Who Compresses More: Obj1 or Obj2 at C Speeds?

[kolleamm]

You have obj1 and obj2. As something approaches c speeds it begins to compress. How do we determine which obj is compressed since the movement is relative to the other obj?

 

[Ibix]

Neither object is compressed. Both objects measure the other as length contracted (i.e. shortened), but this is an effect of the relativity of simultaneity and the choice of coordinate systems. Neither will measure any stress in themselves or in the other object (assuming they are both moving inertially) which they would if one or other was compressed.

 

[kolleamm]

Okay I see, so it's basically just an illusion created by the different length of the light's path.

 

[Battlemage!]

Neither object is compressed. Both objects measure the other as length contracted (i.e. shortened), but this is an effect of the relativity of simultaneity and the choice of coordinate systems. Neither will measure any stress in themselves or in the other object (assuming they are both moving inertially) which they would if one or other was compressed.

Okay I see, so it's basically just an illusion created by the different length of the light's path.

But how can that be entirely true? If you do a detailed twin paradox calculation the fact that distance for the traveling twin according to Earth is shorter plays a role in the calculations that show differential aging, as discussed in this link here. Take note how crucial the length contraction calculation is. Without that calculation the distance the twins measure will not be what was shown, and that was crucial in showing the difference in their age at the end.

http://www.scientificamerican.com/article/how-does-relativity-theor/

Without that length contraction calculation you wouldn't get all the rest. It can't just be an "illusion" anymore than differential aging is. No one actually feels compressed, but how can it just be an illusion? If you look at the Lorentz transformation, a transformation from one frame to another for location will involve a time component as well as a spatial one, and his also holds for a time transformation. The "weirdness" of time cannot be separated from the "weirdness" of space, otherwise why are both included in the Lorentz transformation equations?

Besides, isn't length contraction just the displacement coordinate transformation when separation in time is zero? That is,

Δx' = γ(Δx - vΔt) IS the length contraction formula when Δt = 0, with L₀ = x'₂ - x'₁ = Δx' , isn't it? L₀ = γL => L = L₀/γ.

That seems pretty straight forward, and it tells me that length contraction is as real as the Lorentz transformation equations themselves are. Is this a fair conclusion?

 

[Ibix]

Okay I see, so it's basically just an illusion created by the different length of the light's path.

It's not an illusion, precisely. Any measurement you make, using light or not, will get you the same contracted length. You could use calipers, as long as you were quick enough to do it while the object passes at 0.99c or whatever, and you'd have a physical record of the object being only 14% as long as when measured at rest.

The easiest way to visualise this is in the "block universe". The universe is four dimensional - three spacelike dimensions and one timelike one. Tricky to visualise, so let's imagine a three dimensional universe with two spacelike dimensions and one timelike one. A circle, in this universe, becomes a cylinder because it's a circle at every instant. Beings in the universe see it as a circle because they are only seeing a slice of the cylinder, the slice that exists "now".

However, in relativity, "now" is a slightly flexible concept. Observers in relative motion don't agree on the definition of "now", and the definitions are rotated with respect to each other. That means that someone at rest with respect to the circle sees now as slices perpendicular to the cylinder - so sees a circle. Someone in relative motion has a now that is not quite perpendicular to the cylinder, so they see a diagonal slice through it - an ellipse.

That argument will lead you to visualise length dilation, not length contraction. That's because this is a purely Euclidean model and spacetime has a slightly different geometry called Minkowski geometry. That turns out to be why time is different from space; it also leads to length contraction in the full version of this argument. To see exactly how things work, you'll need to look up the Lorentz transforms. I'd also recommend looking around this forum for things called Minkowski diagrams, which are simple graphs that can really help with visualisation - they're effectively the formal form of the description I've given here. I've posted a few, and a poster called ghwellsjr used to post a lot of them.

 

[Ibix]

That seems pretty straight forward, and it tells me that length contraction is as real as the Lorentz transformation equations themselves are. Is this a fair conclusion?

Length contraction is a real effect in some senses. However it doesn't impose any stresses on the contracted bodies, and the exact value you measure for it is dependent on your choice of simultaneity convention. As are the Lorentz transforms.

 

[pervect]

Okay I see, so it's basically just an illusion created by the different length of the light's path.

Length simply isn't a property of an object alone, it's a property of both an object and a choice of a frame of reference, sometimes called a choice of an "observer". By some definitions (but not all), 'real' properties of an object don't depend on the frame of reference or observer, they only depend on the object itself. In that specific sense, one might say that length isn't "real", because it depends on the observer.

However, different people have different ideas on what constitutes "reality", so it's better not to phrase things in terms of what is "real" and what is "illusion".

[add]To give a specific example of the need for caution, "energy" is a quantity that depends on both the object and the frame of reference (i.e. the observer), but one might be justly criticized if one were to claim that this observer dependence meant that "energy isn't real".

It's also worth noting that there is a property of an object much like length that is independent of one's choice of frame of reference (or choice of observer). This property is called "proper length". One can think of proper length as the length as measured by an observer (frame of reference) in which the object is at rest. The way this definition is worded though, the observer independence is a tautology, so it's a bit uninteresting. What's more interesting is defining the proper length of an object in such a way that any observer can measure it. This is possible, but it requires mathematics to express the needed concepts.

 

[Mister T]

You have obj1 and obj2. As something approaches c speeds it begins to compress. How do we determine which obj is compressed since the movement is relative to the other obj?

When you state "as something approaches c speeds" you are assigning, without thinking about it, a special status to the object that's moving at near speed c. But in fact the same can be said of both objects, or neither object. The two objects move at a speed near c relative to each other. Neither has a status that's different from the other.

 

[MrRobotoToo]

You have obj1 and obj2. As something approaches c speeds it begins to compress. How do we determine which obj is compressed since the movement is relative to the other obj?

An observer at rest with respect to obj1 will consider obj2 to be length contracted, and vice versa. Length is a frame-dependent quantity.

 

[Battlemage!]

Length contraction is a real effect in some senses. However it doesn't impose any stresses on the contracted bodies, and the exact value you measure for it is dependent on your choice of simultaneity convention. As are the Lorentz transforms.

Yeah that's what I thought but this thread combined with the weird way distance is defined in GR as I read about it threw me off a bit. Just trusting the math it's pretty clear that if time dilation is 100% real than so is length contraction... in flat spacetime anyway...

 

[Ibix]

Yeah that's what I thought but this thread combined with the weird way distance is defined in GR as I read about it threw me off a bit. Just trusting the math it's pretty clear that if time dilation is 100% real than so is length contraction... in flat spacetime anyway...

I think @pervect put it better than I did. "Real" isn't a helpful term here since it doesn't have a good definition.

How do you measure length? Basically you measure the coordinate of the front of the object and the coordinate of the rear of it and take the difference (I'm assuming a friendly coordinate system where that operation makes some kind of sense). That's what a ruler does - it defines one dimension of a convenient coordinate system with the origin at the zero. If you are trying to measure the length of a moving object, however, you have to measure the end positions simultaneously. But different reference frames have different notions of simultaneity. So length contraction comes from the fact that the two frames measure different things and call them length.

Is that "real"? It's definitely not an illusion. Nor is it sloppy experimental practice, which could have similar results. And it's definitely not a compression. It's just different.

 

[haushofer]

You have obj1 and obj2. As something approaches c speeds it begins to compress. How do we determine which obj is compressed since the movement is relative to the other obj?

And so is the notion of "who is contracted". If it was not, you could determine who is "really moving", which is against the principle of relativity (= all inertial frames are equivalent).