On Monday, September 8, 2025 at 5:59:04 PM UTC-6 Brent Meeker wrote:
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. *Wrong. In flat space there is no gravity, and a clock coasting in flat space runs faster than the clock residing on the Earth in its gravity field. The gravity field in GR slows the clock rate compared to an observer in free fall -- one of the effects on GPS clocks. AG* Second, the traveler and the stay home person each see the other's clock as running slow. *Yes, that's the paradox, and it's not caused by assuming absolute simultaneity (as I think the video recommended by Clark alleges, which I have not yet viewed), but the erroneous assumption that the twins are in symmetric situations. One twin accelerates and the other does NOT. AG* 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* -- 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 [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/28b74bd3-37bb-4b15-96aa-c3a36fa19a61n%40googlegroups.com.
