When helium 4 becomes a super fluid does the proper time change, can this be detected?
This understanding is not correct. There is nothing such as a unique way of identifying a "point in space" as that would be coordinate dependent. Proper time is an invariant quantity related to a clock following a particular world line.My understanding of proper time:
Every point in space is affected differently by time and gravity so has a different relative time, this goes for the 1st floor and the 50th or my toe and my eyebrow.
You started off talking about proper time and now you have switched to relative time. Time relative to WHAT? Do you mean the proper time throughout the life of the material? If so, that question has already been answered.Can the relative time of a superfluid be proven to be constant though it's change or phase change as you put it.
I believe tick rate differences have been measured at height differences as low as 1m, so differences between your head and toes are detectable. But this is the gravitational field of the Earth. My number above is a back-of-the-envelope estimate of the equivalent effect due to the gravity of a jar of liquid helium (or, indeed, a jar of water) and sounds optimistic on reflection. Its gravity just isn't important to anything.I understand the immeasurable diffences of my head and feet but I'm sure differences in relative time have been shown at the top and bottom of a skyscraper.
As phinds says, relative to what?Can the relative time of a superfluid be proven to be constant though it's change or phase change as you put it.