Length contraction and general relativity

In summary, the concept of length contraction in general relativity is not as straightforward as it is in special relativity. The size of objects is relative to the observer's reference frame, which takes into account both their motion and their position in a gravitational field. Therefore, the answer to whether an object will get longer or shorter in space depends on the observer's chosen coordinates.
  • #1
johann1301
217
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Can one detect length contraction due to general relativity? I.e does length/width/height change with distance to a gravitational centre? If so does the object get longer or shorter?

I know this is the case with increasing speed in special relativity, but what about GR...

If i went into space, would my physical body be subject to any kind of of change in size?
 
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  • #2
The first thing to get about either special or general relativity is that there is no such thing as the absolute size of objects, there isn't even absolute comparisons between the sizes of two things that are in relative motion (in special relativity), or in relative motion in two different places in a gravitational field (in general relativity). Thus one should not talk about things "getting longer or shorter" in some kind of definite, widely-agreed-on, "invariant" way. You see language like that a lot, but it's quite confused. Instead, relativity is about recognizing that if you compare the length of two objects, the answer you get depends on how you do the comparison, which is often called your "reference frame". Loosely, this means how you are moving relative to the objects (in special relativity), or where you are in a gravitational field relative to the objects (in general relativity).

Often, the two objects you will care about are a ruler that is in your hand, and some other ruler that is somewhere else or moving some other way. Then if you adopt standard conventions about how to make length comparisions (which means, more technically, choosing a standard way to coordinatize the spacetime, which in general means making a choice of a grid of observers whose rulers and clocks you will use to talk about the places and times where events occur), you will find that both in special relativity and in general relativity, you will reckon the other ruler to be shorter (if it is moving relative to you or at a higher gravitational potential), or longer (if it is lower in a gravitational potential than you are), relative to the ruler in your hand.

So I think your answer is, in general you must combine the effects of motion and the effects of gravity, and you must choose coordinates, to decide how a length comparison will turn out. The answer you get depends on your choice of coordinates unless you restrict to questions that deal strictly in the "invariants" (and length is not one of those, that was one of the big surprises of relativity).
 
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1. What is length contraction in general relativity?

In general relativity, length contraction refers to the phenomenon where the length of an object appears to be shorter when it is moving at high speeds relative to an observer. This is due to the warping of space and time caused by the presence of massive objects.

2. How does length contraction relate to the theory of general relativity?

Length contraction is a consequence of the theory of general relativity, which explains the effects of gravity on the fabric of space and time. The theory predicts that the closer an object is to a massive body, the more it will be affected by the curvature of space-time, resulting in length contraction.

3. What is the formula for calculating length contraction?

The formula for length contraction is given by L = L0/γ, where L is the contracted length, L0 is the original length, and γ is the Lorentz factor. The Lorentz factor is dependent on the velocity of the object and is equal to 1/√(1-v2/c2), where v is the velocity of the object and c is the speed of light.

4. Can length contraction be observed in everyday life?

Length contraction is only noticeable at extremely high speeds, close to the speed of light. In everyday life, the effects of length contraction are too small to be observed. However, it is a crucial factor in understanding the behavior of particles in particle accelerators and other high-speed experiments.

5. How does length contraction affect the measurement of time?

According to the theory of general relativity, time also experiences dilation at high speeds, meaning it passes slower for an object in motion relative to an observer. This is directly related to length contraction, as the slower passage of time contributes to the appearance of a shorter length for the moving object.

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