On 9/11/2025 4:31 AM, Alan Grayson wrote:
On Wednesday, September 10, 2025 at 11:27:19 PM UTC-6 Brent Meeker wrote:
On 9/10/2025 6:41 PM, Alan Grayson wrote:
Every point in spacetime has a label, called cooordinates. So
every event happens at some label.
But the label is arbitrary. You draw a different map and give it
a different label. But it's the same event. It doesn't become
two different events because two different brought different
clocks to it.
If not that, then what? I see this in those spacetime diagrams.
If their clocks disagree at the reunion, how do you define "the
event"? AG
It's the event of Red and Blue meeting again.
Brent
*You have both accelerating in one of your diagrams, which is NOT how
the TP is described, while also claiming there is no acceleration in
explaining the TP. Is it any wonder that your presentation is
unintelligible? *
Unintelligble to those who can't grasp that the same phenomenon can have
multiple realiations. I claim that acceleration is not necessary to the
TP and I have shown two versions in which there is no acceleration and
one version in which both twin accelerate the same; yet all three
versions produce the same "paradox" Now what do you make of that? For
your convenience I repeat them here.
Real experts in relativity theory don’t find the Twin's Paradox
fascinating or even interesting to discuss. But I sometimes see other
physicists say misleading things that imply that it’s all about inertial
v. non-inertial motion, i.e. acceleration. This is fine for the
simplistic story of the one twin who stays on Earth, the inertial twin,
and the non-inertial twin who travels far and returns at relativistic
speeds. And remember the twins are just for dramatic effect. We're
really talking about ideal clocks carried along the two paths. Clocks
immune to the stress of space travel. Here’s the simple version:
And sometimes even physicists point to that turn-around at 2011 and say
“It’s the acceleration there that makes the difference.” Well, sort of.
If he’d just coasted inertially he wouldn’t have turned around and come
back…or would he. In fact acceleration is just incidental. I some
versions it's responsible for one path being longer than the other, but
it's the path length difference that's essential, not how it's realized.
This is illustrated in the slingshot version.
Suppose there’s a neutron star out there and our traveler just swings
around it, using Its gravity, but no rocket thrust at all. Notice that
the time in the gravitational field of the neutron star can be neglible
compared to the travel time, so corrections due to gravitational time
dilation can be ignored. The swing around the neutron star is entirely
free-fall, zero acceleration in the general relativistic sense, no
applied force.
But what about accelerating away from Earth and braking to a stop on
return. Not necessary: I've shown Red flying by Earth on his way to the
neutron star where he gets flung around by its gravity and flies by
Earth going the other way. As he passes Earth outbound, he sets his
clock to Earth time and as he passes Earth on the return he and Earth
compare clocks and find the Twin Paradox is the same, a 2yr
timedifference. So it’s not being non-inertial. It’s not some
acceleration induced stress on the clock. Another way to see the same
thing is The Triplet Paradox.
In the Triplet Paradox Red, with his clock, heads out setting his clock
to equal Earth's as he passes. Four years later (ship's time) he passes
Blue who is inbound. As they pass Blue sets his clock to match Red's,
i.e. to 2011. Then when Blue passes Earth he compares to Earth's clock
and finds exactly the same “paradoxical” disagreement.
The Triplet Paradox completely avoids even a change in direction. Proper
time is just measured along three different inertial segments between
the same two events.
And what if there’s acceleration, but each twin experiences exactly the
same acceleration? Just not with the same intervals between them. In
this case Red and Blue are coasting along together. We might suppose
they are approaching Earth and Blue decides to stop there, but whether
some planet is there or not, Blue fires his rockets and stops, while Red
coasts on. But then years later, Red fires his rockets first to stop and
then immediately after to go back. As he is reaching Blue, who has been
stationary all this time, Blue fires his rockets and once again matches
speed coasting along with Red. But their clocks register the same
difference as in the other versions...even though each one experienced
the same accelerations for the same durations.
By now you should be convinced that acceleration, per se, has nothing to
do with the “paradox”. It’s just a matter of different paths between the
same two events having different “lengths”, i.e. different intervals of
proper time. So how should you looks at it? It’s (almost) the same as
two cars who are driven from NYC to L.A. Blue takes a fairly direct
route, while Red decides to visit the Alamo in San Antonio.
Their odometers measure the distance, not the as-the-crow-flies
distance, but the proper distance along their paths. Is there any
paradox that they measure different distances? No, they are just spatial
versions of clocks. The tricky thing is that we have to distinguish
between coordinate time (which are just labels) and proper time (which
are physical measures). Einstein showed that spacetime has a /minus
sign/ in the metric, so /more distance subtracts/ from the proper time.
That’s why the twin who travels the greater spatial distance experiences
less proper time distance. It has nothing to do with acceleration or
not. Usually the inertial path (least spatial distance) is the longest
proper time distance. The exceptions come when gravity bends spacetime
and our mapping doesn’t take account of how it changes spacetime
distances so that they don’t agree with naive space distances.
The misleading thing you will hear even from physicists (I’ve said it
myself) is that time runs more slowly in a gravitational field. This is
given as the explanation of Shapiro delay. But in the analogy above this
is like saying odometers run fast near San Antonio. The right way to
look at it is the clocks are ideal and there is /just less time along a
geodesic path thru a gravitational field/. And paths are even shorter if
you’re standing on a planet’s surface, because in that case your path
isn’t geodesic. The force on the bottom of your feet is pushing you off
the geodesic.
*Moreover, in light cone diagrams, the labeled spacetime coordinates
are referred to as "events" which are, or not, causally connected. So
if I am confused, I suppose I should blame the "experts". AG *
You are. Events are labelled by spacetime coordinates, not the other
way around.
Brent
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