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Relativity Demonstration

This demonstration attempts to show the effects of Special Relativity by Showing you what the universe would look like if you were 100 million kilometers tall. Hold the mouse button down to pause the demonstration at ANY TIME! The info buttons have tons of questions, answers, and information for you to discover. Have fun!

m^A}\Ufff5Ko!ΔSV||<ll7Ӏ7NND;D u\c<(C{An7׵ړB0LYs}C_YecG|yT@N峎Zci0CGk]!m^A}\U5Ko!ΔSV||<ll7Ӏ7NND;D u\c<(C{An7׵ړB0LYs}C_YecG|yT@N峎Zci0CGk]!m^A}\U5Ko!ΔSV||<ll7Ӏ7NND;D u\c<(C{An7׵ړB0LYs}C_YecG|yT@N峎Zci0CGk]!i^A}\Ufff! U&p9 5ok}5&`x?/xξg@ǞrgL&z- 3y贆v iD\^~*-;7b U J3ïj96l9=Ko 9҂ p //'-p)ѝ)h'ho3o.~?*6ɱesJ=7avo8gNeNt(֣CJiO u95eV4qwJKݴ ~[8|?1{_dzmv|( 5 t1A Note on Scale: On this page, the speed of light is 10 pixels per second. This means that each pixel must be 30,000 kilometers across. At this scale, the earth is just 1/3 of a pixel across and the sun is 46 pixels across. The actual distance between the sun and earth is 150 million kilometers, which would be about 10 times the width of the screen. Hairsplitting: Technically, I programmed the speed of light to be 10 pixels per second...You can size the image to be as big as you want. Flash will render the image accordingly.GGGGGGG G G}!t1The Speed of Light, c, is Constant The red lines on this screen represent pulses of light. The speed of light is approximately 300 thousand kilometers per second. If human beings were so gigantic that the earth appeared to be a crumb, we would be very familiar with the limitations of the speed of light. For one, we would be unable to move faster than the red lines on this screen, and it might take several minutes for a message to pass from our brains to our toes.GGGGGG X"o#(

Introduction

What are those grey squares?

The Speed of Light

A Note on Scale

Red Pulses.

What is a Light Pulse?

What is a Light Stream? What is an Event?

The White Circle

#%t1The red light pulses come from the center of the GSV (Gargantuan Space Vehicle). If the pulses were not blocked, they would expand outward in a circle. But the structure of the GSV blocks most of the circle pulse, so only one small arc of the light circle comes out.GGGGGKt1Where do the red pulses come from? (be specific) Click for answer!$ t1What are those things? They are called, (for the purpose of this T1demonstration), Gargantuan Space Vehicles or GSV for short. They are several hundred thousand kilometers across. The sun is shown for size comparison. The owners of these GSV's are a bit eccentric; they are prone to fire pulses of red light to demonstrate relativistic effects for passersby.GGGGGG~t1What are those little grey boxes with the little trianglular chunks cut out of them? Click for answer!G% t1What is a Light Pulse? A pulse of light is different from the light you see from a lightbulb. A lightbulb produces streams of photons coming from a long filament. Thus a lightbulb's photons are produced by many events spread out over many points in space and time. A pulse, on the other hand, is a set of photons produced by exactly one event. At the moment of their creation, the photons are not distributed over a region of space over a filament. They all come from the same point in space and time.GGGGGGGU& t1What is a Light Stream? Whereas a light pulse is generated in an instant of time, a light stream is produced over a period of time. A stream is a temporally continuous emission, whereas a pulse is a temporally discrete emission. A pulse comes from an event, while a stream comes from an object. Click the Show/Hide Light Stream button to show the streams. GGGGGGG G't1Relativity Demonstration This demonstration attempts to show the effects of Special Relativity by showing you what the universe would look like if you were 100 million kilometers tall. Hold the mouse button down to pause the demonstration at ANY TIME! The Info buttons have tons of questions, answers, and information for you to discover. Have fun!GGGGG(I t1What is an Event? An event is a single point in space and time. Examples: 1) The origin of a light pulse is an event. 2) A collision between two particles is an event. Counterexamples: Births, weddings, funerals, yard sales, and parties are not events, because they happen over a region of space, and a period of time. You might be wondering: "Weddings are not events? Surely, that moment of saying 'I do' is an event" Click for answer! GGGGGGGt1It takes only one second for the groom to say "I do", but this process involves thousands of events: thousands of collisions of air molecules with his throat. What difference does one second make? To a traveler going 99% of the speed of light, those events would be spread out over 7 seconds, and 2 million kilometers. For a traveler going 99.999999993302 % of the speed of light, those events would be spread out over 24 hours, and 25.9 trillion kilometers. This idea is discussed in more detail in the Gamma demonstration.GGGGGG4)ct1The White Circle At the moment the centers of the two GSV's meet, a white, circular pulse is released. The pulse is an expanding circle made of light. Light travels at a constant speed for all observers. That means that both GSV's think they are in the center of this circle. Does it look like both GSV's are at the center of the circle?GGGGG t1Does it look like both GSV's are at the center of the circle? Probably not... You may have said yes if you are a 100 million km tall being who perceives space and time differently. You might have reactively converted this problem to a Minkowski spacetime diagram and recognized that both GSV's are at the center of the ellipses created by cutting through the light cone along the plane of their world-regions. 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Though object A is moving, the center of the light circle

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7_roothideCirclest1Question: For GSV2 which edge of the light pulse do you see exiting first? Front or back? Left or right? Click for answer!OGGt1Answer: For GSV2: The left (back) edge of the light pulse exits before the right (front) edge. Remember: Both the left and right edge of each light pulse came from the same event and move at the speed of light.GGG u8w "(T1

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Z9_roothideCirclest1Question: Which object appears to be emitting pulses more frequently? GSV1 or GSV2? Click for answer!OGG-t1Answer: GSV1 appears to be emitting pulses more frequently. This is a result of time dilation. From their own perspective, both vehicles are releasing pulses at the same frequency. Stationary objects in space move fastest through time. Moving objects move through time in slow motion.GGGG:^t1Question: Which object appears to take more space? GSV1 or GSV2? Click for answer!GGt1Answer: GSV1 takes more space. The stationary object, GSV1, is not length contracted, and so appears to take up more space. If both GSV's were stationary, they would take up the same amount of space. GGG,;_roothideCirclest1Question: As you observe GSV2, the rear edges of its light pulses exit before the front edges. Is this true from GSV2's perspective? Click for answer!OGGGt1Answer: No, according to GSV2, the left and right edges of its pulses exit simultaneously. However, it would see the right (back) edge of the pulse from GSV1 leaving before the left (front) edge.GGG<_roothideCirclest1Question: How many treetrunks does each pulse from GSV1 hit? Hold the mouse button down to pause the action so you can count. Click for answer!OGGGQt1Answer: Each pulse from GSV1 hits the same five treetrunks each time. G=_roothideCirclest1Question: How many treetrunks does each pulse from GSV2 hit? Hold the mouse button down to pause the action so you can count. Click for answer!OGGGt1Answer: Each pulse from GSV2 hits six treetrunks. It hits the top of the first tree it approaches, and the trunks of the next six. (it very nearly hits seven trunks sometimes.)GGG>m됧 %`>-a͟! &׈lm}| -@ ]^k xv-p_6|xWk6׿^! xv-o6|xWk6׿^!xv-͟! &׈l|m} ?>@ @?T@ C?T@ R?T@ Ǐ?T@ g@2?T@HH $?T@ {ȏ+?T@ 2?T@ 2@@ Ag:/%h#(

Front and Back

Length Contraction

Desynchronization

Simultaneity

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Time Dilation

Tree Counting GSV1

Tree Counting GSV2

ECo _roothideCirclest1Even though GSV2 is length contracted and its beam is narrower, its pulses still hit more treetrunks! Question: What explanation would GSV2 give for its ability to hit more treetrunks than GSV1? Click for answer!OGGGGG Gx_roothideFillt1Answer: GSV2 would say that the moving trees are closer together. Go to the next page to see.OGG sDg4?.X#(

Inverse Length Contraction

Why can't an event move?

Key Concept of Relativity

?E t1_roott3NFt1Question: Which side of GSV1 does GSV2 think is the front? Which side of GSV2 does GSV1 think is the front? Click for answer!GGG^t1Answer: Both vehicles are symmetrical, so they don't technically have a front or back, but if an object were moving toward you, you would call the nearest side the front. Conversely, if it were moving away, you would call the nearest side the back. The left side of GSV1 and the right side of GSV2 are 'fronts' according to the other.GGGGGdt1What is the definition of motion, and why is it that an event cannot move? Click for answer!Gt1Motion is the change in an object's position over a period of time. An event only exists at a single point in time instead of over a period of time. It can never move, because motion requires time.GGGH*+,- t1 -To Pause: Click, drag the mouse out of the demo, and release. -RePlay: Restart the action. -Info: Information about this page. -Arrows: Change page. -Selecting the text makes it easier to read. Keep the mouse button held down after selecting. -Show/Hide Light Streams: Shows continuous photon streams. -Show/Hide Circles: Shows entire unblocked light pulse. -Instructions may change depending on the page.GGGGGGG*Ie > GK ===GD=== Kn>3.%~Qt?offf333h<@qqqGD===fff2@ժa "ߦZ Q#ZrD ûV7*i(yih ᣂu ƼG$ [ py"<|N"G:CyLuTcuC`.ZuTl|Je > ]Av&n9 Ͱ\ fffh<@qqq3330 aj8IL-TG!BA/$@BnuNB>V%ڴ: !>G:g<&;[&0u ;V[l, rD9Ap9 vU a:Ah>fff%mP<& GͰ\#Ke&]Av&n9 Ͱ\  `zAhuC9,7Cfff333fff2 @ xnq.@INb6Ԅ9!臅u0C0mP#b5CnT.Ha6X#P _$L=~ZC qpc 9Ap  X~MC uŐU z(u2Le& `p Ctr;!9dF`QMIJKLthis _root leftArrowR N?T@ C?T@ R?T@ Ǐ?T@ g@2?T@HH $?T@ {ȏ+?T@ 2?T@ 2@@ uOwx"(T1

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Tree Counting GSV1

Tree Counting GSV2

Inverse Length Contraction

Key Concept

Qo _roothideCirclest1Even though GSV2 is length contracted and its beam is narrower, its pulses still hit more treetrunks! Question: What explanation would GSV2 give for its ability to hit more treetrunks than GSV1? Click for answer!OGGGGG GZ_roothideFillt1Answer: GSV2 would say that the moving trees are closer together.OG? RTimes New Roman@B)o)x`8}- g 0  5dd+TR$ݦ{ow wE_@)Rd<q>LO +d+ CT 5(pxrybGTxw8KN[3mLJjDLUY殒Z~X{5bVǎ#* "QmODzFe˳9auq}5Iօ~@5 8q>LO +,d+ CT5FC1Lqd?@P>CYW*y+ b|`V8Ɏ Y 5gf1Am N::\߆cn &W*j ٰ7wfD^cvI1@%d}iiW/IkoB[&]|_&5f~%Eh NJfv$F1."4Ӥ{"ەtv4m=Ukxm=5fa97wb7) 6fH*ڗijO~m~G%1>h n{K˭55eyE].zR^D85J&qRc4Ǥ[*`:ȇU0gHwQ>ôrl&iR&ܐJlJ'N :w-5g2e vqnBLe1̠$a u8lj&< #Ҙ,ܯq}_z(r@(iDnn[f5Mu@hcXS_+dKdŠq0D 9r ).Q5K;F :x "@]46P Ξ@%N6R_7;,,P\llM{0]vS$i#J, ?jdIm'ۤ5Fەd_e?jS@^ L fS<Ⱥ@d,U}4چ5d MkP O%H)|PsE:Mn-@$j]e1u65f~ܐ:7Cێ ZطmOHf7I DwIY h Li@Ug²B(*HiK)<'o]xvN")؆ʖRҐ)"逴%jeI #u5KESZeզ c[n@=r%0e dc$fqV5 oqMbYLi6A4f-F%2FyDƆ2h9@)Ċ\HNlx%S,Vu2B7Sp0R,z. *r}1C@`HMږ=df+SϢVzY m]u5do4廸ϧ+:kH!"ܠ_T@"Fp#2rw]RAdx\ɦ[( Do%l=a Znv>˭5[x-yk '[G[Dd=fo5d&d8r>LN ,+ CT P,oV8 X\4ħ4"ҒIoJI3 em]$+njѴ5dOf3^MΘ~пH6%&dkh,ma"@F2v%ZHՠ +\'x3].bKLkF5dƜTxbUp ^%5]'6ԑ(Zɞ`_( $q!⽢7т̛`ѻz5KyBD@n+9'*H(% uX4uoS )2$ 4M`[}0v,X5# {EkKhu=Ix7{ n#E%$|p6-ެ߸f,ؕ%$k@5G`QF] Υk[^iMai=>ݽ[߾q] J&[m9z#9*f3)g@Pd:@5Mu@h#xo(`5Lm5KߗN{&i P &F>\RPtE26@es"6M\%w^jͩu0]V5HEgXA:]hxЉ>") @4 Zf]}zɿpj#eSx (j@c={sNK>d5K yO3t߷Rhr2Z H$ (dHUQ6EQߦn лxzi>"Ձ YN\&s,(#*;it-hFkD&E@>5d*wQ wbˏTɀؑ$0oMI\nI *, *RxŦm$-X5CnG`Tӆ$5"@ds "訦B 91T %7dVG;:a Mbl&qRPFH#@lgz%N`$ u]@@/M_k,fIHa&DB{ŖYHI?,5LyPFDg%y W6Ⱥh]Gb{]>)svULFHHt%\`nr 5,V%#]W44nxMi3T@>Ck+D-K!mc~ bhU?WKngkF%[L !()-.:CILMRUacefghiklmnorstuvwoUUUUUU:UrXM(,XF8m_"mP6:HPz`PXEZ5,_4h_Ch_vUh_J5hXmhUhP0ǀ`P8G`P@ǀ`_NX(&4XVP(ǀ`PNow we see what things look like from the other side. The Info Buttons are just reminders of what you saw on the last screen.

Some realities changed, and some did not.

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Here, we have a GSV (Gargantuan Space Vehicle) changing speed and emitting red pulses of light. When each pulse reaches the white line, the GSV accelerates to the right and emits another pulse. When the GSV is going slow, the pulse takes a short vertical path to reach the white line. When it is going faster, it takes a longer, more horizontal path.

U_roothideCirclesButtonlabel1Show Circlest1Question: If you were on board this GSV, in a room with no windows, Would you know whether you were slowing down or speeding up?OGG t1No, all you would know is that you were changing speeds. Acceleration and deceleration are exactly the same sensation. If we were in space instead of standing on earth, we wouldn't think in terms of acceleration and deceleration. We'd just think in terms of changing speeds. Deceleration is simply 'matching pace with the earth's surface.' while acceleration is 'increasing our relative velocity with the earth's surface.' Hey, you found an Easter Egg! Roller coaster simulators take advantage of this effect--by leaning you back or forward as the image on the screen portrays acceleration or deceleration, you feel gravity pulling back or forward on you, resulting in the sensation of acceleration or deceleration. GGGGGGG G G G G uVw^r"(T1

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vWt_roothideCirclesButtonlabel1Show Circlest1Question: What else happens to the GSV as each pulse is emitted?OGPt1Answer: The GSV changes speed right before it emits each pulse. If you look very closely, you can see the GSV's internal structure right as it undergoes its acceleration. This is a side-effect of a superior alien technology that allows it to maintain its structural integrity even as it undergoes mind-boggling G-forces.GGGGGfX7 _roothideCirclesButtonlabel1Show Circlest1Question: This GSV is accelerating incrementally, by 20% of the speed of light with each pulse. From its own perspective, that is a speed change of 30 million meters per second every second. Compare that to an acceleration of 9.8 meters per second every second, which is the acceleration due to gravity. Would any real object, no matter how strong, be able to withstand such acceleration?OGGG G Gt1A true 'point particle' could withstand any acceleration. Its structure would be immune to the crushing and stretching effects of length contraction and desynchronization because it HAS no structure. Very small particles such as atoms can withstand high-velocity collisions, but they have their limits. Particle accelerators are designed to surpass these limits to smash the atoms into smaller particles.GGGGGGY_roothideCirclesButtonlabel1Show Circlest1Question: Does it take the same amount of time for each pulse to reach the line?OGt1Answer: No. The pulses traveling straight down reach the line faster than those which are traveling to the left or right.GGZ_roothideCirclesButtonlabel1Show Circlest1Question: Does the GSV find it takes each pulse the same amount of time to reach the line?OGt1Yes! The GSV sees every pulse take a vertical path to the moving line. Though the apparent speed of the line changes, the distance to the line remains the same. It takes the same amount of time for each pulse to reach the line. We are accustomed to thinking in terms of distance=velocity * time, but since the speed of light is constant, time can be defined as the distance between two events divided by the speed of light.GGGGGG Z[w6x#f(

Slowing Down and Speeding Up

Are pulses emitted at constant frequency?

How about from the object's perspective?

Acceleration and Emission

Inconceivable G-Forces

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wmt1Gamma, or the Lorentz factor appears four times in the equation on the lower left hand cornerof the screen. It is a greek letter and does not appear in this font. It's range goes from 1 and up. It is described in more detail in my other demonstration. Gamma is equal to 1/sqrt[1-(v/c)^2], where v is the velocity of GSV2, and c is the speed of light.GGGx*+,- t1 -To Pause: Click, drag the mouse out of the demo, and release. -RePlay: Restart the action. -Info: Information about this page. -Arrows Change page. -Selecting the text makes it easier to read. Keep the mouse button held down after selecting. -Show/Hide Light Streams: Shows continuous photon streams. -Show/Hide Circles: Shows entire unblocked light pulse. -Instructions may change depending on the page.GGGGGGG <yoI fff(ButtonLabel1Show/Hide Circles 9zo fff(ButtonLabel2Show/Hide HazeK{#  @ h_roothideFillButtonlabel2Beam Width is Hiddent1The light pulses now leave a semi-transparent trail--a path between the pulse and the object which emitted the pulse.Beam Width is ShownNO< GR|xD{ ffHsA HH HHWZJdx^kLength Contraction:

(here, stated without proof)

The apparent length is shortened in the direction of motion, but maintained in all other directions.

(This applies to planets, stars and galaxies as well as squares, circles, and SpoonFed logos.)

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Click on the screen to see the speed of light!

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Desynchronization

From the box, the waves appears to exit all sides simultaneously.

But we see the waves exit the back end of the box first. (The "back end" is the direction from which the object is moving)

The explanation is that the back of the box is in the future of the front of the box. If we had clocks on both the front and back of the box, they would read different times.

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The universe originates from a moving point, and every nonaccelerated observer sees themself at the very center. The outside edge of the universe is extremely dense--possibly infinitely dense!. This dense area is also time-dilated so though it may be 13.7 billion years after the big bang at the center, the particles we can see at the outer visible edge of the universe are only 300,000 years old and moving in incredibly slow motion. This slow motion effect, coupled with the doppler shift, causes them to appear to be only 2.73 Kelvin, even though they are actually at such a hot temperature that Electromagnetism breaks down--called the "decoupling temperature. Incidentally, this model predicts Hubble's Law.

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"Ballistic Model" of the universe: Assumptions:

1) The universe started from a point called the Center of Momentum and is expanding into empty, mostly empty, or HOPEFULLY empty space.

2) Our galaxy is traveling very quickly with respect to the center of momentum

3) In any given direction, from the Center of Momentum, there are about the same number of particles traveling with any given energy.

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Click Center of Circle to see universe from Center of Momentum!

(Click twice more to see error messages!

Use Ctrl-R or refresh to reset.)

#v?$centerclickrepeatlxly_rootsetConstantst1Instructions: 1. To pause, click, drag the mouse out of the demo, and release. 2. Click the RePlay button to restart the action. 3. Hover over the Instructions button to bring up this text. 3. Hover and/or Click on Info buttons for information about this page. 4. Click on the right arrow button to change page. 5. Selecting the text makes it easier to read. Keep the mouse button held down after selecting. 6. The Show/Hide Light Streams is described under 'what is a Light Stream' 7. Instructions may change depending on the page.instructionsTextvgEeventvelocitygTprepareBoxEvtE2yvyxvxv2velocityXYprepareWavettprepareMaskedCircledoIt doIt <<< < < <R  G G G GGGGGAA(R<?R<R NN GNN GR<R<R NN R!!H!NN! GNN! GR"R!!GW! !H!NN! GNN! GR"R!!N P! N G!H!NN! GNN! 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N G   R ?N    RRN  N GNN  GNN  GR NRRNNN =!=NNNNNN "=<H NRRN  N GNN  GNN  GRNNN =!=NNNNNN "=P1 #=$%&OT^ ?T@ T?T@ d#?T@ '*?T@ kJ1?T@JҀ8?T@ BwJ??T@ҐF?T@ GJ@MUŀ:͜PV@QWŀ:͝TXŀ:͝WYŀ:͜@ZZŀ:͝L][uvF^\f 9c@MPQTWZ]^?_roothideCirclescenterclickrepeatlxlysetConstantsvgthisGammagSlidervalueEeventvelocitygTGSV2prepareBoxEvtE2yvyxvxv2velocityXYGSV1prepareWavenumCirclesttprepareMaskedCircleoldValueHandle_yMaxMathpowrounddoitxa_xmouseBox_xround0ya_ymousetatround1ybtbxbCoordst1 x= y= t=t2 x'= y'= t'=bsqrtnThe Lorentz Transformation Equation was developed by H.A. Lorentz near the turn of the 20th century. He was resolving problems involving stellar aberration, the motion of electro-magnetic waves (light) through moving water, and the result of an experiment called the Michelson-Morely experiment, which found that the speed of light was constant. Einstein's major contribution to the theory of relativity was probably the discovery of the equivalence of Energy and Mass. See my other demo: Gamma.historyPassing Event Restart the demo and put the mouse at the center of GSV1. You should see that x=0 and y=0. When the center of GSV2 passes under the mouse, press and hold the mouse button down. The pilots of the two vehicles have agreed to synchronize their clocks at this event. They could have chosen any event to be the passing event, but this seemed like a logical choice. Notice that both vehicleshave the same x,y,and t values.passingY coordinate: Notice that the y coordinate for both vehicles is the same (y=y') no matter where you put your mouse. The y coordinate is perpendicular to the motion of GSV2. The Lorentz Transformation has no effect on the coordinates perpendicular to the motion.ycoordT coordinate: Move the gamma lever all the way up to four, so the time dilation factor is four. Click and hold the mouse button down. Notice that the t coordinate does not change but the t' coordinate does change as you move the mouse around the screen. By moving the mouse left and right, you are moving forward and backwards in time according to GSV2. Now let the mouse button up, move the mouse to GSV1, and leave the mouse stationary. t' is increasing FASTER than t. Now move the mouse along with GSV2. Now t' is increasing SLOWER than t. We see GSV2 traveling slower in time. GSV2 sees us traveling slower in time.tcoordX coordinate: Click and hold the mouse button down. Move it to the left side of GSV1. Make a note of x' and t'. Now move the mouse to the right side of GSV1, release the mouse and wait for t' to equal what it did on the left side. Make a note of the new x'. The difference should be the original width of GSV1 divided by gamma. GSV2 sees GSV1 to be length contracted.xcoordWaves and trees. Restart the demo and make a note of t when the first wave from GSV1 hits the ground. Now make a note of t' when the first wave from GSV2 hits the ground. Make several measurements of t' where the wave from GSV2 intersects with the ground. t' should be the smallest when the center of the wave hits the ground, and it should be equal when the front and back of the wave hits the ground. That's because GSV2 sees the center strike first and the two edges strike later, simultaneously.wavesDon't Panic! Just click the mouse button and hold it down to pause. Ignore the numbers for a moment and move the mouse over the info buttons. The equation to the lower left is called the Lorentz transformation. It tells you that if an event happens at position, x and time, t, that a person moving at velocity, v would see the event occuring at position x' and time t'. The apostrophes are usually pronounced x-prime, y-prime, and t-prime. 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