Hi Edgar, thanks for the reply. But do you agree or disagree with the point
that since different frames are considered equally valid and they define
simultaneity differently, either there would have to be no experimental
means to determine which frame's definition of simultaneity is correct (so
that the assumption of a true definition of simultaneity would be a purely
metaphysical postulate with no experimental significance), or else we would
have to discover new physics that violates the two postulates of special
relativity? If you disagree I think you are misunderstanding something
basic about relativity...on the other hand, if you agree, then which of
those two options are you arguing for?
Also, what do you think of my point that relativity already has a notion of
"time" separate from proper time, namely coordinate time, and that this
allows physicists to make sense of the notion that the two twins meet and
compare ages "simultaneously" even though their ages are different, without
requiring us to choose presentism over eternalism/block time?
Since the block time view treats time as analogous to a fourth spatial
dimension, a spatial analogy might come in handy here. If we have various
paths of some kind (roads, say) on a 2D surface, we have a notion of "path
length" between any two points along a given road, which could be measured
for example by a car driving along the road with its odometer running. This
is analogous to the "proper time" along a given worldline in relativity.
But we could also have a Cartesian coordinate grid on the surface, so that
any two points could be labeled with an x and a y coordinate. Then if we
have roads that start from the same point A, diverge, then reconverge at
some other point B (akin to the world-lines of the twins who depart at some
point A in spacetime and reunite at some other point B), we can assign x,y
coordinates to both the divergence point and the reconvergence point. If
one road was a straight line between A and B while another had some changes
in direction, we will see that the straight-line path always has the
shorter path length (analogous to the fact that the inertial twin always
has a *larger* elapsed proper time--the reason it's larger rather than
shorter is because path length for a straight segment of a path in
Euclidean space is calculated by sqrt[(change in x coordinate)^2 + (change
in y coordinate)^2], whereas proper time for an inertial segment of a path
in spacetime is calculated by sqrt[(change in t coordinate)^2 - (change in
position coordinates)^2]...the fact that you have a minus sign in the
square root rather than a plus sign turns out to imply that in spacetime, a
straight path between points is the *longest*, not the shortest). But
despite the fact that the two roads have different path lengths between A
and B, so that cars that started from A and took each road would reunite
with different odometer readings, the two cars do meet at the same x or y
coordinate (either one can be treated as analogous to the t-coordinate in
spacetime). Clearly this does not imply that other "earlier" parts of the
road have ceased to exist when the cars meet, they're just at a different
spatial position; and similarly a block time advocate can say that even
though the twins do meet at the same t-coordinate, this doesn't mean that
earlier segments of their worldline have ceased to exist as a presentist
would believe, they're just at a different "position" in spacetime than the
event of their meeting.
On Wed, Dec 25, 2013 at 2:59 PM, Edgar L. Owen <edgaro...@att.net> wrote:
> Good physics based post. Yes, Brian Greene mentions "everything travels
> through spacetime at the speed of light" in both his books but only in
> passing as a curiosity without recognizing its profound significance.
> Thanks for your link to your physicsforums post. The meaning of 'speed
> through time' is actually pretty clear as it's based on the universally
> accepted fundamental equation for 4-d spacetime in which the t variable has
> to be multiplied by c to make sense. That has to be accepted if we accept
> that spacetime is a single 4-dimensional structure which everyone agrees is
> fundamental to relativity theory. The equation for velocity through
> spacetime works the same way and has to be accepted for the same reason.
> Once you accept time as distance along a 4th dimension you have to accept
> velocity through time and all the math of relativity works fine and is
> consistent. I don't think there should be any reservations about this.
> The problem with all your other comments (which I agree with as I scanned
> them) is they refer to clock time, not the P-time of the present moment. Of
> course clock time t values vary in a number of ways, but the key insight is
> they always vary in the exact same present moment which is proved by the
> time traveling twins reuniting with different clock time t's but always in
> the exact same present moment.
> This proves there is a single common universal present moment in which all
> clock time variations occur. And as you infer proper time is the direct
> experience of P-time which is the same for all observers even as their
> clock times are running at different relativistic rates.
> On Tuesday, December 24, 2013 8:26:00 PM UTC-5, Edgar L. Owen wrote:
>> Liz states that "Special relativity shows that there is no such thing as
>> a "common present moment". but this is incorrect.
>> Actually special relativity shows exactly the opposite. In my book I
>> explain how this works. It is well known, though little understood, that
>> everything without exception continually travels through spacetime at the
>> speed of light according to its own comoving clock. I call this the STc
>> Principle. This is a well known consequence of special relativity but
>> actually as I point out in my book this is an even more fundamental
>> Principle than Special Relativity and Special Relativity is properly a
>> consequence of it and can be derived from it.
>> What the STc Principle says is that the total velocity through both space
>> and through time of everything without exception is = to the speed of
>> light. This is the reason that time slows on a clock moving with some
>> relative spatial velocity, as Special Relativity tells us.
>> It also demonstrates that the speed of light is properly understood as
>> the speed of TIME. That's what c really is. Light just happens to move
>> entirely in space according to its own comoving clock, therefore its entire
>> spacetime velocity is in space only.
>> Anyway it is precisely this STc Principle that puts both the arrow of
>> time and a privileged present moment on a firm physical basis. Why? Because
>> it requires that everything must be in one particular place in spacetime
>> (the present moment) and moving at the speed of light (the arrow of time).
>> So exactly contrary to your statement, it is precisely special
>> relativity, properly understood, that puts both the arrow of time and a
>> common present moment on a firm physical basis.
>> This insight simultaneously solves two of the big problems of the
>> philosophy of science, the source of the arrow of time, and the reason for
>> a common present moment, though no one seems to have recognized this prior
>> to my exposition in 1997 in my paper 'Spacetime and Consciousness'.
> You received this message because you are subscribed to the Google Groups
> "Everything List" group.
> To unsubscribe from this group and stop receiving emails from it, send an
> email to everything-list+unsubscr...@googlegroups.com.
> To post to this group, send email to email@example.com.
> Visit this group at http://groups.google.com/group/everything-list.
> For more options, visit https://groups.google.com/groups/opt_out.
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
To post to this group, send email to firstname.lastname@example.org.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/groups/opt_out.