On 9/8/2025 3:54 AM, Alan Grayson wrote:
On Sunday, September 7, 2025 at 10:35:55 PM UTC-6 Alan Grayson wrote:
On Sunday, September 7, 2025 at 10:30:32 PM UTC-6 Alan Grayson wrote:
On Sunday, September 7, 2025 at 10:25:04 PM UTC-6 Alan Grayson
wrote:
On Sunday, September 7, 2025 at 9:26:43 PM UTC-6 Brent
Meeker wrote:
On 9/7/2025 6:46 PM, Alan Grayson wrote:
On Sunday, September 7, 2025 at 7:36:32 PM UTC-6
Brent Meeker wrote:
On 9/7/2025 5:52 PM, Alan Grayson wrote:
On Sunday, September 7, 2025 at 2:29:11 PM UTC-6
Brent Meeker wrote:
On 9/7/2025 12:12 PM, Alan Grayson wrote:
*In reality, there surely IS acceleration,
even though it might not be necessary to
use it to solve the problem. Can the
traveling twin return without acceleration?
Of course not! AG*
Actually he can. All he has to do it
slingshot around a distant planet in order
to head back to Earth:
*
*
*But that's NOT how the TP is defined! AG *
What is this "defined"? It's not /*defined*/
anywhere.
*That's how it's described in almost any text one can
find. You have a private definition. AG*
It's just a thought experiment that was
paradoxical in Newtonian mechanics. Every version
I've shown you is paradoxical in Newtonian
mechanics /*in exactly the same way*/. If you'd
open you eyes and mind, you'd see that they give
an intuitive grasp on why they all give the same
answer in relativity and so resolve the same paradox
You may object that he accelerated in
turning around. */But general relativity
teaches us that force free motion in a
gravitational field is geodesic and there is
no acceleration./*
*So the traveling twin turns around without
acceleration? AG *
Read my last sentence above over again a few times.
Brent
*
*
*I did, initially. During the turnaround the motion
is NOT force free, which GR allows, and one can apply
the Equivalence Principle, and then time dilation. AG *
You seemed to have missed GR 101 where it is explained
that gravity is NOT a force.
Brent
*
*
*It's your way or the highway. Or shall we say a touch of
arrogance? Haven't you ever heard of the EP? Let me remind
you. Gravity is locally equivalent to acceleration, so
when the traveling twin accelerates, it's equivalent to
being in a gravity field, where clock rates are slower
compared to rest frames. Where did I use the word "force"?
AG *
*
*
*The traveler accelerates by applying a force, not by the
force being applied by the gravitational field. Do you get it
now? AG*
*
*
*How does the traveler do that; by firing a rocket attached to his
butt. Same way he left the stationary observer! GR allows the
traveler do that. AG *
*I see a problem with this GR scenario. If the traveler is partly
coasting on a geodesic path, his clock will be running faster than
than his stationary twin, so he will age at a greater rate. *
That's confused on several points. First, nobodies clock runs fast or
slow because he's coasting...in a straight line in flat space in this
problem. Second, the traveler and the stay home person each see the
other's clock as running slow.
Brent
*OTOH, during periods when a force is applied to accelerate (not by
any gravity field), his clock will slow down, compared to its rate
while he's in geodesic motion. So for the traveler to return to Earth
younger than his twin, his slower clock while accelerating, must be
large enough overall, to cause his clock to fall behind his stationary
twin. The traveler could apply a continous but changing acceleration,
say by traveling in a circle, but whether his clock will slow enough
to make him age less than his stationary twin I don't know. AG*
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