Let's suppose I am an ant who lives in a 2D curved space. Locally the world seems 2d-euclidean to me, but it is not if I consider a large portion of space.

Now let's consider a human being who lives in curved 4d spacetime. Locally the spacetime seems 4d-euclidean --> in fact, the space itself appears 3d-euclidean to us. But if we consider a larger portion of spacetime, then the curvature will inevitably be evident.

However: if I look around me in any moment, the space seems to me 3d euclidean EVERYWHERE, not only locally. I mean, it seems like I can extend my 3d-euclidean-grid forever in space (at least according to my eyes).

How can this be possible if spacetime is curved? Do our eyes give us misleading impressions?

  • 2
    $\begingroup$ how would our eyes see light following the curvature of space as not being straight $\endgroup$ – Adrian Howard Sep 9 at 11:41
  • $\begingroup$ @adrian I don't know. But what our eyes see is an euclidean 3d flat space even though it is not... do you agree? $\endgroup$ – Federico Toso Sep 9 at 11:52
  • $\begingroup$ My eyes currently tell me that there is no universe beyond my living room. Should I believe them? $\endgroup$ – WillO Sep 9 at 11:58
  • $\begingroup$ Maybe read Kant $\endgroup$ – Stéphane Rollandin Sep 9 at 12:36
  • $\begingroup$ Consider to define the word Euclidean. It has different meanings in the litterature. Do you mean flat? $\endgroup$ – Qmechanic Sep 9 at 15:42

You need sensitive instruments/telescopes to see that light does not always follow straight lines, but it is possible - see Tests of General Relativity.

In the everyday world, if I want to send an apple from A so that it arrives 1 second later at B 1 metre away, then I have to throw it so that it follows a ballistic trajectory. If I just aim it in a straight line from A to B at a velocity of 1 metre per second then it will fall to the floor. This is actually evidence that our local 4D spacetime is curved by the nearby presence of a large mass (the Earth). But we don't intuitively think of it that way.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.