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# The Lorentz Contraction, or, How Motion Affects Space (Part 2)

In Part 1, we compared, from a purely mathematical perspective, the predicted amounts of time that it would take Scotty's Clocks V and H to complete their respective ticks, as calculated from * our* point of view standing at the train crossing. This comparison has certainly given us a lot to digest (…*burp*…oh, ah, pardon me, er, excuse me…), or maybe even given us indigestion itself (…*barf !*…sorry about the nice wool sweater…). So, to give our innards a bit of relief, we summarize our previous reasoning as follows:

## Thought Experiment #2 – A Quick Recap

1) Scotty’s train moved through the crossing at the ** constant** speed

*v*

*relative to*.

**us****used some high school algebra to calculate**

*We***it would take the photons in each of his clocks**

*how much time**V*(positioned

*vertically*) and

*H*(positioned

*horizontally*,

*along the direction of relative motion,*and

*directly**) to*

**beside**Clock V**, as observed**

*complete their respective ticks**from*. What, then, did

**point of view**__our__**discover about the**

*we**relationship*between these respective amounts of time, namely,

*t*and

_{V}*t*, and what did this discovery lead

_{H}**to**

*us***would happen?**

*predict*2) From ** our** point of view, that is,

*as measured by*, we have calculated that:

**us**using**our**watcheswhere *h* is the distance between the reflective surfaces of the mirrors, *v* is the relative speed of Scotty’s train, and *c* is the speed of light.

3) *t _{V}*'s and

*t*'s

_{H}*numerators*are the

**, that is, they**

__same__*both*equal

*2h / c*.

4) However, we have shown that *t _{H}*'s

*denominator*, which is equal to

*1 - v*

^{2}/ c

^{2}, is

*always*__less__than*t*'s

_{V}*denominator*, which is equal to

*sqrt(1 - v*

^{2 }/ c^{2}).

5) Thus, by the basic *mathematical *properties of the operation of *division*, the amount of time *t _{H}*

*must***the amount of time**

*always be*__greater__than*t*, because a

_{V}

__lesser__*means a*

**denominator****. Hence, the relationship**

__greater__quotient*t*>

_{H}*t*

_{V}**.**

*must always be true*6) And this relationship led ** us** to

**that, from**

*predict***point of view,**

*our***would observe**

*we**Clock H*ticking at a

**than**

__slower__rate*Clock V!*So, as a direct consequence of our prediction,

__we__would observe that Clock H

__falls out of its original synchronization__with Clock V!

Having gotten this far, what, then, can we quickly ascertain about the *‘behaviour’* of Scotty’s *photon Clocks V and H*, as observed from **our** point of view standing at the train crossing? Well, from our

*first*thought experiment on

*time dilation*, we know that the

**of Scotty’s train**

*motion*

*relative to**causes*

__us__**photon to travel its**

*Clock V’s**double diagonal*path to complete 1 tick. And to make a long story short, this results in

*Clock V*– and

**aboard Scotty’s train – ticking by at a rate that is**

*time itself*times ** slower** than the

**rate of time passage that**

*normal***clocks are ticking at. However,**

*our***have just finished**

*we***, as a result of our very recent calculations, that this**

*predicting*

*very same**will cause*

**relative motion****photon to travel its**

*Clock H’s*

*long**left to right*but

*short**right to left*paths to complete 1 tick, which will result in

*Clock H*ticking

**than**

__even more slowly__*Clock V!*Hence, if

*the slowly ticking*

*Clock V is***then**

__in sync with the rate of TIME PASSAGE ITSELF ABOARD SCOTTY’S TRAIN__,

__WHAT__is the__even more slowly__ticking Clock H__in sync with__, HUH??## Thought Experiment #2 – Sync Or Sink

“So what? What does any of this horse manure have to do with length contraction? This sounds more like some cheap, second-rate, plagiaristic rehash of the time dilation phenomenon, for the love of fartology…”. Okay, let’s grab a couple of sodas from the coolerator and chill, because we are finally getting to the crux of the matter. Once more, we ** must** put ourselves into

**shoes, and take a look at things from**

*Scotty’s***perspective. Hence, we recall that before boarding the train, he**

*his**synchronized*

*Clock V*and

*Clock H,*so that

*both photon clocks were ticking with the*. He then brought the clocks on board the train with him and situated them so that they were

**same**cadence**in the**

*both**side by side**vertical*position, as depicted in

*Figure 1.1*. And then, with the train moving smoothly in a

*straight line*and at a

*constant relative speed v*, that is, with the train in

*uniform motion*– Whoa! Hold on a second… Since we are looking at things from

**point of view, our previous sentence should actually read, “And then, with the**

*Scotty’s**moving smoothly in a*

**outside world***straight line*and at a

*constant relative speed v*, that is, with the

**in**

*outside world**uniform motion*” (now continuing on with the rest of the sentence), and with

**of his photon clocks happily**

__both__**, Scotty next**

__ticking in sync__

*re-positioned**Clock H*so that it was

*still directly beside**Clock V*, but was now lying

*horizontally*on the passenger car’s floor, such that its photon was now bouncing forward and backward between its mirrors, namely, bouncing

*along the same line as the outside world’s motion*. This is depicted in

*Figure 1.2*. To recap, then, Scotty’s

*Clock V*remained in its vertical position, while his

*Clock H*, although

*still directly beside**Clock V*, was now in a horizontal position along the direction of motion of the outside world.

** THUS**, expressing our previous query a little differently (but in an equivalent way) this time, the humungous conundrum is this:

*It was argued*,

*near the very beginning of our detailed and systematic ‘mathematical comparison’*of

*t*vs.

_{V}*t*,

_{H}*that*,

**because of special relativity’s first and second postulates***Clock V and Clock H will*

__always remain in sync__**,**

*as observed from*.

**point of view**__Scotty’s__*However*,

*as observed from*,

**point of view**__our__*it seems*,

*as a*,

**direct result of**__our__mathematical calculations*that*

*(the horizontally re-positioned) Clock H will*

**slow down and**with Clock V as we watch Scotty’s train rumbling through the crossing!__fall out of sync__**, we must ask ourselves:**

*HENCE**Will*,

**now**__Scotty__**observe his Clock H**__also__**and therefore**__slow down__**with his Clock V as a**__fall out of sync__**direct consequence of**__re-positioning__Clock H*as*

**have just**__we__**predicted?****“YES, he will”, or, “NO, he won’t”? There is**__only__THE answer!## Thought Experiment #2 – The First Fundamental Postulate, Revisited

Just before we reason out ** the** answer, let’s quickly remind ourselves of special relativity’s

*first fundamental postulate*, which, as we know, is also called the

*principle of relativity*, because it plays a crucial role in all of this hoopla. Simply put, it states that: There is

**experiment that one can perform,**

*absolutely*__no__**, that will detect or reveal a state of**

*in the*__whole__of physics**, namely, a state of motion**

*uniform motion**in a smooth*,

*straight line and at a constant*,

*or unchanging (relative) speed*. Using less technical jargon, one

**uniform motion. In fact, one can consider oneself to be**

*cannot ‘feel’***while the**

*at rest**‘outside world’ is*

*in motion*

*instead*. And why is this so? Because

**of the laws of physics behave in**

*absolutely*__all__*exactly the same manner*for those in a state of uniform motion as they do for those in a state of rest. Mother Nature does

**conduct herself differently depending on one’s state of uniform motion or one’s state of rest. By the laws of physics, then, the two situations are**

__not__**, and therefore, by these**

*equivalent**same*laws of physics, the two situations are

**. Hence, with regard to**

*indistinguishable**relative uniform motion,*,

**no one**

*and that means*, can ever prove or say that,

__absolutely no one__

*“Yes, I am the one who is*__truly__in motion!”## Thought Experiment #2 – The Revenge Of The First Fundamental Postulate

Now, because of special relativity’s *first postulate*, then just as in our *first* thought experiment about the time dilation phenomenon, Scotty has every right to assume that **he and his train are the ones at rest**, and it is in fact we, the train crossing, and the rest of the outside world that are moving past him at the constant relative speed

*v*instead. And therefore, from

**point of view, a**

*Scotty’s***re-positioning of his**

*simple**Clock H*

*should*__not__*with his*

**cause it to slow down and fall out of sync***Clock V*whatsoever, as

**have boldly predicted it**

__we__**do! And why not? Well, because to Scotty,**

__should__**is the one at rest, and hence, if Scotty were to observe his**

__he__*Clock H*to suddenly, and for

*no*apparent reason at all, slow down its ticking and fall out of sync with his

*Clock V*as a

**of it**

*result***being moved from one position to another, then**

*merely***Hence, with one quick move of a clock, Scotty would end up utterly and totally destroying the**

*Scotty would be able to use*__this very result__to deduce that__he__was__definitely__the one in motion!*first postulate*, that is, the

*principle of relativity*, which is, as we know by now, one of the foundational laws that govern the workings of the universe itself!

Our comprehension of this idea will be much enhanced if we try to clarify things a little further, because we are dealing with a deeply fundamental yet much understated concept that underlies *all of* *reality*. As the *first postulate* asserts (and as we *revisited* just a few paragraphs ago), there is ** absolutely no** physical experiment that Scotty can perform aboard his train,

**, that will detect or reveal**

*in the*__whole__of physics**. Let’s keep this fact first and foremost in our minds. For instance, Scotty can toss a baseball inside his cabin and work out its trajectory, throw a paper airplane from one end of his cabin to the other and analyze its aerodynamic properties, play a game of pool with the Maitre d’ and calculate the paths that the billiard balls will take after they hit one another, wash his hands in the cabin’s restroom and determine the changes in water pressure as it is forced through the network of connected pipes, put up his Christmas tree and measure the electric current that is drawn by its string of coloured light bulbs, utilize his portable EEG unit and measure his brainwave activity to ensure that he is not going insane, or perhaps,**

*whether his train is in a state of*__uniform motion__*just*take his pet dog Mooklamax for a short, leisurely walk inside his passenger cabin and measure the amount of tension in the leash. In essence, then, Scotty can basically do…

**And the subsequent**

*anything!!**results*–

**, that is,**

*as observed from*__his__point of view**– of**

*as measured by*__him__*any*and

*all*experiments that

**performs on his**

*he*

*relatively**moving*train, would be

**to the results**

*completely*__identical__**would measure, had**

*he***performed these very same experiments on the**

*he*

*relatively**motionless*train station platform instead (provided, of course, that all of the

*initial*conditions and parameters, again, as measured by

**, such as throwing angles and forces, applied water pressures, electrical voltages, and so forth, were likewise completely identical).**

*him*Hence, saying it once more, **no** experiment can detect or reveal a state of

**. And the scope of what defines an**

*uniform motion**experiment*must therefore also include the

*moving*or

*re-positioning*of any and all types of

*clocks*– from wristwatches and tuning forks to atomic clocks and

*photon clocks*. Thus, we can consider Scotty’s re-positioning of his photon

*Clock H*, from its original vertical position to its new horizontal position, to be a valid physics experiment in and of itself, albeit a very lame one (we’re sure he’d rather get some exercise and walk Mookie instead). But as lame as it is, this sad excuse for an experiment must still, of course,

*, that is,*

**obey the first postulate****.**

*its*__result__CANNOT “tip Scotty off” in__any__way whatsoever as to whether__he__is in uniform motion## Thought Experiment #2 – THE Answer To Our Question

**We**, on the other hand, have calculated and established from the outset that,

*from*, the relationship

**point of view**__our__*t*>

_{H}*t*is indeed a

_{V}**of the fact that Scotty**

__direct result__**, combined with the fact that Scotty’s train is**

*re-positioned his Clock H from the vertical to the horizontal position***. And this relationship led**

__moving__in the horizontal direction__relative to us__**to**

*us***that**

*predict***between Scotty’s**

*Clock H’s ticking*__should__slow down, and that there__should__be a__resultant__failure in the synchronization*Clocks H and V*. It only takes the failure of

**experiment, no matter how infinitely lame, to completely demolish even the grandest of physics theories, and**

*one**special relativity*is not exempt. Because now, if

**, as**

*Scotty***, were to**

*we have predicted***observe his**

*indeed***as a**

*Clock H suddenly slow down and fall out of synchronization with his Clock V***of his**

__direct result__**, then he could use this**

*“Re-positioning of My Clock H*__Experiment__”

*same*

**‘**to

*failure in synchronization*__result__’**as to his train’s**

*“tip him off”***. And**

*motion***would likewise deduce and immediately proclaim, being a very astute but loud-mouthed engineer, that,**

*he***. And in doing so, Scotty would**

*“Yes, my train, and*__not__the outside world, is the one that is__truly__moving in the horizontal direction,__because__my Clock H slowed down its ticking and consequently fell out of sync with my Clock V!”

*torpedo the*__principle of relativity__and sink it into oblivion!And so, we have to take some valium to once again seriously calm down and collect our thoughts, because the **first postulate cannot tolerate even the slightest of contradictions**, as it has proven

*(thus far!)*to be one of the fundamental principles upon which the

*Supreme Reasoner*based the universe’s design! Hence, if we

*again*ask ourselves:

**Then, after our careful re-examination of the**

*Will*__Scotty__observe his Clock H slow down and thus fall out of sync with his Clock V as a direct result of it being re-positioned, as__we__have predicted it should do?*principle of relativity*, our

**answer can**

**be:**

*only***And why must this be so? It must be so, because there is absolutely**

*“NO, he won’t. Scotty will NOT observe his Clock H slow down even one iota, and therefore, he will continue to observe his Clock V and his Clock H ticking in sync with each other even after Clock H’s re-positioning, as if nothing had happened at all”.***that Scotty can carry out – in fact, there is absolutely**

*no experiment***that Scotty can perform, that will detect or reveal whether he is in**

*NO SINGLE ACTION***– period.**

*uniform motion***, since the clocks**

*And hence***, then**

*CANNOT be BOTH in sync AND out of sync**from*

**vantage point standing at the train crossing,**

__our__*must therefore*

__we__**observe that**

*also**Clock H*and

*Clock V*

**period.**

*remain in sync,*–__regardless__of any re-positioning^{[5]}

## Thought Experiment #2 – Something Still Seems Amiss Around Here…

This conclusion, however, just seems to create another logical absurdity, and here’s the reason why: We have just asserted assertively that *Clock H* and *Clock V* **must remain in sync from Scotty’s point of view (and therefore, from our point of view also)**, so as

**to pulverize and destroy the**

__not__*principle of relativity*– period. And yet,

**have painstakingly, and**

*we***error, used a good portion of our discussion thus far to**

*without***that as**

*calculate and prove***and**

*observed*

*measured**from*,

**point of view**__our__*t*, which is the amount of time that it takes

_{H}*Clock H*to complete 1 tick, will

__always__be greater than*t*, which is the amount of time that it takes

_{V}*Clock V*to complete 1 tick! Hence, it appears that from

**perspective,**

__our__**have**

__we__**but to observe that**

__no alternative__*Clock H*will

**slow down and tick**

__still__**than**

*more slowly**Clock V*as we watch Scotty’s train motor through the crossing, and will thus

**with**

__still__fall out of sync*Clock V!*

How is it possible for ** Scotty** to observe that both clocks continue to tick in sync, while

**calculate that these**

*we***clocks should fall out of sync?? What the hell kind of circus is this?? Where are the dancing bears?? Is the**

*same**principle of relativity*nothing more than physics folly?? Can these two apparently irreconcilable facts be reconciled!? Nonetheless, let’s follow Einstein’s

*successful*endeavor to do so, for the sake of our imploding heads. Can anyone of us use a few capsules of Quadruple Extra Maximum Strength Tylenol right about now?

## Thought Experiment #2 – Special Relativity’s Cookie Recipe: Lots Of Chocolate, And Add Some “Shortening”

“Whoa! Stop right there, you good for nothing sad sack! You’re way out of line this time, so jam it, pizza face! We just spent *five* full pages, using all of that highbrow math, proving that *Clock H* must *indeed* fall out of sync with *Clock V!* But now, it doesn’t!? What in the name of the fact that you suck is going on here, jerk!?” To answer, we can rest assured in knowing that there is ** nothing** wrong with our reasoning or our mathematics. The equations that

**have obtained – which were derived from**

*we***point of view – for both the amounts of time**

*our**t*and

_{V}*t*are indeed quite correct, because we effectively applied the rules of only the most basic algebra and geometry. Hence,

_{H}**are certainly**

*we***correct in concluding that**

*mathematically**t*>

_{H}*t*, which further leads to the inference that from

_{V}**point of view,**

*our**Clock H*must therefore fall out of its original synchronization with

*Clock V*.

Stating things in an **equivalent** way, our result that

*t*>

_{H}*t*

_{V}**, as observed from**

*can only mean*__one__thing**perspective. It can**

__our__**mean that**

__only__**1**

*Clock H’s photon must travel a*__longer__total distance to complete**1**

*tick than Clock V’s photon must travel to complete*

*tick, BECAUSE of the*__fact__that__both__photons must__always__move at the__same__unchanging speed of light*c*And to illustrate this

**(that is, because of special relativity’s**__second postulate)__!*‘equivalent way’*of looking at things, we first remember one of the three basic relationships between

*speed*,

*distance*, and

*time:*

*DISTANCE TRAVELED* = *SPEED OF TRAVEL* x *TRAVEL TIME*

Next, we let *d _{V}* equal

*the total distance that Clock V’s photon must travel to complete*1

*tick*, and we let

*d*equal

_{H}*the total distance that Clock H’s photon must travel to complete*1

*tick*, with both distances being, of course, observed from

**point of view, that is, measured by**

__our__**using**

__us__

__our__**. Therefore, by this basic relationship for the quantity**

*rulers**‘distance traveled’*, the distances

*d*and

_{V}*d*must be given by the simple equations:

_{H}*d*=

_{V}*c*x

*t*, and

_{V}*d*=

_{H}*c*x

*t*, where

_{H}*c*is the

*constant*,

*unchanging*speed of light, and

*t*and

_{V}*t*are, once again, the travel times for each photon to complete their respective ticks, as observed from

_{H}**point of view, that is, as measured by**

__our__**using**

__us__**watches. And since**

__our__*t*>

_{H}*t*, then it immediately follows from these simple equations that

_{V}*d*>

_{H}*d*also, because both photons must always move at the

_{V}*same*,

*unchanging*speed of light

*c*! Therefore,

**1**

*Clock H’s photon must travel a*__longer__total distance to complete**1**

*tick than Clock V’s photon must travel to complete***as observed from**

*tick,***point of view, which leads to the inference that from**

__our__**perspective,**

__our__*Clock H*must fall out of its original synchronization with

*Clock V*.

** BUT**, as we have just discovered, on the other hand,

**demands that**

*reality itself*

*Clock H*

*must remain in sync***with**And

*Clock V!**Clock H*remaining in sync with

*Clock V*

**the fact that,**

__necessitates__**to**

*contrary***calculated results,**

__our__*Clock H’s*and

*Clock V’s*photons

**both travel**

*must***distances in completing their respective ticks, that is to say,**

__equal__*d*=

_{H}*d*, and

_{V}

__not__*d*>

_{H}*d*,

_{V}**as observed from**

*must instead be true***point of view! Hence, we have**

__our__**choice but to conclude that**

__no__*somehow, by some means*,

*t*=

_{H}*t*

_{V}

__instead of__*t*>

_{H}*t*as

_{V}**and**

*observed***from**

*measured***perspective, so that**

__our__*d*=

_{H}*d*can be made a reality, thereby keeping

_{V}*Clock H*and

*Clock V*in sync with each other! But how can this possibly be achieved, as observed from

**perspective? Well, here is**

__our__*Einstein’s*solution: For

*t*to

_{H}**to**

*become*__equal__*t*, the

_{V}**that**

*total distance***photon has to travel to complete 1 tick must**

*Clock H’s*

*therefore***, or**

__contract__**, as observed from**

__shorten__**point of view, such that it becomes**

__our__*to the*

**equal****that**

*total distance**Clock V’s*photon has to travel to complete 1 tick! That is to say, the total distance,

*d*, of the

_{H}*forward and backward*path that

__we__observe*Clock H’s*photon to travel to complete 1 tick must

**so that it becomes**

__decrease__in length**to the total distance,**

*equal**d*, of the

_{V}*double diagonal*path that

__we__observe*Clock V’s*photon to travel to complete 1 tick! And consequently – okay, let’s get ready for this doozy – the

**way that this**

*only***in**

*equality**path lengths*can be achieved is

*if:**AS OBSERVED FROM OUR POINT OF VIEW STANDING AT THE TRAIN CROSSING, the*

__distance__between the reflective surfaces of

**Clock H’s mirrors (and moreover, the**__full length__of Clock H__ITSELF__)__shrinks__or__contracts__so that it becomes

__shorter__than its original (i.e., its normal) value of h!Alrighty, then. Let’s see just how the mechanics of this newly introduced *distance shortening* phenomenon, formally known as the *Lorentz **Contraction*, ** can** keep

*Clock H*in sync with

*Clock V*, and therefore remedy the

*universe*around here…

## Thought Experiment #2 – The Fix Is On!

Okay, here’s where things get a bit tricky, *so let’s stay sharp!* Now, ** we** have already calculated that the travel times that the photons (in

*Clock H*and in

*Clock V*) need to complete their respective

*single*ticks, namely, the travel times

*t*and

_{H}*t*– which are

_{V}*both*observed from

**point of view, that is to say, which are**

__our__*both*measured by

**using**

__us__**watches – are given by their respective equations**

__our__For the intention of complete clarity in our following explanation, the equation for *t _{H}* can be easily re-written into the following form:

where *h* is, of course, the ** normal** distance between the reflective surfaces of the mirrors, as shown in

*Figure 1.2*(and also in

*Figure 1.1*).

*And at this point in our discussion, we carefully note that for the sole purpose of simplicity, we will assume the thickness of the mirrors themselves to be extremely minuscule and therefore negligible. Hence, this will make the normal distance *

*h*

**between the reflective surfaces of the mirrors**__effectively equal__to the full (normal) length of the Photon Clock H itself.So, as we have just discovered, if the value of *h* ** decreases**, that is, if the length of

*Clock H*

**as observed from**

*shortens***point of view (by an amount, or**

__our__*factor*, which is yet to be determined), then the relationship that

*t*=

_{H}*t*can be made a

_{V}*reality*, thus keeping

*Clock H*

**with**

*in sync**Clock V*and therefore

*upholding*the highly regarded

*principle of relativity*.

Okay, then let’s *shorten* the ** normal** length (as observed from

**point of view) of**

__our__*Clock H*, which is equal to

*h*, by multiplying it with an already all too familiar quantity, namely, the quantity

and see where this leads us! We remind ourselves that *v* is the speed at which Scotty’s train, and hence, his clocks, are moving ** relative to us**.

*“But how will h be ‘shortened’ by multiplying it with the quantity*

*sqrt(1 - v*

^{2}/ c^{2})*?"*, we wonder. Well, we recall that we have already shown that this quantity,

*sqrt(1 - v*, is

^{2}/ c^{2})**1. And therefore, if we define a**

__always__LESS than**quantity to be equal to**

*new*then this new quantity must clearly __always__ be LESS than *h.*

“Okay, that’s the last straw! What can possibly result from all of this pointless, haphazard, face planting into walls in the dark guesswork, you lousy punk? Is it because you feel lucky?... Well do ya, PUNK!!??”. Easy, Detective Maclanahan – the valium is in the medicine cabinet.

** We can therefore think of this new quantity**,

*h x sqrt(1 - v*,

^{2}/ c^{2})**,**

*as being a CONTRACTED***. We will call this length**

*or SHORTENED length of the Photon Clock H ITSELF as observed from*__our__point of view, with this shortening in length occurring ALONG THE DIRECTION OF RELATIVE MOTION*h*, where

_{C}*“C”*stands for

*“contracted”*. This is shown by

*Figure 1.3*.

And hence, this new, ** shortened** length is given by the equation

So, if we now substitute this ** shortened** length,

*h*, so that it

_{C}

*replaces**Clock H’s*

**length,**

*normal**h*, in our

*original*equation for

*t*(which we re-wrote into the form above), we get the following:

_{H}*This means that: IF, AS OBSERVED FROM OUR POINT OF VIEW, Clock H ITSELF, which is moving at the speed *

*v*

**relative to US,**sqrt(1 - v__SHORTENS__by a factor of^{2}/ c^{2})

*ALONG THE*__DIRECTION__OF RELATIVE MOTION,__THEN__the time*t*

_{H}**1**

*, which is the amount of time, as measured by*__us__using__our__watches, that it takes Clock H’s photon to complete

*tick, will*__DECREASE__so that*t*=

_{H}*t*

_{V}!

*Hence, this SHORTENING OF THE LENGTH OF CLOCK H will keep it IN SYNC with Clock V, as it MUST be, according to special relativity’s FIRST FUNDAMENTAL POSTULATE, otherwise known as the PRICIPLE OF RELATIVITY!**Stating things in an EQUIVALENT way, this means that: IF, AS OBSERVED FROM OUR POINT OF VIEW, Clock H ITSELF, which is moving at the speed *

*v*

**relative to US,**__SHORTENS__by a factor of

*sqrt(1 - v*

^{2}/ c^{2})**1**

*ALONG THE*__DIRECTION__OF RELATIVE MOTION,__THEN__the forward and backward path that__we__observe Clock H’s photon to travel to complete**1**

*tick will*__DECREASE__IN TOTAL DISTANCE so that it becomes__EQUAL__to the TOTAL DISTANCE of the double diagonal path that__we__observe Clock V’s photon to travel to complete

*tick! And since BOTH photons must ALWAYS move at the SAME, UNCHANGING speed of light**c*

**, then the travel time***t*

_{H}

*, as measured by*__us__using__our__watches, will ALSO__DECREASE__so that*t*=

_{H}*t*

_{V}!

*Hence, this SHORTENING OF THE LENGTH OF CLOCK H will keep it IN SYNC with Clock V, as it MUST be, according to special relativity’s FIRST FUNDAMENTAL POSTULATE, otherwise known as the PRICIPLE OF RELATIVITY!*## Notes:

[5] Yes, *Clock V* and *Clock H* must *remain in sync* due to special relativity’s *first postulate* (i.e., the *principle of relativity*), but ** both** clocks must also be ticking at a rate that is

**than the**

*slower***rate of time passage by a factor of**

*normal*(as observed from ** our** point of view), due to the

*time dilation phenomenon*.

## Continue To Part 3

- The Lorentz Contraction, or, How Motion Affects Space (Part 3)

The 2nd in a series of articles on Albert Einstein's Special Theory of Relativity

## Go Back To Part 1

- The Lorentz Contraction, or, How Motion Affects Space (Part 1)

The 2nd in a series of articles on Albert Einstein’s Special Theory of Relativity

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