Is there an equivalence principle for space and time which states
something on the lines of it not being possible to tell if a change in
a measurable quantity is with respect to time or space purely from the
data?

Thanks

wrote:
Is there an equivalence principle for space and time which states
something on the lines of it not being possible to tell if a change in
a measurable quantity is with respect to time or space purely from the
data?

As you are posting in a relativity newsgroup, let me assume relativity
applies, and one can model the world as a spacetime manifold. Let me
assume the "measurable quantity" is some type of tensor field on
spacetime, and that it varies from place to place in the manifold. Then
whether the variation is with respect to space or time depends on how
one defines "space" and "time". That is, how one applies spatial and
temporal coordinates onto the manifold. One is free to do that in almost
any way (the basic restriction is that there be a 1-to-1 mapping between
coordinate 4-tuples and points in the manifold; that is, that the
coordinate values be unique).

So it's not that one is "unable to tell", but rather that one can tell,
but the meaning is essentially arbitrary. Different people (using
different coordinates) can obtain different answers for the same
variation, and neither is wrong.

The same holds true for many quantities that are not
tensor fields. In particular this is true for any
measurement of a distance or a time interval. But if
you want to discuss measurements of Voltage or
temperature or many other quantities, it may or may
not hold.


Tom Roberts

On Apr 3, 3:07*pm, wrote:
Is there an equivalence principle for space and time which states
something on the lines of it not being possible to tell if a change in
a measurable quantity is with respect to time or space purely from the
data?

It's not really a well-formed question.

Do a map alignment to north and do a survey to the fencepost to
determine its measurable coordinates along the N-S direction and E-W
direction relative to where you are standing. You now have two
measurable quantities.
But then you use a compass to realign the map to magnetic north, and
your two measurable coordinates change. Now, was this due to a change
in the N-S direction or due to a change in the E-W direction? Well,
both, right? But the *distance* that you can calculate from the E-W
and N-S coordinates will be the same for either map alignment.

It isn't much more complex than that. A change in the frame of
reference will change certain *components* of some quantities (like
the time and space coordinates between one event and another event),
but there will be other quantities that you can calculate from those
components that will be the same regardless of frame of reference,
even though the components individually change.

The big change introduced by relativity is that, a hundred years ago,
we thought certain quantities were the same from reference frame to
reference frame. It turns out they're not, but other ones are. Finding
out which ones are the real ones that are the same has turned out to
be tremendously useful.

PD

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"PD" wrote in message
...
On Apr 3, 3:07 pm, wrote:
Is there an equivalence principle for space and time which states
something on the lines of it not being possible to tell if a change in
a measurable quantity is with respect to time or space purely from the
data?

It's not

Well done, Duck. It's not an egg for breakfast, either.