# Why does space contract?

1. Dec 26, 2012

### Tommy1995

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

2. Dec 26, 2012

### DiracPool

Do you mean space contraction or length contraction?

3. Dec 26, 2012

### Tommy1995

Aren't both of them essentially the same thing?

4. Dec 26, 2012

### Tommy1995

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. Dec 26, 2012

### WannabeNewton

I assume you mean the Lorentz contraction? Let's say in our rest frame with coordinates $(t,x,y,z)$ that we see a ship pass by, with velocity $v$ in the $+x$ direction, that has a length $L$ as measured by an observer in the rest frame of the ship with coordinates $(t',x',y',z')$. Say that we have an event $A$ occurring at the very front of the ship and an event $B$ 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 $\Delta x'_{AB} = L = \gamma (\Delta x_{AB} - \beta c\Delta t_{AB}) = \gamma\Delta x_{AB} = \gamma L'$ so $L' = \gamma ^{-1}L = L\sqrt{1 - \frac{v^{2}}{c^{2}}} < L$. 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. Dec 26, 2012

### arindamsinha

I asked this question recently, except I used the term 'distance contraction' instead of 'space contraction'. Turns out it is essentially the same thing as length contraction, based on the answers I got.

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.)

Last edited: Dec 26, 2012
7. Dec 26, 2012

### Staff: Mentor

The reason why is because the laws of physics are the same in all frames and also the speed of light is the same in all frames.

8. Dec 26, 2012

### DiracPool

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 mass-energy 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. Dec 26, 2012

### Staff: Mentor

But if I do the calculations in a frame in which Bob is at rest, what is George's energy? A lot more than 1 Gev, and also a lot more than the 3 TeV that we'd use if the did the calculations in a frame in which Alice is at rest. No matter which frame we do the calculations in, we will end up with an equally energetic collision.

10. Dec 26, 2012

### Staff: Mentor

Please don't do that. If you believe that it is related, then simply post a link in one thread. Do not duplicate the question, it just leads to confusion.

11. Dec 26, 2012

### Staff: Mentor

Here's a purely classical example.

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 $E=\frac{1}{2}mv^2$ 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. Dec 26, 2012

### Tommy1995

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. Dec 26, 2012

### sweet springs

A kind of rotation happens. In geometry rotation around the origin does not change the value of x^2 +y^2 before and after. Similarly relativistic 'rotation' does not change the value of t^2 - x^2 where latter sign is minus different from ordinary geometry. The effect of contraction of x is canceled by extension of t time.

Regards.

14. Dec 26, 2012

### arindamsinha

Thanks.

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. Dec 27, 2012

### Naty1

16. Dec 27, 2012

### Staff: Mentor

I agree with arindamsinha, neither is the result of the other. You can certainly conceive of transforms that have length contraction but not time dilation or transforms that have time dilation but not length contraction.

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

17. Dec 27, 2012

### Staff: Mentor

Although this is to some extent an aesthetic preference, I find myself saying they both follow from relativity of simultaneity, which in turn follows from the two postulates. It's easy to get RoS from the two postulates, and once you have that, time dilation and length contraction follow naturally:
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. Dec 27, 2012

### Staff: Mentor

I think all three follow from the two postulates. It is also easy to come up with transformations that have time dilation not relativity of simultaneity or that do not have time dilation but do have relativity of simultaneity, so I think that it is incorrect to say that time dilation follows from relativity of simultaneity. Similarly with length contraction.

I had a LONG conversation with mangaroosh on this topic, but basically it didn't go much further than post 2: