How to change the timezone in photo metadata?

Question

After returning from a recent trip out west, I forgot to change my camera's timezone to the local time.  As a result, hundreds of photos from a long weekend trip were recorded with the wrong timezone.  I imported them to Lightroom 5 and discovered the problem.  Of course, I used the Edit Capture Time feature as described in the online help: https://helpx.adobe.com/lightroom/help/metadata-basics-actions.html#change_the_photo_captu re_time
But that changes the time of each photo's metadata, rather than the timezone.  There's a subtle difference; the better solution would be to change the timezone so that all future interpretations and exported times would be correct.  For example, here's the original metadata from a RAW image:
DateTimeOriginal                : 2014:08:23 09:13:45
Timezone                        : -07:00
and here's what appears on an exported JPG file, after the capture time was edited:
DateTimeOriginal                : 2014:08:23 11:13:45
TimeCreated                     : 11:13:45
DigitalCreationTime             : 09:13:45
DateTimeCreated                 : 2014:08:23 11:13:45
DigitalCreationDateTime         : 2014:08:23 09:13:45
[These metadata reports were produced by exiftool.]  Notice how the RAW image includes Timezone (though sadly the JPG export does not).  More to the point, look at the variety of timestamps produced for the JPG file, none of which mention the timezone and two of which have the wrong time (9:13am instead of 11:13am).  Without the timezone information the latter is hard to interpret and looks inconsistent.  Is this a bug in LR5?  or is it a missing feature (to not record the timezone on export)?

Answer 1

There's not a simple explanation of the behavior you're observing.  It's not a bug -- LR is doing a reasonable job of following imperfect industry standards. 
The photo/camera industry in general does not make it easy to deal with time zones. LR's general approach is to preserve whatever time zones are present in the metadata but otherwise ignore them -- it doesn't change them, and it doesn't display them. As you discovered, the Edit Capture Time command does not let you change time zone, but it does preserve whatever time zones are present in the metadata  (but see below for one exception).   LR's handling of time zones conforms with Metadata Working Group's Guidelines For Handling Image Metadata 2.0, an industry standard supported by Adobe, Apple, Canon, Microsoft, Nokia, and Sony.
The EXIF metadata inserted by cameras does not provide an official field to record time zone (folklore among metadata geeks is that one of the technical leaders of the spec, when challenged about that, asked why anyone would want time zones).  Some cameras insert the non-industry-standard EXIF field TimeZoneOffset.  I don't know the entire history of this field, but it's not defined in the EXIF 2.2 or 2.3 specs, nor mentioned in the Metadata Working Group's Guidelines For Handling Image Metadata 2.0.  The field is not well-defined -- it only allows offsets of whole hours, whereas over a billion people live in a time zone whose offset is +5:30 (India). 
LR preserves EXIF:TimeZoneOffset in your original photo, but it otherwise ignores the field, and it doesn't get copied to exported photos.  This is not unreasonable, given that the field is non-standard.
The XMP metadata fields, typically inserted by software applications, do support time zones, but including a time zone is optional.  LR preserves XMP time zones that are present when the image is imported, even if you change the date/time with Edit Capture Time.  Your original photo did not contain any XMP fields (cameras typically don't insert XMP), so there were no time zones there for LR to preserve.
The Digital Creation date/time fields you observed are intended to record when an image was digitized.  With digital cameras, that's generally the same as capture time, but with scanned images, the date/time of digitization (scanning) is different from the date/time the image was originally captured.  LR's handling of these two different date/times isn't great, but it's adequate for most users.  LR will insert the digitization date/time when an image is first imported (if it doesn't already exist), but Edit Capture Time changes just the capture time, not the digitization date/time.  (A few years ago Adobe changed Edit Capture Time in a point release to also change digitization date/time, on the theory that LR is designed for images from digital cameras, and the two date/times should always be the same; but a number of users who also used LR to manage scanned images complained loudly that LR was overwriting precious metadata, and Adobe backed out that change in the next release.)
So Edit Capture Time will leave photos taken by digital cameras with an incorrect digitization date/time.  But very few users care about that -- it's only users with scanned images who care about the difference, and at least LR will avoid overwriting digitization date/time.
A suggestion for using Exiftool to examine image metadata: Use the "-a -G" options, which causes Exiftool to show which section of the metadata the fields are coming from.   Given the complexity of the legacy metadata industry standards, this will help you better understand what your camera and software tools are doing.  For example:
[EXIF]          Modify Date                     : 2014:08:31 10:01:45
[EXIF]          Date/Time Original              : 2014:08:13 11:53:44
[EXIF]          Create Date                     : 2014:08:13 08:53:44
[IPTC]          Date Created                    : 2014:08:13
[IPTC]          Digital Creation Date           : 2014:08:13
[XMP]           Modify Date                     : 2014:08:31 10:01:45-07:00
[XMP]           Create Date                     : 2014:08:13 08:53:44
[XMP]           Metadata Date                   : 2014:08:31 10:01:45-07:00
[XMP]           Date Created                    : 2014:08:13 11:53:44
[Composite]     Date/Time Created               : 2014:08:13 11:53:44
[Composite]     Digital Creation Date/Time      : 2014:08:13 08:53:44