcbaGaamiEaaqabaaakeaacaaIXaGaeyOeI0YaaSaaaeaacaWG2b WaaSbaaSqaaiaadIhaaeqaaaGcbaGaam4yaaaaaaaacaGLOaGaayzk aaGaeyypa0Jaam4yaabaaaaaaaaapeGaaiiOaiabgwSixlaacckapa WaaCbeaeaaciGGSbGaaiyAaiaac2gaaSqaaiaadAhadaWgaaadbaGa amiEaaqabaWccqGHsgIRcaWGJbaabeaakmaabmaabaWaaSaaaeaaca WGJbGaeyOeI0IaamODamaaBaaaleaacaWG4baabeaaaOqaaiaadoga cqGHsislcaWG2bWaaSbaaSqaaiaadIhaaeqaaaaaaOGaayjkaiaawM caaiaadogapeGaaiiOaiabgwSixlaacckadaWcaaqaaiabgkHiTiaa igdaaeaacqGHsislcaaIXaaaaiabg2da9iaadogaaaa@708D@          (6)

Thus, as the previous cases, B is moving away from A at the speed of light  and the second postulate is satisfied in this case too. This result is completely incongruent with the classical conception of Galileo’s addition of velocities because this velocity should be u x ' =cc=0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjYdH8pE0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=x b9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaDaaale aacaWG4baabaGaai4jaaaakiabg2da9iaadogacqGHsislcaWGJbGa eyypa0JaaGimaaaa@3F4A@ (velocity should be null because both systems goes at the same speed in the same direction and sense).

Speed of light with observer moving at -c

Consider that the observer A is moving in the negative X axis with the higher possible velocity, the speed of light  according to the inertial frame of reference O in such a way that A is moving away from B with the same velocity that B Figure 5.

Figure 5 System A moving away from system B at speed  according to the inertial frame O.

Then, the system B is moving according to the observer A with this velocity:

u x ' c( c ) 1 ( c ) c = c+c c+c .  c=c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjYdH8pE0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=x b9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaDaaale aacaWG4baabaGaai4jaaaakmaalaaabaGaam4yaiabgkHiTmaabmaa baGaeyOeI0Iaam4yaaGaayjkaiaawMcaaaqaaiaaigdacqGHsislda WcaaqaamaabmaabaGaeyOeI0Iaam4yaaGaayjkaiaawMcaaaqaaiaa dogaaaaaaiabg2da9maalaaabaGaam4yaiabgUcaRiaadogaaeaaca WGJbGaey4kaSIaam4yaaaacaGGUaaeaaaaaaaaa8qacaGGGcGaaiiO a8aacaWGJbGaeyypa0Jaam4yaaaa@5181@          (7)

Hence, as the previous cases, B is moving away from A at the speed of light  and the second postulate is also satisfied. This result is also incongruent according to the classical conception of Galileo’s addition of velocities because this velocity should be u x ' =c+c=2c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=MjYdH8pE0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaq pepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=x b9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaDaaale aacaWG4baabaGaai4jaaaakiabg2da9iaadogacqGHRaWkcaWGJbGa eyypa0JaaGOmaiaadogaaaa@4029@ (because if, for example, I am the system A moving at 10 km/h and I am moving away from system B, which is moving at 10 km/h, my perception should be that the system B is moving away from me at 20 km/h).

Conclusion

In this review we have analyzed the measurement of the speed of one photon (system B) from different frames of reference in 1D. This study has been developed applying the Einstein’s addition of velocities law. All the studied cases provide the same results, the velocity of the photon is always the speed of light  independently of the reference frame. Then, these results verify the second postulate of Einstein and the relativistic addition of velocities in one dimension. This work can be useful for teachers or students of science education to explain and understand easily the second postulate of Einstein’s Special Relativity Theory.

Acknowledgments

None.

Conflicts of interest

The author declares there is no conflict of interest.

References

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