Does space contraction regard the moving body or the path?

[alba]

Consider the path of a proton at 7 TeV Ke at LHC.
Wikipedia says:
Length contraction is the phenomenon of a decrease in length of an object as measured by an observer which is traveling at any non-zero velocity relative to the object. This contraction (more formally called Lorentz contraction or Lorentz–FitzGerald contraction after Hendrik Lorentz and George FitzGerald) is usually only noticeable at a substantial fraction of the speed of light. Length contraction is only in the direction parallel to the direction in which the observed body is travelling

But I read everywhere that the path of a moving body is shortened by gamma factor, which is right? Can it be both? How long is one circle in the proton's frame?

 

[Ibix]

If you are moving with respect to me you are length contracted according to me, but I am length contracted according to you. (Edit: note that what you are thinking of as the path is basically a ruler at rest with respect to you, along which I travel - the ruler is just as contracted as you are from my perspective.) You also need to consider time dilation and the relativity of simultaneity in order for this to make sense.

I'd suggest starting by considering only motion in a straight line. Circular motion has some complexities due to the constant acceleration of the circling object that make life rather more complex.

 

[alba]

If you are moving with respect to me you are length contracted according to me, .

I'd appreciate if you considered also the concrete example at LHC, to make things more clear.

But what do you mean by 'you'. Consider a spaceship approaching or passing another body,my question is what is contracted, theship or the trajectory?
In my picture I have also considered time dilation : a proton makes one full circle in 1/8282500 second in its frame, where in the lab1 /11100 second has passed.
Now , the path is not moving, and should therefore not shrink, what does SR say in reality, is wiki right or not?

 

[Ibix]

I'll point you to my edit of my last post, which I suspect I may have made too late. The point is that from the perspective of a moving object, be it a person or a proton, it is at rest. From its perspective, then, the thing you are describing as not moving (the LHC for example) is moving. This is called the principle of relativity. Informally, it means that both "the train moved past the stationary tree" and "the tree moved past the stationary train" are valid descriptions of what you see out of a train window. In the case of the LHC it means that, from our petspective, the protons are time dilated and length contracted but from the perspective of the protons the LHC is length contracted and time dilated.

It's actually more complex than that with the LHC because the protons aren't moving inertially. However one could imagine an alien zipping past the Earth at 0.999c (or whatever) who is momentarily moving parallel to the protons in the ring. Certainly it would be length contracted and time dilated from our perspective. We would be length contracted and time dilated from its perspective.

 

[alba]

From its perspective, then, the thing you are describing as not moving (the LHC for example) is moving. T.

If two ships/protons/trains are moving at .999999991 relative to each other they don't know who is at rest. Proton/ship/train A will see ship /train/proton B approaching at a speed and contracted, why should he see space contracted too? Now suppose proton B is moving at .99999991 c in the opposite direction, what will he see? Is B doubly contracted, is speed doubled: 1.9999999982 c, is the path only once contracted. If they are back-to -back in the lab frame they'll crash after 1/ 2* 8282500 s in A's frame and after 1/ 22200 s in labframe?

Can you please clarify this basic notion: a ship long 21 m, circling the Earth at .99 c is contracted to 3m, according to SR as watched through a telescope from earth, right? but on the ship they do not realize, right? So,is the contraction real or just an optical illusion?

 

[phinds]

If two ships/protons/trains are moving at .999999991 relative to each other they don't know who is at rest. Proton/ship/train A will see ship /train/proton B approaching at a speed and contracted, why should he see space contracted too? Now suppose proton B is moving at .99999991 c in the opposite direction, what will he see? Is B doubly contracted, is speed doubled: 1.9999999982 c, is the path only once contracted. If they are back-to -back in the lab frame they'll crash after 1/ 2* 8282500 s in A's frame and after 1/ 22200 s in labframe?

You need to Google "relativistic velocity addition"

 

[Mister T]

So,is the contraction real or just an optical illusion?

It's real. It's been measured, and calculated. The measurements match the calculations.

It would be better if you gave examples of straight line motion. Once you get that sorted then if you want you can look at more complicated examples involving circular motion.

You mentioned the factor gamma $\gamma$. If you had two identical space ships passing each other, observers in each ship would conclude that the other ship is contracted by the factor $\gamma$. So, for example, at a relative speed of about 87% of the speed of light, $\gamma=2$. People in each ship use tape measures and determine that their ship is 100 meters long. They will each conclude that the other ship is only 50 meters long.

We usually don't use the word "see" to describe this observed length contraction. What we see is what things looked like in the past, because it takes time for light to travel. But, what we observe is what we conclude after allowing for light travel time. We would say that each of us observes the other's ship to be 50 meters long, yet we each observe our own ship to be 100 meters long.

 

[PAllen]

To get at another question of the OP: distance contraction versus length contraction. They are really the same thing, as I hope I can clarify.

Consider a pair of ships A1 and A2 that are at mutual rest; and another pair of ships B1 and B2 that are at mutual rest. However, the A pair and B pair are approaching each other at high relative speed. Each pair of rockets measured their mutual distance at 10 km, and their lengths at 100 meters. If the relative speed is .87 c, each A ship determines that the B ships are 50 meters long and separated by only 5 km; and vice versa.

Space contraction is a misnomer. The feature that a very fast rocket can get from Earth to a star in a 'short' time, while seeing the Earth and star moving by at < c, is because the Earth and star are (nearly) comoving, thus forming a composite object that is length contracted. My example above shows how all aspects of contraction are symmetric.

As to whether the effect is 'real', consider an observer co-moving with a muon created in the upper atmosphere. The muon is not moving and not time dilated. Yet it really does reach the ground with high probability. Unless you declare this frame is under-privileged, you must accept that length contraction of the Earth's atmosphere is just as real as the time dilation that is important in the Earth frame.