The Twins Paradox.
If one twin gets on a rocket it looks, from our perspective, that she flies away for a few hundred years at great speed.
But from her perspective, it looks as if we (and the other twin) fly away for a few hundred years at great speed.
If there are no preferred reference frames, how do we decide which position is "normal" and thus how do we calculate that one twin would age more?
You could have just read the first paragraph of Wikipedia for the answer Stripe:
"However, this scenario can be resolved within the standard framework of special relativity (because the twins are not equivalent; the space twin experienced additional, asymmetrical acceleration when switching direction to return home), and therefore is not a paradox in the sense of a logical contradiction." Cite
The supposed paradox is only generated when you do not count in different acceleration frames that one twin passes through. Thus both twins are not in inertial frames of reference.
This is why I was very careful to layout each statement as "inertial frame of reference." All inertial frames of reference are equivalent.
So the distinction is all about gravity and nothing to do with speed.
Smart guy.Einstein answered the question with the difference in gravity frames, yes.
Seems to me there's no difference. :idunno:But in general, we can answer the question with the accelerating twins frames not being inertial. The frames are not equal because one twin is accelerating (being non-inertial).
Yeah. Gravity affects clocks.Also, this is really just a comparison of clocks. We can do the same experiment with twin clocks rather than two people. The twin paradox is essentially the problem Bob originally presented.
Seems to me there's no difference. :idunno:
Yeah. Gravity affects clocks.
Rather than leave this sitting on my hard drive, I thought I'd post this updated version on TOL in case anyone wants another shot at it. -Bob Enyart
A Layman Questions Gravitational Time Dilation
* Einstein’s theory of General Relativity indicates that gravity influences time, in that time flows relatively more slowly in a stronger gravitational field as compared to time in a weaker field.
* Actual experiments and observations provide evidence for GR time dilation. For example, clocks at different Earth altitudes run at different rates, thus the mile high atomic clock in Colorado runs a few ticks faster per year than the one close to sea level in Greenwich, England.
* Most physicists and cosmologists accept GR time dilation, and thus, that time is relative to a particular frame of reference.
And in that context, when Googling “Gravitational Time Dilation” I get: Google 7 from AbsoluteAstronomy.com: “Gravitational time dilation is the slowing down of the passage of time anywhere in the gravitational field.” Google 11: “The short and sloppy versions say: "… ‘Time runs slower as you descend into the potential well of a uniform pseudo-force field.’” From Google 9: “The idea of relativity is to throw out the concept of us traveling through time inescapably, and accept time as just another dimension.”
Consider this exaggerated scenario to illustrate my opposition to time dilation, and then I’ll suggest a practical experiment that could test my conclusion.
Two atomic clocks have been running on Earth for billions of years, one at the base of Cheyenne Mountain, and the other at the summit, sitting inside of a well-maintained Chinook cargo helicopter. The clock on the peak has been running faster by a few nanoseconds per year, but over the eons, it has advanced to twenty-four hours ahead of the clock far below, and it’s readout, in year, month, day, hour, minute, second, and nanosecond, is just now turning over to indicate exactly twenty-four hours ahead of the other clock, on a Friday at exactly high noon. This illustrates Einstein’s prediction that time would run relatively slower at a stronger gravitational field, as exists at the bottom of the mountain (we can ignore gravitational anomalies in mountains). Thus, the clock at the mountaintop is now one-day ahead of the clock below. The clocks were installed to sit in virtual perfect longitudinal alignment (at 104-50-01.9000W), so that as the earth orbits the Sun, both clocks cross an imaginary vector from the Sun in unison. The operator of the clock below, who was hired because of his PhD in physics, has just begun reading today’s newspaper. The operator can read today’s paper, because they both exist at the same time. He is alive, and wanting and able to read, and today’s paper has been printed, and just delivered to his facility, and since they are both there, the operator and the paper, at the same time, he can read that paper. However, if he wanted to read tomorrow’s paper, he could not do it immediately, because tomorrow’s paper is twenty-four hours behind him in time. (Behind him is the correct direction. He is ahead of tomorrow paper. Like a NASCAR driver who finishes 24 seconds before another, our operator is here now, a full 24 hours before tomorrow’s paper hits the newsstands. Remember after all, the river of time flows backward, not forward -- from the future through the present into the past. Imagine something floating in that current, like next Christmas, which is in the future, drifting toward the present, but eventually will be remembered only in fading prints in family photo albums. But I digress…) Assuming that the newspaper’s production schedule remains constant with past performance, the operator will have to wait for twenty-four hours to pass before he can actually come into contact with tomorrow’s paper, or for that matter, with anything that is twenty-four hours into the future. Now, back to the clock on the peak. The operator has kept an eye on that clock from it’s installation until today (he’s now near retirement age), and with a telescope, he’s been able to watch the nanoseconds ticking more quickly than those of his clock. (Of course he realizes that with the limitation of the speed of light, he’s seeing the Summit hands move picoseconds after they actually do, and that does not confuse his understanding.) Being an educated man, he believes that time has been flowing faster for the clock above, and that is why the Summit Clock is twenty-four hours ahead of him and his clock.
Now, it seems to me that the operator is confused, and that physicists must actually be referring to some other effect when they say or imply that gravity actually affects time as compared to other frames of reference. The seventh site found by a web search on the topic, (Google 7), states: “Gravitational time dilation is the slowing down of the passage of time.” Seemingly implying that time flows at different rates for the two clocks. If that were literally true, then it seems the two clocks would exist in two different time frames, now separated by twenty-four hours, and the operator at the base shouldn’t even be able to see the clock at the summit, since it is 24 hours ahead of him in time. After all (Feynman and QED notwithstanding), this guy just can’t see that far into the future.
Now THE PLOT thickens! The helicopter (which has been maintained all these years at great taxpayer expense) suddenly transported the Summit Clock to the Base Clock, and the two clocks were set next to each other so that they actually touched! And the contact between the two clocks happened exactly ten minutes after noon on Friday according to the Summit Clock (rounding to the nearest whole second).
So, here is my question. What time would the Base Clock show at the moment that they made contact?
Calvinists, most physicists and evolutionary cosmologists would all answer that at the moment of contact, the Base Clock would read Thursday at 12:10 p.m. Well, even a broken clock is right twice a day. And for what I know of Relativity (not much) they all happen to be correct! Consider how this thought experiment refutes time dilation. Whenever physicists claim that GR proves that gravitational gradients affect time, they are wrong. They don’t. Gravity does not affect time: it affects clocks. And that is not the same thing. If gravity affects only clocks, and not actual time, then like tomorrow’s paper, the Summit Clock would not be one day into the actual future, as compared to the Base Clock; and if it were quickly transported down the mountain (where it would begin ticking off time at the same rate as the other clock), then the Summit Clock would continue to give readouts offset exactly twenty-four hours ahead of the Base Clock. (The brief trip down the mountain had a relatively negligible impact on its timekeeping.) However, if different gravitational gradients truly affected time, and the Summit Clock were truly one day ahead in time of the other, then the helicopter should not be able to bring them into contact after a mere ten minute trip! The duration of the flight was measured at 10 minutes by both clocks within less than a billionth of a second. (Having worked at McDonnell Douglas on the AH-64 Apache attack helicopter, I know a bit of about these machines, enough to state authoritatively that helicopters are not time machines.) If the Summit Clock truly experienced time faster than the Base Clock, then once the helicopter brought the clock to the base of the mountain, at that point, then another twenty-four hours would have to pass by before the operator at the base could even see the Summit Clock sitting there (after returning from lunch, behold, the clock cometh!). So the operator would have waited until Friday, at ten minutes after noon, before he could see the clock suddenly appear on the ground next to his Base Clock. But, that is not what would happen, is it? What actually would have happened is, having packed a sack lunch that day, he saw the clock at the same moment that it was being delivered. The Summit Clock and the Base Clock had been ticking at different rates for billions of years. Yet both had traveled around the Sun the exact same number of times. Both clocks saw the exact same number of sunrises and sunsets! However the Summit Clock’s readout suggested that it had seen one additional sunrise and sunset than had the Base Clock, which of course it had not. The Summit Clock and the Base Clock both revolve around the earth’s axis in the same solar day at the exact same longitude, so to interpret their readouts as measuring different length days is to be confused. Genesis says that God gave us the Sun (and other astronomic bodies) for “seasons, and for days and years.” It turns out that God gave mankind great timekeepers (and less misleading ones than our atomic clocks as interpreted by theorists)! The movements within our solar system give us a more correct understanding of the absolute nature of time than do the ticks of atomic clocks. So, whatever cosmologists are actually trying to say when they speak of time dilation, here is the truth. Gravity does not affect time. Gravity affects clocks.
In this scenario, as with the real world atomic clocks in Greenwich and Boulder (one across the Atlantic, and the other a few miles up Highway 93 from Denver Bible Church and our KGOV.com studio), both clocks exist in the exact same ultimate time reference, and always will, as long as they both shall tick. The false theory of epicycles did a better job of predicting the positions of the planets in the sky as compared to early Copernican calculations, yet epicycles were incorrect. Relativity’s time dilation does a great job of predicting the read out of an atomic clock at various altitudes and accelerations (experimentally, what, to within less than 1% of theoretical performance?) But that does not prove that time is relative. Rather, it proves that gravity affects clocks. Imagine if ancient Eskimos used a seal bladder to keep time, filling it up with water, and counting sixty drips for each minute. (Why sixty? Well, since the earth originally orbited the Sun in exactly 360 days, the ancients divided circles into 360 degrees, and a hexagonal system of time developed, with the day and night divided anciently into 12 hour segments, and measurements of time divided into convenient hexagonal units.) Anyway, occasionally a drunkard would wander by and squeeze the bladder, bringing a native physicist to suggest his theory of alcoholic time dilation! So, both the Eskimo clock and the atomic clock prove the same thing. When exposed to different gravitational gradients (and drunken tantrums), it is the various measuring instruments of time, like atomic clocks, seal bladders, GPS satellites, metabolism, etc., that are affected. A simple experiment is worth a thousand theories, albeit like Schrodinger's Cat, this one is a thought experiment. The Summit Clock and the Base Clock both go around the world in the same day with the exact same duration, so they cannot disagree on the length of a day or of an eon. If this Summit Clock experiment is valid, then we find out that the amateurs are wrong, and also, that the amateurs include a lot of professionals. And Calvinists too. For my interest in all this is theological. Biblically, I have been convinced that time is an eternal attribute of reality, and thus, of God’s existence, seen most easily in that He is relational. And many Calvinists and others teach that God is outside of time existing in an eternal now, and that He created time. So Calvinists commonly quote popular understandings of General Relativity’s time dilation as evidence for their claim that time is not absolute, and thus, God can exist outside of time. So, I have a vested interested in refuting that. Thus I argue that when folks say that time speeds up or slows down in different frames of reference, what they really mean is that stuff affects clocks.
My theological bias does not change the fact the Earth does not orbit the Sun at two different rates simultaneously. In this clock scenario, at exactly high noon on the Friday in question, the two clocks crossed an imaginary vector from the sun in exact unison, as they’ve done every day of the experiment, so they cannot show an actual difference between them in the duration of a day, since they themselves exactly mark the rotation and orbit of the earth, marking the passage of each day. They have been simultaneously crossing such vectors that mark out a single day, and they’ve simultaneously crosses such vectors seven times marking a week, and 365 times (or so) marking a year, and so on, marking out the centuries, millennia, and eons, in exact synchronicity, such that these clocks physically demonstrate zero difference in the length of a day or an eon for the two clocks. Thus, because adding zero plus zero billions of times will never accumulate to a 24-hour difference in time, the variant readouts of the clocks is only superficial, and does not indicate that time ran faster or slower in a different frame of reference, but rather, that gravity affects clocks.
And here is my suggested experiment: let’s hike to the top of 14,110-foot Pike’s Peak and enter the snack bar at the summit, grab the old round wall clock, the one that’s been up there so long that when removed it will leave a clean white circle on the wall. And then we’ll ride the train down to the base of the mountain in Manitou Springs, and rush the old ticking clock a few miles to the Clock Tower at the University of Colorado in Colorado Springs. And when we get there, we will touch the two together, and see if the space-time continuum ruptures, or anything like that.
-Pastor Bob Enyart.com
DenverBibleChurch.com & KGOV.com
(( If Time is “Absolute” )); - then the Time of the Lord’s coming is ( “Absolutely” ) Known, or can be Known “Absolutely”!! -- Or maybe very close??? – Pray Tell!! - What sign shall we watch for if there IS No Sign given???
Paul – 072213
(Hi Paul? (Have you ever ((programmed)) ((in) Lisp)? (Just curious. )))
Speaking of the great tribulation before his Second Coming, Jesus said that those days would be shortened, and Peter, who was there on the Mount of Olives when the Lord taught that, later wrote that believers could "hasten" the coming of the Lord. Our philosophically-based theological systems (like Calvinism and Arminianism, and unlike Open Theism, opentheism.org) that reject both of those teachings, and so their proponents look for ways to nullify them. But as with so much biblical material, as at rsr.org/time, when the scriptures do weigh in on the subject, at least on the surface, they never teach that God is outside of time, but rather, many times over, they show that He is in time.
Thanks for the question!
- Bob Enyart