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Why does space contract? 
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#1
Dec2612, 01:27 AM

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In simple terms could someone please explain to me the reason why space contracts when approaching the speed of light?



#2
Dec2612, 01:43 AM

P: 573

Do you mean space contraction or length contraction?



#3
Dec2612, 01:48 AM

P: 39

Aren't both of them essentially the same thing?



#4
Dec2612, 01:49 AM

P: 39

Why does space contract?
But if I had to choose i guess space contraction, as a rocket zooms through space at near speeds of light, the space infront of it will contract in length



#5
Dec2612, 01:58 AM

C. Spirit
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I assume you mean the Lorentz contraction? Let's say in our rest frame with coordinates [itex](t,x,y,z)[/itex] that we see a ship pass by, with velocity [itex]v[/itex] in the [itex]+x[/itex] direction, that has a length [itex]L[/itex] as measured by an observer in the rest frame of the ship with coordinates [itex](t',x',y',z')[/itex]. Say that we have an event [itex]A[/itex] occurring at the very front of the ship and an event [itex]B[/itex] occurring at the very back of the ship such that both events occur at the same coordinate time  all of this of course as measured in our rest frame. The Lorentz transformations tell us that [itex]\Delta x'_{AB} = L = \gamma (\Delta x_{AB}  \beta c\Delta t_{AB}) = \gamma\Delta x_{AB} = \gamma L'[/itex] so [itex]L' = \gamma ^{1}L = L\sqrt{1  \frac{v^{2}}{c^{2}}} < L[/itex]. So you can see that in our rest frame we measure a smaller length for said passing ship in comparison to the length of the ship as measured by an observer in the ship's rest frame.



#6
Dec2612, 04:17 AM

P: 181

Length/space contraction is the counterpart of time dilation (the faster you go, slower your time gets). Say you are going to travel from Earth to a destination 1 light year from Earth. If you go at a (relatively) small velocity, say about 1/50th the speed of light, you will take about 50 years to reach according to your clock, because time slowdown is quite negligible at that speed. Now, let us say you are traveling close to the speed of light. Your time (and you clock) will slow down significantly compared to someone who remained on Earth. According to someone on Earth, you still take about a year to reach. But your clock having slowed down might show only one day has passed. Knowing that you are traveling approximately at the speed of light, you will infer that the distance was 1 light day. If you travel even closer to the speed of light, your clock may record passage of only a minute by the time you reach. Again, knowing you are traveling at approx. c, you will infer the distance was 1 light minute. So, depending on the velocity at which you travel, you will infer the distance to be shorter accordingly. The faster you travel, the shorter the distance will be. This is length contraction, or 'space contraction' if you prefer. (If you were traveling at a speed sufficiently close to that of light, you could even cross the Universe in a few seconds. You would be alive and well during that, barring any unfortunate collisions with other Universal matter. So the Universe itself could be just a few meters wide for you in that kind of exterme velocity situation.) 


#7
Dec2612, 07:06 AM

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#8
Dec2612, 08:04 AM

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I'm posting this in this thread and in the "mass gain at high velocities" thread because they are related.
Well, now I’m thinking that it may help to approach the problem from a different angle. I just started thinking that as Bob starts approaching the speed of light by firing his rocket pack at full blast, Alice sitting at home will see Bob get shorter (length contraction) and heavier (relativistic massenergy increase). However, Bob, being in his own reference frame, will see none of this change. This seeming inconsistency leads us to somewhat of an epistemological question which is, “Is Bob actually getting heavier and shorter, or isn’t he?” The easy answer would be to say it depends on your reference frame and that’s all we can say about it, but let’s think about this a little deeper with a practical example. Let’s shrink Bob down to the size of a proton and have Alice watch him race around the LHC while she is safely stationary in her own reference frame at the Atlas building. To Alice, Bob started out his “jog around the track” at 1 GeV, but now he’s put on a few pounds and is riding about 3 TeV. However, Bob still thinks he weighs 1 GeV because he’s in his own reference frame. Well, he thinks so, until he runs into George coming at him from the other direction and instead of them just bumping chests at 1+1=2GeV, they explode upon impact at 3+3=6 TeV. So how do we explain this? What actually happens at the collision point in space between Bob and George? It doesn’t seem possible that, ostensibly in the same position in space, we could have one interaction at 2GeV and another at 6TeV, and that it all depends on who is looking at it? Do have something wrong here? 


#9
Dec2612, 08:39 AM

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#10
Dec2612, 08:52 AM

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#11
Dec2612, 08:56 AM

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An elephant has a mass of about 1000 kg. A bullet fired from an elephant gun has a muzzle velocity of about 100 meters/sec and a mass of about 10 grams. How energetic is the impact of the bullet on the elephant? That's easy, we just use the classical expression [itex]E=\frac{1}{2}mv^2[/itex] for the kinetic energy of the bullet, and we get 50 Joules. (Note that I have chosen to work with a frame in which the elephant is at rest). Now let's do the exact same calculation, except that we'll work with a frame in which the bullet is at rest. Now we see a 1000 kg elephant smash into a stationary bullet at 100 m/sec, and the kinetic energy going into the collision is 5,000,000 Joules. But it's the same collision either way, just a different but equivalent mathematical description. If you carry the calculations through (conservation of momentum is a big help here) you'll discover that despite the enormous discrepancy in kinetic energy (50 J vs 5000000 J) the same amount of energy goes into making a hole in the elephant. 


#12
Dec2612, 07:56 PM

P: 39

arindamsinha, nicely said!
So length contraction would be a result of time dillation, because time is shortening to such a small amount of time we could look at it from the perspective of distance travelled and divide that by velocity in order to get the time taken. Length would have to change in order for the equation to make up for the time! tyvm 


#13
Dec2612, 08:25 PM

P: 449

Regards. 


#14
Dec2612, 10:00 PM

P: 181

Actually, I am not sure whether in Relativity we can say length contraction is a result of time dilation. Best to say the two phenomena go hand in hand. The difference is philosophical of course, the science is the same. 


#15
Dec2712, 08:54 AM

P: 5,632

[QUOTE][could someone please explain to me the reason why space contracts when approaching the speed of light?/QUOTE]
Dalespam has the answer Einstein discovered: Einstein took a different view, that the speed of light is the constant in all [inertial] reference frames. For this to be how our universe works, Einstein realized that the struggles of other of his contemporaries, Lorentz and Fitzgerald, to explain time dilation or length contraction relative to an imaginary 'ether' were more simply answered if the speed of light was constant. So in Special Relativity Einstein figured out relative velocity affects time and distance; in GR he went further and found that gravity is the curvature of space and time...Spacetime curvature IS gravity. Nobody knows exactly why our universe works this way. 


#16
Dec2712, 04:27 PM

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I would say that both are results of the two postulates: the principle of relativity and the invariance of c. 


#17
Dec2712, 04:48 PM

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Time dilation is two observers unable to agree that the tick and tock events of their respective clocks happened at the same time. Length contraction is me locating the two ends of a rod at the same time and measuring the distance between them, and someone else doing the same thing and finding different endpoints and hence a different length. Works best for me... De gustibus non est disputandam... YMMV 


#18
Dec2712, 04:56 PM

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I had a LONG conversation with mangaroosh on this topic, but basically it didn't go much further than post 2: http://www.physicsforums.com/showthread.php?t=575332 


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