B Length Contraction: Apple Hanging from Tree & Earth

[Hernik]

Hello. Apologies, if this is already answered in other threads. Please redirect me, if that is the case.

Imagine an apple hanging from a tree. Will there be length contraction between the apple and the earth in the frame of reference of the earth, as well as of the apple?

All the best, Henrik

 

[Hernik]

Maybe it is better to ask: Will the apple see a length contraction in the direction of the earth, and will the earth see a length contraction in the direction of the apple (although probably rather small)?

 

[Vanadium 50]

"Contraction" implies a difference. In this case, difference with what?

 

[Hernik]

Thanks for your answer. Unfortunately, I don't understand. Apple and earth are co-moving, so no difference there. I suppose.

 

[Ibix]

Length contraction is a phenomenon that occurs when comparing measurements made using two inertial reference frames and the object being measured is at rest in one. I don't understand what measurements you are planning on comparing here.

 

[Hernik]

Thank you for helping me fraze this better. Maybe this will do: If you pick two different points at the same distance to the earth: A and B, and in A, an apple is placed, in B, nothing, would there be a length contraction between the apple at A and Earth compared to B and Earth? (Assuming Earth to be a perfect sphere).

 

[Hernik]

Sorry about the spelling, phrase, I meant.

 

[Nugatory]

If you pick two different points at the same distance to the earth: A and B, and in A, an apple is placed, in B, nothing, would there be a length contraction between the apple at A and Earth compared to B and Earth?

No, because you have specified that A and B are both at the same distance from earth.

But I'm still not sure what you're asking.
Are you asking whether the presence of the apple makes a difference? No, as long as the mass of the apple is negligible compared with that of the earth (and if it is not, we open up a whole different can of worms - let's not go there). The distance between the earth and point in space where the apple is will be the same whether the apple is there or not.

There is a different can of worms, in many ways more interesting, involving how we define/measure that distance. If your question involves opening that one.... by all means do so.

 

[Hernik]

Thanks. Well. How to ask a question. I guess, what I am thinking, is along the lines of: I would presume, the apple's presence would enhance the gravitational field slightly between the apple and the earth. And I would further presume that to give rise to a slight spacetime distortion in the area between the apple and the earth. And, that such a spacetime distortion involves a slight length contraction. You say no. I a wrong, right? (edit, spelling)

 

[Hernik]

...mixing up gravitational field and space time distortion. They are the same, so one not giving rise to the other.. sorry. Apart from that, I am still wrong, I understand?

 

[phinds]

such a spacetime distortion involves a slight length contraction

as long as the mass of the apple is negligible compared with that of the earth (and if it is not, we open up a whole different can of worms - let's not go there

 

[Hernik]

Thanks. Close the thread please.