Does migrating to Apple's new Photos app actually double my storage requirements?

Short answer, no. The measuring tool you are using doesn't take the time to deduct the space saved when files are hard linked, so it over-counts the space used.

The Libraries are using 'hard links' to the real location of the files, so both appear to be approximately the same size, but each actual photo is only located in one place on your hard drive, with pointers from both Libraries.

Deleting either Library will not affect the storage space, only deleting both would actually remove the 50GB of data from your drive.

See: Photos saves disk space by sharing images with your iPhoto or Aperture libraries

More on hard links from Ars Technica:

A hard link is simply a reference to some data on disk. Think of a file as a combination of a name and a pointer to some data. Deleting a file really means deleting the name portion of that duo. When there are no more names pointing to a particular piece of data disk, then that disk space can be reused."

If you work hard to clean up your photos after switching to the photos app, or tell iCloud photos to optimize disk usage, then your disk usage will actually go up, because the iPhoto library will still point to the old files, and they will not be deleted from the drive until you delete the old iPhoto library.

I was just working on a Macbook Air that had a nearly full drive. No matter what I did to reduce the size of the photo library, disk space just kept going down. Deleting the old iPhoto library freed up 20GB of space!

Ok, I believe it takes up double space. I just deleted my iPhoto Library.migratedphotolibrary which was about 90gig of space. HD went from having 220gig of free space to having now 316gig. So I freed up about 90gig of space. Plus when I went to empty the trash folder it took a few minutes.

I've spent a lot of time to solve this issue and hope this it can help even if it's not the most common cause of the issue.

The problem for me here is to know if Photos and iPhotos store your photos twice in two different spaces of your hard drive or only one with a symbolic link.

I said that to me this is two different places (and it is not a good thing) If you look at the sizes of a particular picture in both directories, they are not the same. Thus to me it is not the same object (a hard link would have EXACTLY the same size) If you do 'ls -lha' for these 2 files (same picture):

/Users/doubelle/Pictures/iPhoto Library.migratedphotolibrary/Data/2015/01/18/20150118-110234/2pfRkFdYTrSDeax1Tqq6DQ

/Users/doubelle/Pictures/Photos Library.photoslibrary/Data/2015/01/18/20150118-110234/2pfRkFdYTrSDeax1Tqq6DQ

You obtain these different file sizes

-rw-r--r--@ 1 doubelle staff 38199 1 jul 22:47 IMG_0762.jpg

-rw-r--r--@ 1 doubelle staff 37136 1 jul 22:48 IMG_0762_migrated.jpg

That way you can know if a file is linked or duplicated.