What Is the Meteor's Altitude Due to Length Contraction?

In summary, the Earth observer sees a meteor at 650m altitude. If the meteor is traveling at 0.92c, the altitude measured by an alien resting on the meteor would not be the same due to differences in inertial frames and measurements. The solution is to plug in Lo = 650 and solve for L, but the reason for this is not clear. Measurements from frames of reference moving in relation to the object being measured will appear to change, resulting in different values for Lo and L.
  • #1
debroglieman
2
0
An observer on Earth sees a meteor approaching rapidly, heading directly for the Earth's surface. At a certain instant, the Earth observer sees the meteor at 650m altitude. If the meteor is traveling at 0.92c, as recorded by an Earth radar, what would be the altitude as measured by the alien resting on the meteor?



L=Lo (ɣ)



I know the solution is to plug in Lo = 650 and solve for L, but not know why this is so. It seems that the two inertial frames are identical, and as such the answer should be 650m? Advice/solution appreciated.
 
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  • #2
No. The inertial frames are (not) identical (but symmetric), but measurements from them disagree anyway, such as those of distance. Remember that lengths appear* to change from frames of reference moving WRT the object whose length is being measured.

*for lack of better wording
 
  • #3
Okay, so how do I know what is Lo and what is L?
 

FAQ: What Is the Meteor's Altitude Due to Length Contraction?

How does altitude affect length contraction?

The theory of relativity states that length contraction occurs when an object is in motion at high speeds. However, altitude does not have a direct effect on length contraction. It is the relative velocity between the observer and the object that causes length contraction, not the altitude.

Can length contraction be observed at high altitudes?

Yes, length contraction can be observed at high altitudes. This is because at high altitudes, objects are moving at high speeds relative to the observer on the ground. This relative velocity causes the object to appear shorter in length to the observer due to length contraction.

Does altitude affect the magnitude of length contraction?

No, altitude does not affect the magnitude of length contraction. The amount of length contraction is solely dependent on the relative velocity between the observer and the object, not the altitude.

Is length contraction at high altitudes significant?

It depends on the altitude and relative velocity between the observer and the object. At everyday speeds and altitudes, the amount of length contraction is very small and not noticeable. However, at extremely high altitudes and speeds, the effects of length contraction can become more significant.

Can length contraction be explained by classical physics?

No, length contraction is a phenomenon that can only be explained by the theory of relativity. In classical physics, there is no concept of relative velocity and therefore, no concept of length contraction. Only when an object is moving at high speeds relative to the observer, can length contraction be observed and explained by the theory of relativity.

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