# The Naked Scientists Forum

### Author Topic: What about length contraction and free fall?  (Read 3309 times)

#### jeffreyH

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##### What about length contraction and free fall?
« on: 28/12/2014 21:35:18 »
An infinitesimal amount of what we term spaghettification should occur within a free falling body due to infinitesimal differences in the gravitational force at different points in the body at differing radial distances from the source. Depending upon the dimensions and mass of the falling body these differences could be significant between the points nearest and furthest from the source. Therefore this indicates no length contraction during free fall. Is this correct?

#### Atomic-S

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##### Re: What about length contraction and free fall?
« Reply #1 on: 29/12/2014 06:08:37 »
The differences in gravitational force between points on the side near the source and points on the side away from it can indeed be extremely various, varying from insignificant up to overwhelming.  It depends on the second derivative of the gravitational potential with respect to distance.  For a classical gravitating body, the potential varies inversely as the distance, the force inversely as the square of the distance, and the second derivative inversely as the cube of the distance. Very dense and massive sources will have extreme nonlinearity near them, which is the source of the tidal stress. However, an object of low density, even if quite massive, will exhibit much less of this effect upon objects at its surface. In all cases, the field at large distances from the source will show very little tidal stressing because it is much more uniform. Not the strength of the field, but its nonuniformity, is the cause of tidal stressing, or "spaghettification".

All of the foregoing is true of a free-falling body.

In the case of objects in fields of common strength , the tidal stressing does indeed alter the length of the object, by reason of the modulus of elasticity of the object (to include also that portion of it that is ascribable to the object's own gravity).  That is why we observe tides on Earth. At high tide, the effective width of the Earth is slightly increased along the axis from the point of high tide to its corresponding point on the opposite side. As any object, such as a comet, approaches a gravitating body such as the sun, the nonuniformity of gravitation increases and stretches the object in the direction of the nonuniformity.  There is also a space-time effect having nothing to do with the elasticity of the object but rather with the shape of space-time within a gravitational field that alters measurements in that direction, although this effect is likely much less than the effect due to elasticity. In the case of an observer traveling with the object, the relativistic space-time effect would be nullified by their common reference frame, and the observer would observe only the effect of elasticity (insofar as the entire object could be regarded as being within the observer's reference frame, which would be the case until the nonlinearity became phenomenally great, as near a small black hole, at which point a proper analysis requires regarding different parts of the object as being in different reference frames).

As for length contractions during free fall:  As noted already, nonlinear gravitation will cause an elastic expansion of length even under conditions of classical physics.  Relativistic changes of length would not occur, as seen by an observer moving with the object, to the extent that the object is effectively wholly within his reference frame. A more difficult question is what happens to the observed length in the aforementioned case where that is not a good approximation, and I do not know the answer.  Another question is how the length may change as seen by some other observer, and in general, it is not the same for other observers. The observer of greatest interest is probably one that is at rest with respect to the source and well beyond its significant gravitational influence. If memory serves me correctly, to such an observer, the object will appear to be contracted in the direction of the field, although not necessarily enough to offset the elastic stretching.  The matter is further complicated by the fact that the length will be affected also by the object's speed. Therefore, the question actually is not a simple one.

#### jeffreyH

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##### Re: What about length contraction and free fall?
« Reply #2 on: 29/12/2014 14:29:47 »
The answer is definitely not simple. Thanks for the detailed answer. You make some interesting points which I hadn't considered.

EDIT: If in the same gravitational field an object is propelled directly away from the source while another is dropped into free fall then would the upward moving object experience contraction while the free falling one experiences stretching? How could this be tested experimentally in earth gravity?
« Last Edit: 29/12/2014 14:41:08 by jeffreyH »

#### yor_on

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##### Re: What about length contraction and free fall?
« Reply #3 on: 01/01/2015 11:47:11 »
It's a very difficult question Jeffrey. What would a frame of reference be defined as here? Microscopically? Or as macroscopic observers? But all free falls are geodesics, ideally. And as they can have different speeds, various speeds defines length contractions too, comparing, just as gravitational potentials does. With a higher gravitational potential the speed of the particles/constituents inside that 'gravitational patch' will vary in its 'free fall' from 'parts' in a lower gravitational potential. Then you have the way ones particles, making up ones body, counteract it by other forces keeping yourself together.

#### Atomic-S

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##### Re: What about length contraction and free fall?
« Reply #4 on: 03/01/2015 05:27:52 »
When you say "propelled directly away", you do not specify whether a motive force (e.g., rocket engine) is being applied at the time. An object that is tossed upward, once leaving the tosser's hand, is in free rise (neglecting atmospheric effects) even while it is going up. It enters free fall when starting down again. The operative word here is "free", and as long as it is, the physics is basically the same. For this reason, I would believe that the length of an object as viewed by an observer at rest with respect to the source and well beyond it, will not be affected by the direction  of the flight parallel or antiparallel to a given direction at a given point. I am of course assuming that the flight is free.

#### jeffreyH

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##### Re: What about length contraction and free fall?
« Reply #5 on: 03/01/2015 16:34:11 »
When you say "propelled directly away", you do not specify whether a motive force (e.g., rocket engine) is being applied at the time. An object that is tossed upward, once leaving the tosser's hand, is in free rise (neglecting atmospheric effects) even while it is going up. It enters free fall when starting down again. The operative word here is "free", and as long as it is, the physics is basically the same. For this reason, I would believe that the length of an object as viewed by an observer at rest with respect to the source and well beyond it, will not be affected by the direction  of the flight parallel or antiparallel to a given direction at a given point. I am of course assuming that the flight is free.

Yes the flight was to be considered as free with an initial force upward to start the process. The difference is that one path is moving initially to a higher gravitational potential while the other is constantly moving towards a lower gravitational potential. I would say that these two situations are not equivalent. Simply because the initial impetus upwards could in theory achieve escape velocity while in the downward direction this could never be the case because it always starts from within a stationary frame with respect to the source.

#### yor_on

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##### Re: What about length contraction and free fall?
« Reply #6 on: 23/01/2015 21:32:44 »
It's pretty simple, unless you want to compute geodesics? Define a 'point like' particle of a evenly distributed mass (rest mass in this case) in a flat space, then introduce tidal forces. As it is point like it can't be split.

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##### Re: What about length contraction and free fall?
« Reply #6 on: 23/01/2015 21:32:44 »