Does acceleration solve the twin paradox?
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- čas přidán 8. 05. 2024
- Special relativity is known to make mind-blowing predictions, perhaps most notably the Twin Paradox, in which two individuals claim that the other person’s clock is doing something funny. There have been many explanations, including two videos, one here on the Fermilab channel and one by fellow CZcamsr Sabine Hossenfelder. These two videos seem to contradict each other, but they really don’t. In this video, Fermilab’s Dr. Don Lincoln explains how the two videos can be reconciled.
Sabine’s video
• Special Relativity: Th...
Don’s first twin paradox video (with math)
• Twin paradox: the real...
Don’s second twin paradox video (without math)
• Twin paradox: the real...
Fermilab physics 101:
www.fnal.gov/pub/science/part...
Fermilab home page:
fnal.gov - Věda a technologie
This is a very elegant explanation. "Change in frame = acceleration" that's a great way to look at it. With this simple concept, you resolved the discrepancy between your and Sabine's analysis. Thanks!
Reviewing concepts using multiple perspectives creates much deeper understanding. We're reconciling how different people present information and that's really helpful for very unintuitive topics.
The wavelength of light increases while traveling because light experience time. Albert Einstein didn't care about what light experiences. Wave symmetry is changing relative to their speeds, and it doesn't change the absolute time they experience. Believing in Einstein's relative time is like believing in the creator God. Both of them don't exist in reality.
No it's not elegant. He did say that acceleration *was not* the main key while stating that "change of ref. frame is the key". I got that answer a lot myself when I pointed out that it was the same and usually people respond with vague, dishonest, arguments like "you don't understand it" or "you have to do the entire math behind it".
He's just another fine example of everything that goes wrong in modern physics, no understanding but a lot of hypocrisy.
But there was no discrepancy between both explenations if you would listen to Don in this video. Understanding the topic to its very core would leave you without "discrepancy" after watching both videos. It is only ones lack of understanding that creates "discrepancy".
@@smlanka4u You are wrong. The wavelength increasing with time isn't a factor of the time that light experiences but the warping of the spacetime in which the light inhabits. Light redshifts over greater distances because of the expansion of the space which the light inhabits. You can get the same effect at the event horizon of a black hole due to the gravitational warping of around the horizon.
Very cool sir; you are, once again, a truly fine physics teacher. Thanks for letting us tag along on the journey. May you and Sabine live long, prosper & continue to inspire!
Love both your and Sabine's channels! My mind *needs* stimulation! LOL Thanks for the video!
Thank you Don! I got in a lot of arguments over the twin paradox and always referred my opponents to your excellent video on the subject where you model the same scenario with 3 reference frames.
Equivalence, similarity = DUALITY!
Time dilation is dual to length contraction -- Einstein.
DUALITY (Isomorphism):- two equivalent descriptions of the same thing or state -- Leonard Susskind, physicist.
The twin paradox is duality.
"Always two there are" -- Yoda.
Antinomy (duality) is two truths that contradict each other -- Immanuel Kant.
It took me way too long to understand the twin paradox and I have to say that the biggest cause of this delay was from science educators trying to avoid the math, using metaphors, simplifications, etc. As soon as I understood the Minkowski metric, things fell into place. Suddenly this whole debate about acceleration being the cause of time dilation or not seemed to be missing the point. The key detail of the twin paradox is that the two twins end up in the same reference frame but one of them travels through multiple reference frames (at least 2, assuming infinite acceleration at the turn around). But I think this is much easier to understand if we go one step further and assume that the two observers start at the same event and end at the same event (same point in spacetime), which is implied by the usual setup of the twin paradox. So we have two worldlines (paths in spacetime) which start in the same place and end in the same place, but one of them is a straight line and the other is not. Then you just need to account for the Minkowski metric and you see that the shortest (straight line) path between two events is actually the one with the longest proper time, any other path experiences less time. I realise this is a bit more involved but I think with some nice graphics and a slightly friendlier explanation it would help a lot of people get their heads around it. I don't think you can really appreciate what's happening without understanding the way distances (proper times) are calculated in spacetime.
The total spacetime between two spacetime points is equal for all paths. Only question is size spacial component and temporal component.
@@gravitationalvelocity1905 Yes, but the point is about the difference in total percieved proper time for both twins, not difference between time component of spacetime vector from event of departure to event of meeting. In the latter case the 2 time components are equal in every reference frame, because they are the same component of the same vector. In the former though, the sum of experienced times wrt proper frames of reference for each segment of the path is considered (these segments may be infinitesimal in case of finite acceleration, which leads to integral, or there may be finite number of them, e.g. two as in the version of experiment with separate traveller in the opposite direction).
If acceleration does not matter, there is no way to make any difference between the two twins, it is as simple as that. Don explications are incorrect and could be reversed to the other twin. The only correct interpretation is provided by Sabina.
Beside the last video on the channel about traversable wormhole and the bunch of irrealistic speculations it contains (aside a ridiculous confusion beween decrease of energy and negative energy), cast a lot of doubts on the relevance of the science developed in some institutions.
@@gravitationalvelocity1905 What do you mean by "total spacetime"? The spacetime interval between two events depends on the path along which you measure it.
The answer to the Twin Paradox in special relativity is that the twin scenario exceeds the limits of the theory of special relativity, just as high velocity or strong gravitational fields exceed the limits of classical mechanics.
I love when content creators respond to challenges to their videos raised by other creators. I especially love it when they're both held in such high esteem. Thank you for addressing the apparent tension between these two entries, it had been bothering me.
Don's explanation is non-physical. If you reduce the acceleration period to zero, you get an infinite acceleration, and the turn-around point is a singularity in general relativity.
Different explanations have been going on between physicists on this since Paul Langevin brought it up in 1911 and Hermann Weyl specifically mentioned twins in 1922 ( yes over 100 years back ! ). Far longer than CZcams was around ...
Langevin used the acceleration explanation as did Weyl, but later Lord Halsbury and others introduced the 3 brother technique to eliminate the acceleration. Since then both acceleration and non acceleration explanations have been classed as dynamic and kinematic explanations respectively.
It could be argued that the Twin example, as actually stated, is better explained by the dynamic interpretation. However it can also be argued that the kinematic argument gives a more comprehensive answer as acceleration is not needed, as stated by Fermi labs.
The problem is that the Twins Pardox is not a very good example to show what it was designed to show, that biological forms suffer time dilations, not just clocks. It's not very good because the example uses a ship accelerating and turning around, when it was meant to show time dilation due to Special relativity which is uniform translations and therefore uniform velocities.
As L.Benguigui
wrote though:-
"I am sure that the twin paradox will provoke again and again papers since it is not a problem to solve but it is in itself a social and psychological phenomenon. There is no end."
Especially it seems in the comment sections of youtube videos ...
Ironically nowadays we don't need a thought experiment to show constant velocity shows time dilation. We can measure cosmic rays, GPS signals, atomic clocks, particle collider collisions etc to show the Einstein was correct with special relativity. All of these have a time dilation component that does not require acceleration relative to the observer.
Now, do the math of PHYSICS instead of elaborating with abstract frames, individual observers who "perceive" something etc. And you will experience a revelation. And, you can not use "cosmic magical hands" when creating thought experiments, which is supposing that other objects "come flying" (without acceleration) and involve them in the thought experiment.
Time is a physical phenomenon which has its root in the rate of change in subatomic particles in the atoms. Einstein didn't know that 1905. We now, for example, measure time as a certain change in Cesium atoms.
1. The Newtonian equation V^2 = 2 • a • s says that the result of an acceleration, a certain distance, is V^2. That is the exact same V^2 which is in the time dilation equation in SR. It means that all physical (real) time dilation occurs during the acceleration phase, while the acceleration force CREATES the velocity. There is no continuous physical time dilation taking place after that (moving inertially), which is perfectly logical, because after acceleration/deceleration phases relative movement comes into play again (as before the acceleration phase).
2. Replace the V^2 is in the SR time dilation equation with 2 • a • s.
3. Take a look at the gravitational time dilation equation. No one, except airheads, deny that it physically calculates the time dilation of, for example, a clock on the earth ground compared with a place in space with hypothetically zero gravitation. Without any observers "perceiving" things, from this and that perspective etc.
It is a truly objective physical phenomenon.
4. And now, take a look at the equation for escape velocity, V^2 = (2 • G • M) / s , and replace (2 • G • M) / s in the gravitational time dilation equation with V^2.
5. It has now been shown/proven that only acceleration must be the cause (not relative velocity) of time dilation concerning movement of objects. Because the two time dilation equations are the SAME EQUATION, expressed with different variables in their original form. And what does that mean ? It manifests Einsteins equivalence principle mathematically, that an atom is affected in exactly the same way being in a gravitational field, as being accelerated with the same acceleration outside of a gravitational field. And therefore, there doesn't exist, mathematically, any physical time dilation after an acceleration phase has ended for an object, creating a relative movement between two objects.
End of story. If the equivalence principle and the time dilation equations are true, which they "have to" be (otherwise the whole house falls down), then nothing but acceleration/deceleration creates physical time dilation.
Special theory of relativity, without any acceleration histories of objects, ONLY has observational time change effects, due to changing distances between objects. Then both observers can say that "I perceive/see that your clock runs slow". But that has nothing to do with physical time changes (time dilation). That is what Einstein meant, even though it seems that he was doubtful after Hermann Minkowski had introduced the spacetime diagrams (which represent a false continuous velocity based time dilation). Remember what Einstein said: "after mathematicians have invaded my theory, I don't seem to understand it myself".
Don (and many others) is hopelessly lost here, I hope he can change his view and come to his senses. And I am not sure that Sabine has the correct view on this. And they may both be trying to protect, what they think Einstein meant.
Then the question ofc arises, WHY are subatomic processes in atoms slowed down while being stationary in a gravitational field, or the equivalent situation, mechanically being accelerated outside of gravitational fields ? No one knows yet, but the best explanation so far imo is the River model. watch?v=hFlzQvAyH7g
@@zakelwe "Ironically nowadays we don't need a thought experiment to show constant velocity shows time dilation. We can measure cosmic rays, GPS signals, atomic clocks, particle collider collisions etc to show the Einstein was correct with special relativity. All of these have a time dilation component that does not require acceleration relative to the observer."
All objects moving in a circle/orbit experience centripetal acceleration, all objects falling through the atmosphere (muons) experience deceleration, etc. There is no case, without a form of acceleration involved, which has proven to create time dilation .
@@Music_Creativity_Sciencedo the same experiment where the travel twin goes around the universe then comes back to earth. He doesn’t need to stop, only records time when he passes by. That way you see how acceleration is also relative and not as fundamental as frame of references
I like the "no acceleration" gedanken experiment you describe in your earlier video. Another way of showing that the time dilation does not occur specifically in the acceleration phases of the trip is to use a set of triplets. Leave number one on earth, accelerate number two toward the distant star, but as soon as you've reached cruising speed, turn her around and send her back to earth, and send number three on the entire trip to the star and back. You can make the accelerations experienced by two and three identical. When all three are back together again in one's rest frame, two will have aged less than one, but three will have aged less than either, showing definitively that the time dilation occurred during the entirety of the trip, including during the non-accelerated "cruise" phases. Just as in your experiment, it is the motion that matters, not the acceleration.
change of inertia stays after acceleration. it is all about forces/energy.
Equivalence, similarity = DUALITY!
Time dilation is dual to length contraction -- Einstein.
DUALITY (Isomorphism):- two equivalent descriptions of the same thing or state -- Leonard Susskind, physicist.
The twin paradox is duality.
"Always two there are" -- Yoda.
Antinomy (duality) is two truths that contradict each other -- Immanuel Kant.
"Acceleration - acceleration - pause" is a different experience than "acceleration - pause - acceleration", so they're not equivalent.
I don't like "switching frame of reference" explanation because "frame of reference" concept is not physical. It's not a thing you _experience_, it's just a label you put on things. Unlike acceleration, which you experience (and can measure). Physical theory is meaningful as long as it ties measurable things (proper acceleration) to other measurable things (proper time). All the mathematical shenanigans in between are for convenience only.
I love this channel and prof.Don sir’s explanation
So amusing,it’s been 3 years since I’m watching his videos…
This video was necessary. Thanks for clearing the doubt, sir. 😊
Love both your channel and Sabines, thank you Don!
You make complex things look simple! Brilliant!
Definitely think yours is clearer! Showing each object as being in a separate frame of reference makes a lot of sense.
Being a huge fan of both you and Sabine... I'm so happy that you were both right - Keep producing these amazing videos
er, Don says Sabine got it wrong, because an object does not need to accelerate to slow time down. It just needs to be moving faster than other object it is measured against .
No, he says there are two ways of explaining the phenomenon and that Sabine used one way and he used the other.
I really liked what you said about how two people can say things that appear to be in conflict, but aren't. I have no idea how many times people have thought that I was disagreeing with them, when in fact I was offering my own perspective on why I thought they were right. But it has gotten pretty frustrating.
the struggle is real
Equivalence, similarity = DUALITY!
Time dilation is dual to length contraction -- Einstein.
DUALITY (Isomorphism):- two equivalent descriptions of the same thing or state -- Leonard Susskind, physicist.
The twin paradox is duality.
"Always two there are" -- Yoda.
Antinomy (duality) is two truths that contradict each other -- Immanuel Kant.
I know that feeling!
Oh man I love seeing dialogue between science educators like this. Doesn't matter to me if someone was wrong or someone had a better or worse way to explain things. Discussions like this only help me understand complex subjects better.
You are only talking about Special Relativity. In General Relativity, a single non-inertial reference frame is allowed for the spaceship’s entire journey. The person in the spaceship can believe that he is standing still by believing that there is a gravitational field present throughout all of space, and that gravitational time dilation is what causes him to be older than his twin.
There's another explanation I found in the book "Philosophy of physics". It's just as simple as:
Time passed for an observer is just length of his world line in Minkovski metric. And if you calculate, you'll see that observer in the rocket has shorter world line.
I like that explanation, but it's really the same thing as Don's when you think about it. I didn't bother watching the video of Don's without the math, but the one where he goes through the Lorentz transforms from the 3 observer's points of view essentially describes a shorter time line for the rocket.
Equivalence, similarity = DUALITY!
Time dilation is dual to length contraction -- Einstein.
DUALITY (Isomorphism):- two equivalent descriptions of the same thing or state -- Leonard Susskind, physicist.
The twin paradox is duality.
"Always two there are" -- Yoda.
Antinomy (duality) is two truths that contradict each other -- Immanuel Kant.
@@jd9119 of course it's the same. The same theory underneath
Great video! I like the illustration of the twins, but, the thought of two Don’s and double the dad jokes is a little frightening 😊
Thanks! Cool that professional scientists record these lectures videos. Be advised, Dr Greene has recorded a free course of special relativity for anyone interested in. In long math version of that course one can calculate this paradox thing. And after that it's not paradox at all. Hope Dr Lincoln records a math version of his own some day or writes it on Fermilab Physics 101 page.
with a total nonsense about Twin Paradox!
Regarding Fermilab, Dr Lincoln has already made the math video mentioned on the description. In addition to that in Fermilab archives there is a downloadable pdf-document "Lecture notes/Barletta, Spentzouris, Harms: Review of formulas for relativistic motion".
@@jkinkamo start to reason by yourself if u are not an ape, but probably you are such.I know Dr.Lincoln Junk@put my comment there fortunately not deleted on the absurdity of 3-travelers argument as the same fiction like with that of "acceleration". ps. do you (Dr.LLincoln) know the 1st Relativity Principle(2nd is just a supplement to the first one, then use your non-ape mind to get a perfect conclusion!
Lorentz gamma factor is the key, and Dr Lincoln of Fermilab has recorded a math video on that. Dr Greene on his WSU course (strongly recommended math version of his Special Relativity) presents the same fact in very detailed manner. Everyone could calculate this paradox thing in order to prove its validity.
Thanks. I found your explanation much more enlightening, Adding acceleration makes a nice story with twins, but the clocks are much simpler to understand. Or at least to have a feeling of understanding. Good luck with some comments of FB physicists 🙂
Equivalence, similarity = DUALITY!
Time dilation is dual to length contraction -- Einstein.
DUALITY (Isomorphism):- two equivalent descriptions of the same thing or state -- Leonard Susskind, physicist.
The twin paradox is duality.
"Always two there are" -- Yoda.
Antinomy (duality) is two truths that contradict each other -- Immanuel Kant.
You have a feeling of understanding. That's all.
One way to show why acceleration itself doesn't explain the paradox is the use of two similar experiments, where we let the twin travel twice the distance, but still using the same acceleration.
In that case, the effect will approximately double. And so it can't be explained by the acceleration as we used the same acceleration.
Great explanation, thanks for this Dr. Don. As I follow (and love) both your and Sabine's channel, it's a relief that you both are right.
Also, many many thanks for your high quality content, it's incredibly valuable for a curious and interested layman to find such excellent videos on CZcams 💛
This whole twin paradox issue continues to be a really embarrassing topic for the entire physics community. I recommend that both Don and Sabine stop making twin paradox videos until they actually educate themselves on what Einstein stated in his own theory.
To start with, Sabine was critical of anyone who thinks that: "Einstein’s special relativity can only deal with constant velocity and to deal with acceleration, you need general relativity." She goes on to say: "You don’t need general relativity or gravity to solve the twin paradox." With this statement, it is clear to me that she doesn't understand the difference between a mathematical method used to arrive at a certain result and Einstein’s actual physical explanation for what is happening during the twin paradox.
In step 3 of Einstein's own 1918 twin paradox paper he states: "A homogenous gravitational field appears, that is directed towards the positive x-axis. Clock U1 is accelerated in the direction of the positive x-axis until it has reached the velocity v, then the gravitational field disappears again. An external force, acting upon U2 in the negative direction of the x-axis prevents U2 from being set in motion by the gravitational field."
Now we all know that turning around in a spaceship is actually not real gravity but there is a reason Einstein chose his words carefully in that description. It is because all of the work he published in 1905, 1911 along with GR in 1915/1916 led him to the understanding that time dilation experienced between 2 observers with different relative velocities is not the same as time dilation experienced between 2 observers in different positions in a gravitational field or in different positions of an accelerating system. That's because Einstein understood that the entirety of his theory implied that relative velocity would produce a reciprocal effect (each would see the other's clock running slower at the same time) but 2 observers in varying positions of gravity field or accelerating system would not see a reciprocal effect and instead see an equal but opposite effect (Lower clock sees higher clock running faster while higher clock sees lower clock running slower).
This in fact was the entire premise behind his 1918 twin paradox resolution. It acknowledged the strange reciprocal effect during the inertial portion of the trip, but was able to break the symmetry - not with fantastic spacetime diagrams or magical "changing frames" in mid-journey, but with an application of a time dilation effect outside of the confines of special relativity. This is because staying within the confines of special relativity during the acceleration phases correctly documents the instantaneous rate of velocity changes and (therefore the instantaneous velocity differences at any given point) but it would just observe more reciprocal time dilation added to the reciprocal time dilation already experienced during inertial velocity.
Nobel Prize winning physicist Max Born understood this very well and performed a step-by-step mathematical treatment of this in his book "Einstein's Theory of Relativity" originally published in 1922. He concludes his mathematical treatment by saying: "Thus the clock paradox is due to a false application of the special theory of relativity, namely to a case in which the methods of the general theory should be applied."
Don, on the other hand makes the assertion that the crucial thing is that the Earth clock sits in one frame while the rocket clock exists in two frames - and that is what breaks the apparent paradox.
Don also states that: In the “classic” twin paradox, the only way for a single twin to inhabit two frames is to accelerate. He then argues that he and Sabine are really saying the same thing and therefore are both correct because in the end they are each using separate methods to achieve the ever-important frame change for the rocket. That’s all very nice but if they are doing all of this in the name of preserving “Einstein’s Relativity” they should know that both of their explanations have nothing to do with what Einstein required to resolve the paradox.
I have my own separate issues with Einstein’s resolution, that I won’t get into here, but I will say that at least Einstein was smart enough to understand that a “frame” is not a physical object, nor is it an absolute thing of any kind. It is a non-physical tool used to provide reference when describing or assigning motion to a coordinate system, which could then be compared to other coordinate systems that either have the same (or different) velocities compared to the first coordinate system.
In Einstein’s step-by-step explanation, his Earth twin resided in the K frame for the entire twin paradox journey. And the traveling twin resided in the K’ frame for the entire journey. With this, Einstein could show what each twin experienced and observed from their perspective frames.
Toward the end, Don goes on to say: “All of the explanations that invoke general relativity or gravity are all incorrect.” And a moment later he says: “Once again, Einstein rules.”
So Einstein’s own theory, in Einstein’s own words, uses general relativity to resolve the paradox. Don, on the other hand says that using general relativity is incorrect but goes on to say “Einstein rules.“
Unbelievable. I would say, this is so farcical that you can’t make this stuff up - but apparently many people can, and continue to get away with it on a daily basis.
@@chriskennedy2846 Sounds to me that the discussion about the twin paradox is clearly not settled. I'll have a look at your videos and also watch again minutephysics' series of relativity videos and try to dive deeper into it 🧐
Equivalence, similarity = DUALITY!
Time dilation is dual to length contraction -- Einstein.
DUALITY (Isomorphism):- two equivalent descriptions of the same thing or state -- Leonard Susskind, physicist.
The twin paradox is duality.
"Always two there are" -- Yoda.
Antinomy (duality) is two truths that contradict each other -- Immanuel Kant.
@@chriskennedy2846 Thanks for posting this. Don's "explanation" has been pissing me off to no end. It's truly pathetic how obviously wrong it is to anyone who understands special relativity.
@@chriskennedy2846 Yeah --- even given the fact that linguistic confusion often times plays a large part in scientists INABILITY to explain complex mathematical concepts to ordinary people who don't have advanced math backgrounds --- I don't understand why Don here would flippantly say GENERAL RELATIVITY has nothing to do with why "the twin on earth" is so much older than the "twin on a rocket traveling" in good fractions of the speed of light (upon the latter's returning to earth some years later).
Special Relativity (EMC2) is the aspect of Einstein's work that DOES NOT have any thing to do with why that paradox could be the case...
For this paradox to be fully appreciated .... imagine you're the TWIN left on Earth; your other TWIN's the one traveling AT THE SPEED of light.
In that case, your TWIN's aging is AS STATISTICALLY INSIGNIFICANT as the aging of the PHOTONS that left those early galaxies some 13.5B years ago... photons that have just been received by the JAMES WEBB SPACE TELESCOPE the last few months.
Naturally, if your TWIN's has embarked on such a tour around the visible universe, at the speed of light... when she returned, not only you but Earth and the Sun, too, will have died... with the sun going off is main sequence in fusion activities.
Why?
Because, according to GR --- not according to special relativity --- the MORE EXTREME a CURVATURE OF SPACE-TIME you're subjected to (and still live, of course), the FASTER time passes for you.
Logically, then, traveling AT the speed of light means no time has passed for you (you haven't gone through hard, eternities... even if you've traveled from a place & time 13.5B years ago/away & having just arrived on Earth, today)...
In a pop culture colloquialism, if you're traveling at the speed of light, you're in a "time bubble." At that speed, the harshness & cruelty of TIME don't apply to you (nor photons).
The two pop culture mediums that explored this "time bubble" thing, that just popped into my head, are the children's book TUCK EVERLASTING a small movie titled TIME TRAP.
In TIME TRAP, the students --- who were looking for their lost professor ---- were trapped in a cave. They could see strange lights blinking above them, through a small hole/shaft that lead to the outside... but the shaft was not big enough for them to easily climb through...
Once, after some great effort, they're able to make it out of the cave, they were puzzled by a landscape so different from the one they knew only a few days previously, when they first entered the Cave...
After some shock, they came to the conclusion that those "blinking lights" which they saw through that shaft, while trapped in that cave... had been endless sun rises over MILLIONS of years!
Again, if you WERE TRAVELING at the speed of light.... you're "experiencing" an EXTREMELY DISTORTED SPACE-TIME environment (i.e., you're existing in a "time bubble") ...
Back to reality.....
GR, therefore, is the Einstein theory that GPS, your iPhone, speed differentials, and other such technologies & ideas deal with.... not special relativity.
Why do we SYNCHRONIZE the clocks on our devices & the clocks in the satellites hundreds of miles above the surface of the earth, or those on the JWST, a million miles away from earth?
Because, according to GR, the surface of the Earth is MUCH CLOSER to a massively DISTORTED SPACE-TIME REGION, so clocks down "here" on the surface of Earth are moving slightly SLOWER.
The CONFUSION arises from a misunderstanding that people have over "slower" and "faster" clocks: "time passing slowly" for you (the Twin on earth) just means you are SUBJECTED to the harshness & cruelty of every nanosecond of time, of every sun set & every sun rise...
Your Twin, who's in a time-bubble zipping across the cosmos at the speed of light... she's operating on a different set of circumstances & conditions... For her, as it is for A PHOTON (traveling around 186,000 miles per second) .... the passage of 13.5 BILLION YEARS (in space and in time) is just a moment ago (at the very most)...
This, again, is in the domain of GENERAL RELATIVITY, not that of Special Relativity.
I'm so glad this video exists. Before this, I didn't understand either explanation.
I still don't, but now I also don't understand how they can be compatible, and I've always been partial to the Rule of Threes.
awesome, as always
The only way to truly comprehend the "paradox" is to calculate the proper times of the two spacetime paths in terms of Minkowski metric. That is, the solution is a mathematical calculation.
I wouldn't say the only way -- but it's certainly a fine way.
@@onehitpick9758 There are dozens of variations of the Twin Paradox, and this calculation is ultimately how to find the answer for all of them.
But can we really say that its the rocket that inhabits two frames (without thinking about the acceleration)? I can see that everyone agrees that there are 3 frames, but couldn't you name them also as "stationary rocket", "the outgoing earth" and "incoming earth"? This paradox would be easier to understand by imagining two rockets in an empty space. The other one goes high speed in one direction and comes back. We can see that there are three different reference frames but the only way to decide which rocket experiences two frames is by an experiment that demonstrates the acceleration of the moving rocket. So the acceleration really is the thing that breaks the symmetry and it plays a key part in solving this paradox.
Correct me if I’m wrong.
Without acceleration there is no way to tell if instead of the rocket turning around, the earth started to move towards the rocket at twice the rocket’s speed.
One of frames changed but we don’t really know which one.
Not without acceleration.
Don's previous video on this topic (which started this whole argument) uses three inertial observers, who were already in constant motion before the experiment started. I'm not going to summarize it here (just watch that video), but I will suggest that you go through the setup with four observers rather than three. It will make things much clearer. Have two observers "at rest" relative to each other, located at the "Earth" and "Turn Around Location". And the third observer moving left at a constant velocity, and the fourth observer moving right at the same constant velocity. (So, v and -v from the reference frame of the first two observers.)
There are three factors to consider for how each observer measures the current time:
1. Trying to synchronize all of the clocks to the same start time.
2. Kinematic time dilation --- this is the part that is confusing people
3. The doppler shift if each observer is looking at the others --- not really relevant to the "paradox"
It's the kinematic time dilation part which makes the twins experience different proper time... but you can also get the same result from switching between the clocks at the "Earth" location and "Turn Around" location.
@@bogdanieczezbyszka6538 Yeah, thats what I think.
In order to have three reference frames with only two observers, one of them must accelerate (to switch from one reference frame to another), and everyone will agree which one. If you have three observers, no acceleration is necessary, because you can have one reference frame per observer.
Yes, you could define 3 frames that way, but they would not be inertial frames. In the "stationary rocket" frame, the speed of light is not constant. The speed of light in only constant in inertial reference frames, which is the whole point of defining 3 inertial frames for the twins scenario. Also note that in the "stationary rocket" frame, earth's velocity exceeds the standard speed of light during acceleration, resulting in earth's clock running much faster than the ship's clock in that frame.
Always the most awesome opening and closing cards!
Don, Well said. You are correct! Your explanation is scientificaly robust and 100% correct. Another area which causes much confusion amongst physicists is the subject of relativistic mass. There is only one (invariant) mass which you have correctly pointed out in another video.
A point I used in a comment on the Sabine video is that you can reproduce the relativity math with two rockets, one headed away from earth and one headed toward earth, that encounter and exchange clocks including when the first rocket left earth. The result is the same, yet no acceleration was involved.
How can you exchange clocks without decelerating (them)?
Why not use two Earths, one headed away from the rocket, and one headed towards the rocket, that encounter and exchange clocks?
Hint: acceleration is involved.
@@TheChzoronzon when the two rockets meet at the same point in time and space, they can synchronize clocks. Of course, they will experience time dilation differently at that point, but you can still start a new timer reliably.
This is exactly Don's original explanation.
@@TheChzoronzon Send a very short message as a quick set of radio signals or laser pulses indicating what your clock is and what earth’s clock was when you left.
Let's all say prayers for Physics girl channel Diana...She is very sick again in Hospital ICU long COVID again..
German channel follower here: love your explanation! Hope that whatever problem Dr. Don is having with his left arm, will get better soon!
That's a great explanation of the LINCOLN paradox! :D
I agree that your explanation gets at the fundamental concept better. If acceleration were really key, then the final age of the traveler would depend strongly on the acceleration phase of the trip, which you've shown it doesn't.
if you put the twin onto a gravitational field which has equal accelerating 'force' then this twin would age less same way as on a spaceship, providing the spaceship has uniform acceleration. so general relativity is involved in some way if you accept the equivalence principle.
It doesn't as you say
@@tokajileo5928 That's not relevant to this arguement
Now I’m even more confused than I was before. I saw Sabina’s video and it made sense to me. Then after watching your video with the explanation you and she were generally saying the same thing, I’m finding it difficult to reconcile the two. I guess I’ll have to watch both videos a few more times until it makes sense.
Draw it out on paper and do some math... the *only* thing that matters is the length of something's path through 4D spacetime. That's always the answer, no matter how you do the experiment. The counterintuitive part is that longer spacetime distance means shorter proper time, because of the minus sign on the time coordinate.
Think of it this way: Don emphasizes that changing your reference frame (which requires acceleration) results in less proper time; Sabine emphasizes that acceleration (which requires changing your reference frame) results in less proper time.
In other words, a change in reference frame requires acceleration, and vice versa.
@@dollabz777 Acceleration requires a change of reference frames, but not vice versa. You can change reference frames without having any object that is accelerated. The use of a reference frame doesn't require that there is an object in it.
This was Don's original experiment setup.
@@LarsPensjo How can you change reference frame without acceleration?
This whole twin paradox issue continues to be a really embarrassing topic for the entire physics community. I recommend that both Don and Sabine stop making twin paradox videos until they actually educate themselves on what Einstein stated in his own theory.
To start with, Sabine was critical of anyone who thinks that: "Einstein’s special relativity can only deal with constant velocity and to deal with acceleration, you need general relativity." She goes on to say: "You don’t need general relativity or gravity to solve the twin paradox." With this statement, it is clear to me that she doesn't understand the difference between a mathematical method used to arrive at a certain result and Einstein’s actual physical explanation for what is happening during the twin paradox.
In step 3 of Einstein's own 1918 twin paradox paper he states: "A homogenous gravitational field appears, that is directed towards the positive x-axis. Clock U1 is accelerated in the direction of the positive x-axis until it has reached the velocity v, then the gravitational field disappears again. An external force, acting upon U2 in the negative direction of the x-axis prevents U2 from being set in motion by the gravitational field."
Now we all know that turning around in a spaceship is actually not real gravity but there is a reason Einstein chose his words carefully in that description. It is because all of the work he published in 1905, 1911 along with GR in 1915/1916 led him to the understanding that time dilation experienced between 2 observers with different relative velocities is not the same as time dilation experienced between 2 observers in different positions in a gravitational field or in different positions of an accelerating system. That's because Einstein understood that the entirety of his theory implied that relative velocity would produce a reciprocal effect (each would see the other's clock running slower at the same time) but 2 observers in varying positions of gravity field or accelerating system would not see a reciprocal effect and instead see an equal but opposite effect (Lower clock sees higher clock running faster while higher clock sees lower clock running slower).
This in fact was the entire premise behind his 1918 twin paradox resolution. It acknowledged the strange reciprocal effect during the inertial portion of the trip, but was able to break the symmetry - not with fantastic spacetime diagrams or magical "changing frames" in mid-journey, but with an application of a time dilation effect outside of the confines of special relativity. This is because staying within the confines of special relativity during the acceleration phases correctly documents the instantaneous rate of velocity changes and (therefore the instantaneous velocity differences at any given point) but it would just observe more reciprocal time dilation added to the reciprocal time dilation already experienced during inertial velocity.
Nobel Prize winning physicist Max Born understood this very well and performed a step-by-step mathematical treatment of this in his book "Einstein's Theory of Relativity" originally published in 1922. He concludes his mathematical treatment by saying: "Thus the clock paradox is due to a false application of the special theory of relativity, namely to a case in which the methods of the general theory should be applied."
Don, on the other hand makes the assertion that the crucial thing is that the Earth clock sits in one frame while the rocket clock exists in two frames - and that is what breaks the apparent paradox.
Don also states that: In the “classic” twin paradox, the only way for a single twin to inhabit two frames is to accelerate. He then argues that he and Sabine are really saying the same thing and therefore are both correct because in the end they are each using separate methods to achieve the ever-important frame change for the rocket. That’s all very nice but if they are doing all of this in the name of preserving “Einstein’s Relativity” they should know that both of their explanations have nothing to do with what Einstein required to resolve the paradox.
I have my own separate issues with Einstein’s resolution, that I won’t get into here, but I will say that at least Einstein was smart enough to understand that a “frame” is not a physical object, nor is it an absolute thing of any kind. It is a non-physical tool used to provide reference when describing or assigning motion to a coordinate system, which could then be compared to other coordinate systems that either have the same (or different) velocities compared to the first coordinate system.
In Einstein’s step-by-step explanation, his Earth twin resided in the K frame for the entire twin paradox journey. And the traveling twin resided in the K’ frame for the entire journey. With this, Einstein could show what each twin experienced and observed from their perspective frames.
Toward the end, Don goes on to say: “All of the explanations that invoke general relativity or gravity are all incorrect.” And a moment later he says: “Once again, Einstein rules.”
So Einstein’s own theory, in Einstein’s own words, uses general relativity to resolve the paradox. Don, on the other hand says that using general relativity is incorrect but goes on to say “Einstein rules.“
Unbelievable. I would say, this is so farcical that you can’t make this stuff up - but apparently many people can, and continue to get away with it on a daily basis.
Excellent explanation!
There are not only 3 reference frames but infinite many. The key point is that you have to stay in your chosen reference frame to do the math (how fast clocks are running). The travelling twin is changing velocity (from away from earth to back to earth) at one point regardless which reference frame you are choosing as long as you don't change this once choosen.
Yes, changing velocity is acceleration. And it will complicate the math to deal with a time consuming finite ac- or deceleration of the travelling twin. But all can be done just using the formulas of Special Relativity and some calculus.
This
First, I enjoy your informative and enjoyable videos. Second, what about this variant of the twin paradox? One stays on Earth, the other accelerates 1 g in a straight line but in a closed universe so that the traveling twin returns to Earth without ever turning around. The twins experience the same conditions (they both live with 1 g gravity without interruption, it seems to me), so how would their ages compare? Thanks!
One of 2D equivalent of closed shape is a sphere(3D object). When you move in a straight line along the sphere and return to the starting position, the vector of motion changes direction constantly along the way(due to centripetal acceleration). Closed universe at least 4D sphere? I mean if you moves on the surface of 4D sphere you gets acceleration even if you moves at constant speed
A very elegant question 👍
The answer to all of these twin paradox setups is that the only thing that matters is the length of the observer's path through 4D spacetime. That's it. The counterintuitive part is that longer spacetime distance means shorter proper time, because of the minus sign on the time coordinate.
@@juliavixen176 It's the length of the travellors path compared to the other twin that matters.
Hence velocity
Which is Special relativity in a nutshell
Actually the concept of acceleration is somehow easy to understand and the Don's answer is essentially the same but it requires bit more concrete imagination to understand it.
Excellent explanation, is like kinetics where you are taught about movement without using forces, then mechanics adds the explanation of what causes movement. SR is like that no accelerations only inertial frames of reference.
That was a needed explanation. Jumping reference frames is the key.
The clocks used by the twins tick one-second-per-second, no matter their inertial frame. From the standpoint of each twin, their clock looks and functions normally. But since they are each in different inertial frames, they each measure different distances. The twin traveling to Proxima Centauri and back at 90% of the speed of light measures a shorter distance then the earth-bound twin who is essentially in the same inertial frame as Proxima Centauri. Their clocks tick the same, their yardsticks look the same, the distance each measures is different. Shorter distance equals fewer clock ticks.
That was my thinking, I’d like to know if it is right or not.
@@glennet9613 Hmmmm, who would be qualified to answer that question?
Correct
Plot twist: Don and Sabine turn out to be twins...
Dr. Lincoln is the absolute best explainer of physics on CZcams. Period.
Though I'm subscribed to both channels, I hadn't seen Sabine's explanation yet. This response has helped me understand what I've been confused about, that the reason clocks move differently is because they have different frames of reference (achieved via acceleration).
I'm still chewing on how the frames of reference are or are not arbitrary, but I feel I'm finally getting there.
The hands of a clock are accelerated by an electromagnetic wave. The applied force changes with changes in acceleration/gravity. The human body is accelerated by a different force. You can't apply the physics of a clock to biological processes. They are separate frames of reference - animal, mineral, and vegetable. Each accelerated in time by different forces.
@@stewiesaidthat Either you are mad or the biggest wind up merchant ever
Hi Extraw
They do have frames of reference and that is what makes the difference and you are right, they acheive that in this example through acceleration. In Dr Don's more complete analysis it removes that as different frames of reference are just different speeds.
Its the differing speeds that matter, not how you got there ! Or distance. Only one has actualy travelled more distance, and hence velocity ...and hence special relativity.
Note you have to know what " a frame of reference" actually means in this context. Without that you are lost.
It is travelling at a contstant uniform motion in a a Galilean universe. That is a frame of reference.
Once you change the speed .... another frame of reference.
@Andrew Watson your boy Einstein is the biggest windage ever. Full of hot air. He's taking you sheep down the rabbit hole, and now you can't see daylight. Don't bother trying to find your way out. You are a lost cause and detrimental to the community.
If identical clocks A and B of unknown origin are approaching each other in a void at about half the speed of light, how can we know which one, if either, has the greater velocity?
Hi Dr. Don. I recall watching both of your original videos & no offense to Sabina but I like your explanation the best. After all, next to Physics, Cartoons are everything.😁 [ps; I also love how you'll sometimes do 2 videos on the same topic; one 'without math' and one 'with math' - and how you'll give a warning on those videos that 'math is involved' (IMHO that is too funny😂)]
Except that Don explanations are biaised, only Sabina provides a correct approach to the paradox. If you do not account for acceleration, there is no way to make any difference between the two twins. Without acceleration, all Don says about one twin (the nebulous discourse about two frames compared to one) can be equally applied to the other twin.
@@kantanlabs3859 So Dr Don is 'biased'? Now that's funny. [C'mon, admit it. you just hate Cartoons. (😂)]
@@Condor512 Dont get me wrong, Don is doing a great didactic job in general. But in this case he is wrong² (square) as he insist in repeating the same mistake again: Acceleration is not necessary to solve the twins paradox :-)
@@kantanlabs3859 Groan.........
@@kantanlabs3859 how about 2 objects move at a constant speed and pass over without any acceleration? that's why acceleration isn't a key point.
I remember that Einstein also tried to explain this question and he avoided using 'acceleration' to prove the concept.
However, no matter which way to solve the question, the results are still the same.
Unless we can find a case to differentiate the result of the 2 methods, it is hard to say which methods are better (for understanding the universe).😅
Time dilation is an artifact of Einstein's math errors/failed postulates. Einstein took his SRT ideas from Maxwell and Lorentz, but failed to comprehend what the two were saying,
Paper ...
'Reexamining Special Relativity: Revealing and correcting
SR’s mathematical inconsistency'
Steven B. Bryant
Rindler coordinates just treat acceleration as infinitesimal velocities along the path of the accelerating object. Most popular science descriptions of Special Relativity skip this part because it requires calculus.
Equivalence, similarity = DUALITY!
Time dilation is dual to length contraction -- Einstein.
DUALITY (Isomorphism):- two equivalent descriptions of the same thing or state -- Leonard Susskind, physicist.
The twin paradox is duality.
"Always two there are" -- Yoda.
Antinomy (duality) is two truths that contradict each other -- Immanuel Kant.
@@hyperduality2838 Ron Hatch uses data from GPS and GNSS communication, between satellite and ground clocks, to debunk the Equivalence Principle.
A Canadian GPS software company CEO states that GPS debunks SRT as well.
@@JoeDeglman You need to prove this!
Gravitation is equivalent or dual (isomorphic) to acceleration -- Einstein's happiest thought, the principle of equivalence (duality).
You are saying Einstein is wrong.
Space is dual to time -- Einstein.
Both explanations make clear the asymmetry in the problem, but...
I completely agree that your explanation (that I reached myself before YT even existed) is the more fundamental, in that it explains what gives rise to the apparent paradox, provides the same answer for the same apparent paradox with triplets exchanging information while staying at home, going out, and coming back, all without any acceleration at all, and, maybe most significantly, allows any high school student to do the calculations for themselves.
To say that it's the acceleration that does it, is just a fancy, but ultimately obfuscating way of saying "the travelling twin changes from one reference frame to another" - obfuscating because doing relativistic calculations with actual acceleration is not exactly basic high school maths any longer.
In this case I'd say Sabine did science *with* the gobbledegook. :)
IS THIS THE FIRST PHYSIC BATTLE ON CZcams?
I Love it. If you discuss about science, you always argue with "you are absolutly right but..." followed by your interpretation of the topic.
Definitely not. There was at least a “Mould effect” battle before.
Acceleration-only explanations (I’ve seen videos which claim that the entire age difference occurs during acceleration) have never made sense to me: if it’s just the acceleration, the distance of the trip shouldn’t affect the age difference. The acceleration-only part doesn’t apply to Sabine’s explanation, but it’s one reason the two-frames explanation is much clearer to me.
Yeah, it definitely isn't the acceleration itself producing the time difference. I think physicists often explain it the way Sabine did but are just treating "acceleration" as synonymous with "changing frame", and people who aren't experts get confused by that and end up spreading misinformation. Don was right to emphasize the distinction in his original video.
Bob stays on earth for 50 years and calculates from his frame of reference that Alice's clock will age 30 years as she travels (using 3/5ths). Alice agrees that her clock reads 30 years but determines Bob's clock as being 18 years, 9 on the outbound journey and 9 on the inbound. Year 0 is the the first shared event where they are both in the same place, year 50 is the 2nd shared event where they are both in the same place. Alice starts her return on year 41 having arrived at the other planet year 9 (on Bob's clock according to Alice) The 32 years difference is due to Alice's frame switching from one of moving away to moving toward. From Bob's point of view looking at Alice's clock that change is 20 years.
A photon leaving the sun, from the Earth's frame of reference in which the distance between the sun and earth is constant, takes about 8 minutes. Photons do not experience time, they travel at the speed of light so length contraction makes the earth and sun adjacent in their frame of reference, they arrive instantly. The difference is that we on earth see that the photon left the sun 8 minutes ago, while the photon sees that it left the sun now now. They don't agree what *now* is at some distant point, and it depends on your direction of travel.
The further you travel the greater the difference in *now* is for a given speed.
Acceleration is the second time derivative of distance. It makes no sense to say "it's just the acceleration, the distance shouldn't affect..." Acceleration = distance/time squared.
@@alanjones4358 Normally when we're talking about space travel we're thinking about accelerating for a pretty short amount of time to get up to speed, and then turning the engines off and just coasting until we get to the destination. And the important thing for calculating the time dilation is the time you spend coasting, not the acceleration at either end.
@@Reddles37 Right, but the acceleration causes the change in velocity. It's an indirect cause and effect.
When it comes to so-called paradoxes it is best to simplify the problem as much as possible. The issue with the traditional twin-paradox presentation is that it is complicated by having a traveller make a U-turn. Best to just get rid of that U-turn and not have the traveller return. To illustrate the relative difference in time-passage (note the phrase is important to avoid the idea of absolute clocks) the traveller can just send a signal back with her time-stamp (from a previously sync'd clock with the person on Earth.) The receiver can then receive the signal and know that the traveller is going through space-time differently than the person on Earth.
I tend to follow sabine's explanations more easily. (not just on this but most of her physics explanations). I guess sabine and I have similar thought patterns/ways of reasoning.
Acceleration is speed AND velocity change. Therefore acceleration is also direction change, therefore acceleration explain the paradox ;-)
While I like both Don and Sabina’s videos, in this case I prefer Don’s explanation. It is the different reference frames that is responsible for time dilation. Acceleration is how you know you are changing reference frames.
Sabina was once all political in a science video insulting a candidate. Lost all credibility
The multiple reference frames creates a longer spacial path between the two spacetime points which reduces the time path.
@@jamescollier3 Which video
@@RadioBat Don made two videos. The one with math is better.
Equivalence, similarity = DUALITY!
Time dilation is dual to length contraction -- Einstein.
DUALITY (Isomorphism):- two equivalent descriptions of the same thing or state -- Leonard Susskind, physicist.
The twin paradox is duality.
"Always two there are" -- Yoda.
Antinomy (duality) is two truths that contradict each other -- Immanuel Kant.
I think considering the rocket acceleration felt by the traveller is, at least, the clearest way to show that the twins situations are asymmetrical - and there's no reason they can make the same claims with regard to the other's relative age.
Hi Don!!!! So happy to see you!! This is the strangest video you have done, responding to Sabine. Have you watch the people of the channel "Dialect", they say, in a very inteligent way, that nor you or Sabina, have the right answer to the paradox. Don I really recomend for you to watch that channel, specially the chapter "Even More Paradoxical: The Twin Paradox in Curved Spacetime", which explains with an example why acceleration is not the answer, nor diferent frames is neither. And also the other videos about the twin paradox, they made several, they worth to watch all of them. And would be interesting your reflections about it, after all, physics is everything😁
Dialect’s responses basically boil down to asserting that real forces and inertial forces are equivalent.
Or equivalently, that accelerating reference frames should not act differently from inertial reference frames.
@@thalianero1071 Thank you for your response, I thought it would be nice, Don wath Dialect´s video, indeed he is quoted, but most of all very interesting. What happens if one twin on earth, the other coming in the rocket near earth, which was accelerated, some time ago, but now is moving inertially far from earth, travels some years inertially and returns? The accelleration before gives rocket great velocity, only force a bit to drive back to earth, the twin will be older? Less if he would accellerate the rocket? but he would return earlier. I don´t know
I didn't perceive an emphasis on acceleration in Sabine Hossenfelder's video. The most important takeaway I got from her video was the idea of measuring proper time in the Earth's frame of reference. The observer on Earth experiences an interval of proper time minus any spatial displacement. The observer in the rocket experiences a spatial displacement in the Earth's frame of reference both departing and returning. Because spatial and time displacements sum up by way of hyperbolic geometry in special relativity the proper time interval experienced by the observer in the rocket is shorter than that of the observer on the Earth. That seems clear enough.
I have learned a great deal from both Sabine Hossenfelder's channel and this one, and am glad that they are both doing well.
He is just being nice. You could see clearly that if he wanted to, he could completely destroy her. And the information he provided is enough to make you see, he is just being nice.
Bro it’s two well educated physicists explaining a concept it’s not a WWE match. He didn’t want to “destroy her” he’s just explaining the difference 🧐
Can't we say that acceleration itself is irrelevant, but as any acceleration changes your frame of reference, it's the key?
That's a way to put it, yeah. His point was that there's a change in reference frame, and that change is what acceleration is by definition. They're both saying that you change reference frame, and that's the important part.
Different reference frames can only exist if something accelerated - that's true of the entire universe. Acceleration is more fundamental if it causes the other thing to exist.
@@JohnnyWednesday Then photons accelerate?
@@loc4725 - no time passes for a photon - therefore it doesn't have a reference frame.
I'd say (in general) that anything which supposes infinite spikes in any property (in this case acceleration) probably has something wrong with it. You can't just go from 0 to .9c instantly, nor .9c to -.9c instantly, without infinite acceleration.
Sure, maybe acceleration isn't key to SR, nor even mathematically relevant to its claims about time dilation, but the concept IS key to GR, and so I'd say it is at least important to think about. IMHO though, it goes beyond that: It serves as a point of concern within SR that leads neatly into GR.
I suppose it's a bit like spherical cows in a frictionless vacuum though: Still useful for learning, but something you ultimately grow out of in order to build a more complete, physically real understanding.
Dr Don, what is it about particles that causes them to create mass?
Is it anything to do with the momentum of the movement of the particles? A bit like gyroscopic effect. Where pushing the object is resisted by all of it's constituent particles being in motion.
Is it the angular momentum that creates the mass?
When objects are super cooled and they behave differently, is that partly because the movement action of the particles is reduced, so their momentums are reduced?
Thank you for the excellent videos.
See czcams.com/video/gSKzgpt4HBU/video.html
Inertial mass comes from confinement... I don't really have time to write a really long explanation here, but a simple model is to imagine a massless box with perfect mirrors on the inside surfaces. If you put some massless light in the box, it can bounce back and forth forever, and it transfers momentum to the walls of the box with each collision (bounce) off the mirrors. Since it pushes equally hard on every side of the box, the box doesn't move. Now... from outside of the box, if you push on a side, it will resist moving, because the light travels less distance to collide with the side you push on, and more distance to push on the far side. Resistance to acceleration is inertia-- also known as "mass". Even though all the parts of this setup are massless, the total system has mass exactly in proportion to the amount of momentum that the light has... when you do the math on this, you get E=mc²
Oops, there is a minor error in the video at about 06:45. In the outgoing frame, the earth is "zooming off to the left" but the returning rocket is not "zooming at twice the speed", try that for an Earth speed of 0.8c! The composite speed needs to be calculated using the "addition of velocities" formula of course.
It is not acceleration that is key but the delta-v imparted, the integral of the acceleration over the turnround period, which is what switches the rocket from one frame to the other.
Sabine is an interesting figure. She seems to revel in being an iconoclast with different opinions from the mainstream. But she is also a highly competent physicist and when speaking in her own field, she gives a very good explanation of where she does and doesn't agree with others, why, and the current state of the evidence.
For something like this, the science has been well understood for over a century and they teach it to college freshmen (I learned it in my freshman physics class in 1999, though I had read it in popular books before then). You aren't going to find Sabina contradicting that well established science. She might have a different explanation, but not a contradictory one.
The problem I've had with Sabine is in her recent videos where she ventures outside her field. She speaks with the same confidence, but without the expertise. I have a lot of experience with experts opining outside their fields. It tends to go badly. But within physics, she's awesome.
Her name is SabinE though...
@@nandocova Oops. I'll edit it. Thanks.
Everything that Sabine says in her video is not correct. She makes several misleading statements and especially she says that acceleration is the only cause of time dilation. This is simply false and her examples are extremely selective.
Anyone trying to understand SR from her video is going to have a hard time.
I am sure she knows what she means when she says these things, but as science communication her video fails on most counts.
That's easy to resolve by just realizing that acceleration is the only cause of velocity, and velocity is the only cause of time dfilation.
Sabine isn’t just some CZcamsr. Hossenfelder received an undergraduate degree in Mathematics in 1997 from the Johann Wolfgang Goethe-Universität in Frankfurt am Main.[5] In 2004 she completed a doctorate in theoretical physics from the same institution with a thesis titled Schwarze Löcher in Extra-Dimensionen: Eigenschaften und Nachweis[6][7] (she published a paper in the same year with a similar title in the journal Physics Letters B in English, titled "Black Hole Relics in Large Extra Dimensions"[8]).
Sure. But Fermilab's Dr. Don completed a doctorate in physics 10 years before Sabine. He also has co-authored over 1600 papers.
But since the video says that both Sabine and Dr. Don are saying the same thing, we can be happy that physicists agree when you have them clarify what they mean.
"Sabine isn’t just some CZcamsr."
That's why he responded to her video. If she was "just some CZcamsr" he would have ignored her completely. There are way too many "just some CZcamsrs" out there who believe they know more than professional physicists when it comes to relativity, but don't, to respond to them.
Don your swagger exists in multiple frames bro! Please keep making videos =]
If a twin traveled to another star and stayed there (thus only occupying one time frame), would he still be younger than the twin that remained on Earth? Or older, or the same age?
Given that simultaneity is not a well-defined concept across macroscopic distances, you'd have to bring them to close to each other to get a meaningful answer to that and the answer you get would depend on the way you do that.
Still, the answer by most reckonings is "younger" - he didn't age as much on the way out as the twin who stayed behind, after all.
Continuing to travel at the same velocity when the rocket reaches the star means the rocket does not "stay there." It goes past the star and keeps going.
In that scenario, each twin can deduce that the other twin has aged less. With telescopes, they can observe each other's clocks, but their deductions must take into account the amount of time that the light takes to travel to the telescope... in other words, they each see the other's clock as it was in the past.
@@jounik : No, it's not necessary to bring the twins close to each other, because each twin can use a telescope to see the other's clock. By taking into account the speed c of the light that traveled from clock to telescope, each twin can deduce how long ago the light was emitted from the clock, and can compare the other's clock value to the value that was on his own clock at that moment in the past.
depends on their speed + minor factor that clock of tween on Earth slower than clock of twin on the ship(if their velocity equal)
But lets say Bobs speed >0.01c Bob will be yonger
In order to stay at another star, the traveling twin needs to decelerate (assuming the other star is stationary wrt. the Earth). After that, they will agree that the traveling twin is the younger one. They can exchange signals with each other to compare their ages.
Don you forgot one major rule: The woman is ALWAYS right! 🤣
To complement Dr Don & Dr Sabine, I found Prof Brian Greene’s explanation to be excellent as well… but paradox without acceleration:
czcams.com/video/XFV2feKDK9E/video.html (9:29:28)
Another supplement: minutephysics illustrates concisely how it is indeed all about the change in reference frame, and acceleration is how you achieve that change (without recruiting another observer as Don cleverly did)
czcams.com/video/0iJZ_QGMLD0/video.html
I've been giving this video a bit more thought and I have a few problems with it. As I mentioned, time is a measure of the pace of causality. It seems to be accepted that speed affects the passage of time and thus the rate at which causality takes place. I don't think so. If we look at a black hole, past the event horizon, time stops but really causality stops. And the reason seems to be that the mass of the black hole stops causality and thus time.
With a mass approaching the speed of light, time slows down, which really means that causality slows. The clock on the ship tics because of causality and compared to one on earth, it tics slower in relative terms.
So we have two seemingly opposite situations having the same effect. The speed of the object can slow causality but in the black hole its the lack of speed that stops time and causality.
But there is a common element between the two, mass. The rocket approaching the speed of light has tremendous mass due to it's kinetic energy. e=mc2 says that this kinetic energy is the equivalent of mass. Of course the black hole has an incredible mass. So mass seems to me to be the common element, not speed.
For any object in motion relative to a planetary observer the mass increases while the rate of causality decreases, until the mass, whether through kinetic energy or actual mass causes causality to stop altogether.
I don't know the math, but this seems like rather simple way to reconcile the end result being the same for a moving object and a completely stationary one as found inside a black hole.
I don't understand how you can assume instant acceleration and say it doesn't matter in this example - The acceleration is where energy is 'added' or 'removed' from the system - its the acceleration that alters the apparent rate of time - is that not correct? different reference frames only exist because at some point in time, something accelerated - so how can it not matter?
To put it simply, the time experienced by one reference frame would be twisted instantly if there is a sign change in velocity input on Lorentz’s transformation.
That sign reversion corresponds to the change in frame since the velocity is no longer the same.
It’s all about the math.
I could have done it properly and integrated over the acceleration time, but the explanation is more complicated. And, since you can make the acceleration time arbitrarily small, it doesn't matter.
@@minhdang1775 - So you're saying at the start of the universe, something moved before it Accelerated?
@@JohnnyWednesday I would say between two moments, there is an infinite value of velocities and each individual velocity (position also) correspond to a frame of reference.
acceleration is a continuous series of all velocities until the final.
it’s like in calculus, we add infinite sharp corners to get a smooth curve.
@@drdon5205 - it does matter, because if you make acceleration zero - there aren't any reference frames. You can't say reference frames cause acceleration because the only way to reach the initial setup is by applying acceleration - you can't spawn reference frames into existence as a maths tool - things have to move to their starting positions and velocities or it has no relation to reality.
I agree with Sabina here, acceleration is key Acceleration causes time dilation, earth is not stationary as gravity is acceleration! A rocket would have to accelerate past 1G to have any time dilation affect on the age of the twins.
Acceleration itself is not the cause of time dilation tho
That's wrong and also not what Sabine was saying. The acceleration is only important because it lets you know which twin is which, but it isn't the main source of the time dilation. Also, the gravitational time dilation on Earth is less than one part in a billion, unless you have an atomic clock you can basically just ignore it. Anyway, if acceleration was the important part then you would get the same time difference from flying to the moon and back or flying across the galaxy, but that isn't how it works at all.
Einstein related Gravity and acceleration as one of the same.
That’s how I see any time difference, Gravity/ acceleration will slow down time.
@@phillyg7661 There's more than one way to get time dilation in relativity. Gravitational time dilation is a thing, but you also get time dilation just from going fast and you need to add both effects together. Take the clocks on GPS satellites for example, they go faster than clocks on Earth by 45 microseconds per day because they have less gravitational time dilation, but they also go slower by 7 microseconds per day because of their orbital speed so the total correction is 38 microseconds per day. For an interstellar spaceship the gravitational effect will still only be microseconds per day, but the speed will be much higher so that gives you almost all of the time dilation effect.
@@Reddles37 great clarification, so velocity also has an effect on passing time, I recall the satellite example, I was stuck on gravitational time dilation.
So, if time does not affect a photon, the speed of light must be where time is no longer relevant. Or at least not to light.
At the end of the day, acceleration is an increasing velocity, related to motion in time. Space time.
Cheers
Excellent explanation. However, does the extent of initial acceleration of one reference frame determine the extent of time dilation between two reference frames? I always thought that an acceleration to near the speed of light would produce the greatest time dilation between two reference frames. I am also perplexed as to what causes the extreme time dilation if one were to approach a black hole event horizon. Is this also explained by a change in reference frames or is there some other factor involved?
Acceleration plays an important role in the first framework, which involves the observer who is in a non-inertial reference frame due to their acceleration. In order for this observer to believe they are stationary, they must assume that there is a uniform gravitational field throughout the universe, and this field causes time on Earth to run faster due to the Earth's large gravitational potential. The amount that time on Earth speeds up depends on the distance between the Earth and the observer and the strength of the gravitational field, which is related to the acceleration.
so the answer to your question is Yes, greater acceleration equals greater strength in the gravitational field, which results in a faster speed up of time.
On the other hand, in the second framework, which comes from the principles of special relativity, acceleration is not fundamental to the phenomenon. When an observer accelerates, different frames of reference disagree on what is simultaneous, which is called the Relativity of Simultaneity. Each frame of reference has a unique line of simultaneity, and changing the frame of reference leads to a new line of simultaneity where events may occur in a different order.
An analogy to help understand this concept is standing on a bridge with varying slopes at different positions. The slope at your position determines your line of sight, and to change your line of sight, you must move to a new position. Similarly, in the Twin Paradox, the position on the bridge can be understood as a frame of reference, the slope as the line of simultaneity, and your movement as acceleration. Each reference frame has a corresponding line of simultaneity, and changing the frame of reference leads to a new line of simultaneity where events may occur in a different order.
While accelerating, the observer passes through an infinite number of inertial reference frames, each with a different line of simultaneity where the Earth is in a different timeline. When the twin traveler returns to Earth, they will observe that the clock on Earth has accelerated due to the change in the line of simultaneity. Therefore, in this perspective, acceleration is not a fundamental explanation of the phenomenon.
Both are mathematically correct.
@Metric Identity what does all that have to do with the price of tea in China?
How does a person traveling in space faster than the Earth's rotational speed affect the price of tea in China?
Isn't it about time for theoretical physicists to throw in the towel and admit that acceleration in space has no bearing on the price of tea in China?
The velocity time dilation Equation :- (5+(V/c))^2 seconds observed for the one second experienced on the craft.
🙂
All paradoxes are thought wrong. There are no paradoxes
In Dr Don's original video he did something wrong - or at least very confusing: he had twin C (inbound) add twin B's (outbound) recorded travel time to his own, then compare that result to twin A's (Earth) elapsed time. The reason this is a problem is because twin C accepted twin B's time without question; however, twin C should not agree with twin B that B started his watch at the moment he crossed paths with A. Dr. Don essentially merged the two distinct reference frames into one. I'm disappointed that Dr. Don didn't take the opportunity in this video to address this problem.
Great and intuitive explanation with 3 frames👍
The problem is that no one ever discusses what happens to the clocks on earth as seen by the traveling twin. Assume the distant star is a distance L from earth, and that it travels at speed L/T. When the traveler gets to the distant star, the time for her is (T) / (\gamma), and from her viewpoint (via the Lorentz transforms), the time on earth is T / (\gamma^2). Also, at the star, the spaceship turns around. You can't avoid an acceleration here. For an instantaneous turnaround, the acceleration is a = -2 \Delta V \delta(t-T). This is what puts the spaceship in its second inertial reference frame. But this causes an instantaneous jump in the time on earth as seen by the traveler. Immediately after the turnaround, the time on earth from her point of view is 2T - T / (\gamma^2). You can calculate this by assuming our traveler goes past the distant star by a distance of L, making a total distance from earth of x = 2L (from the viewpoint of earth). Now, rotate the line that connects the distant star at distance L from earth with the ship now at 2L from earth to point the earth, and that becomes identical to the "third twin" we often hear about nowadays.
For both travelers, their time is T / (\gamma). But since they are going in different directions, they "see" (according to the Lorentz transforms) different times on earth. The outgoing traveler sees the time on earth as t = (T) / (\gamma^2). The incoming traveler sees the time on earth as t = 2T - (T) / (\gamma^2). Now let the outgoing traveler make an instant turnaround at the star, and she assumes the same times as the original incoming traveler who came from x = 2L. So during the turnaround, the time on earth made a discontinuous jump from the former to the latter.
(The different times are like the different times in the Andromeda Galaxy, as seen by the two brothers walking in opposite directions on the sidewalk.)
Think about it. If the traveling twin is to age less, the clock on earth must at _some_ point be going faster. With the instant turnaround, there is a discrete jump. With a more realistic turnaround, the clock merely speeds up during the turnaround as seen by the traveler.
This is what you get from the Lorentz transforms.
Another way to go about this is to use Eq. (11.27) from J. D. Jackson, _Classical Electrodynamics_ . But you must use this equation _only_ in an inertial reference frame. In this case, that would be the earth.
The clocks are irrelevant to the solution. They are not in the same frame as the twin.
Spacetime is a fantasy universe in which the space and time frames are combi ed into one, and the physics are defined by acceleration.
You want to use the physics from the real universe, which are based on Force and have separate Space and Time frames.
The Time frame consists of a change/acceleration in mass,
The Spsce frame handles changes in spatial coordinates (acceleration).
You can ignore the clock because it is an instrument that measures acceleration in space. We want acceleration in Time ( a change in mass).
Why are there separate Space and Time frames. Because you can't time travel. If the future doesn't exist, then neither does the past. Only the present exists as an accelerated past event. Once that event is nolonger being accelerated, it dissappears from the time frame.
To resolve the paradox, you need to discard Einstein’s fantasy universe. And that means dismantling the Church of Relativity.
Don here won't tell you the solution. If it does, it means he is a charlatan who has been scamming you. Or is so intellectual stupid that he doesn't understand basic physics.
Is Don and his buddies at Fermilab and universities, and technology institutions truly this ignorant in regards to Relativity. Or are they trying to pull a fast one on you.
As Carl Sagan would say. Both are equally frightening.
Just to clarify my last statement: You use the Eq. (11.27) _from the viewpoint_ of an inertial reference frame. But the proper time in the equation can be of a system exhibiting arbitrary motion, including accelerations.
If I may: you are not arrogant or self promoting, and your videos reflect that. Your arguments may be "arguable," but there is grace in how you present them and how you make room for the possibility that in the future you may have to revise your stands. In other words, you are not dogmatic. You are a good teacher.
Viewers might want to view this video after watching Don's. You learn something every day.
I've just had my Eureka moment - it might help if you are still puzzled. Looking at the three-observers version, it still seems that there are three equivalent perspectives, taking A, B and C respectively as being stationary. That would seem to mean that there is still no asymmetry between our accounts of the three observers' experiences. BUT: only one version, with A stationary, involves both the departure and the arrival occurring in the single reference frame; that of A. In each of the other two versions the departure and the arrival event occur when one of them is moving. That's where the symmetry breaks down, and the puzzle is solved.
Thank you so much this almost clears up everything for me! However, there's one more scenario I have in my mind I just can't resolve.
What about a scenario in which a rocket that never changes speed and has always been travelling at that speed zooms right on by the earth? Let's say there's a station on one side of the earth and the other side, and they're both, as far as it goes, in the same reference point. They can both make an observation of a big ol' clock sitting right on the outside of the ship. The ship can look out and see the two station's clocks too. Which one appears to have slowed time in that instance, and which fast?
Both will see the other clock slowed down. czcams.com/video/Bg9MVRQYmBQ/video.html
@@thedeemon Okay I thought I understood but you've made me completely lost again. That sounds like a complete paradox and I thought the whole point of this situation, the entire point of having a resolution to the grandfather paradox, was to PREVENT a situation where "both see the other's clock slow down" because that's a contradiction. Fermilab help!
@@Dark_Jaguar No, it's not a contradiction, because neither clock slowed down in your scenario. Each clock was always running slow relative to the other frame. The station's clocks were always running slow relative to the ship's frame, and the ship's clock was always running slow relative to the stations' frame.
Even in the standard twins scenario, it is true during all inertial motion that earth's clock runs slow relative to the ship frame, and the ship's clock runs slow relative to earth's frame. Only during acceleration does earth's clock run very fast relative to the ship's frame, resulting in earth's twin having more total elapsed time.
One way to see why there is no contradiction is to consider a ball thrown forward at 50 mph from a train moving at 50 mph: After the ball is thrown, it does not slow down or speed up in either reference frame. It's moving at 50 mph relative to the train, and 100 mph relative to the ground. That's not a contradiction because velocity is relative to reference frame. Similarly, time is relative to reference frame in SR.
@@alanjones4358 The video makes it clear it's not during acceleration, it's that it's in two different frames of reference and it would work in an imaginary universe where there is no acceleration and it just instantly changed direction.
As for the time thing, I think I'd like this guy to answer it if possible. His video here made things a lot clearer, but this answer makes things clear as mud again.
Love the don videos!
If you assume that Ron changes reference frames, then you can resolve the paradox. However, changing reference frames is fundamentally what acceleration is, whether you have the acceleration be instantaneous or more gradual. The only way to resolve the twin paradox is to keep track of changes in reference frames, which under SR can only be done by measuring acceleration.
Or by introducing a third observer who simply occupies the approaching reference frame continuously.
Or just have Ron in a different reference frame to start off with at constant velocity. That solves the paradox as well, but not as it is written here which assumes acceleration.
If we exclude acceleration as Ron explicitly does, then Ron being in a different reference frame does not resolve the paradox. Every inertial observer observes the clocks of every other inertial observer as moving more slowly than their own, so long as there is a difference in velocity. Everyone is aging more slowly than the observer, and every observer measures that everyone else is aging more slowly than themselves.
This is the twin paradox. Observer A measures that observer B is aging more slowly than A, while observer B measures that observer A is aging more slowly than B.
It's only when some of the observers undergo acceleration (e.g. the "instantaneous acceleration" in Ron's example) such that they end up in the same inertial reference frame that the paradox ceases to exist. Just having three observers fly by each other at different points in space and time (as Ron illustrates starting at about 5:00 through 7:00) does not resolve this paradox.
Seems like the “paradox” is more complicated than it needs to be. Why can’t second twin be passing next to the first twin at a constant velocity when the measured period starts and the comparison be made before the second twin turns around? For example, by each transmitting periodic messages to points that are variously equidistant during the journey. More importantly, why do they always need to be twins?
7:30 In an arbitrary non-inertial reference frame, the equation of the total mechanical energy of a particle system is: ∆E=A(internal)+A(external)+A*, where A (internal) is the work of internal dissipative forces, А(external) is the work of external non-conservative forces, А* is the work of inertia forces. In order to preserve the mechanical energy of the system in a non-inertial frame of reference, it is necessary that ∆E =0, however, in an arbitrary non-inertial frame of reference, it is impossible to create a condition for fulfilling this requirement; that is, ∆E does not =0 in any way (by the way, in system C, the condition for fulfilling the laws of conservation of momentum and angular momentum does not depend on whether this system is an inertial or non-inertial frame of reference).
To summarize. They are both correct because the underling fundamental phenomenon is that the whole worldline (trajectory) of the rocket man is not a geodesic of spacetime. In Sabine words this translates in acceleration, in his words translate in different reference frames for the same observer
I teach physics in a technical highschool and my students still misunderstands the phrase about the experience of time and slower ageing. They think that they will observe the clocks in the spaceship slow down when travelling 😊.
Therefore, do not use the misleading phrase of _time slowing down._
Equivalence, similarity = DUALITY!
Time dilation is dual to length contraction -- Einstein.
DUALITY (Isomorphism):- two equivalent descriptions of the same thing or state -- Leonard Susskind, physicist.
The twin paradox is duality.
"Always two there are" -- Yoda.
Antinomy (duality) is two truths that contradict each other -- Immanuel Kant.
The defining perspective is the one determined by the dominating reference frame. For the Earth and the Moon - it’s the Sun, etc…
Very nice explanation. Why is it only the turnaround acceleration that's discussed in the twin paradox explanations? The accelerations required to get up to speed on the outbound journey and slow for landing on the inbound always seem to be ignored.
There is no acceleration required at start and end. Because , at the start , rocket is already at speed when it crosses earth and the rocket is at speed at the end when it flies past earth. there is no acceleration involved at start and end
Your explanation is completely right, but maybe its not necessary to introduce additional frames of ref.
One of the essential properties of frames of references is that they are arbitrarily chosen. And GR is called 'general' because it states that the laws of physics must appear the same in whatever frame of reference you chose to do your observations, even in accelerating ones.
Long story short, in the frame of reference of the travelling twin, one must reach the same conclusion as reached by the static twin, i e., that YOU (the traveler) are the one who ends up being younger at the end, not your brother.
The way the traveler does that (from his unique and never changing frame of ref !) is that he must realize that he indeed accelerates.The traveling twin cannot ignore his acceleration (or else he might think that he is falling under a gravitational field, which would lead to the same conclusion with regards to aging) and therefore must be aware by applying the rules of physics that all his clocks, (including biological clocks) are runing slow. He should thus expect that when he meets again his twin brother (provided the latter has remained static of with constant velocity) he (the traveler) will be younger.
By the same token, the static twin, since he could not ignore acceleration if it happened (or else an increased gravity) he can be sure that he is NOT accelerating. Then he sees his twin brother going afar, which can only mean that he is accelerating, and therefore his brother will end up being younger (whether he returns or not!). In summary, both reach the same conclusion as we, if they correctly apply the laws of physics.
Thanks for the video, it is quite inspiring.
There are some further interesting twists to the story, which we can discuss if necessary.
It seems to be universally accepted that it is TIME which dilates with gravitation or acceleration when there is another option.
If we assume ENERGY dilation instead we get the same result but time may remain absolute.
The hold of gravity and the drag of acceleration/deceleration may impose a limit on all other forms of energy, if this is so then a clock will run slower the stronger the gravity or acceleration/deceleration but that will NOT indicate changes in time but only in available energy.
It will not matter if its a spring wind up clock or an atomic clock, a living cell or any other energized system, we could consider the observation of "time" dilation to be energy dilation and not time dilation.
Maybe off subject, but:
Concerning acceleration and time distortion. What if an object were placed
into a centrifuge, and spun up. Then take that working centrifuge and place
it in/on another, larger centrifuge, and spin that one up. Since the "inner"
object, in centrifuge #1, is accelerating in two different bases, it would
be subject to periodic, cyclical variations in subjective mass as it cycles
in centrifuge #2. Could this oscillation cause a modulation in gravity waves?
thanks! detail question: both approaches agree on t(moving) < t(earth). but if you calculated the value of t(moving) using your approach you would get a different (and incorrect, i would assume smaller) value than using the approach taking acceleration into account. correct? or am i misunderstanding something again?
the two results, if computed properly, must agree with each other. We'll have to use GR and gravitational time dilation to compute how acceleration affects it.
@@thedeemon You don't need general relativity or gravitational time dilation to understand the twin paradox. Special relativity can handle acceleration.
Why do you think you would get a different value for t(moving)? If you're thinking about the time required to slow down, change direction and speed up again, we can just assume this happens in an instant in order to make the two scenarios equivalent.
@@richardjenkins2321 Right, one can use SR and treat acceleration as a change of frame of reference. Or one can use GR and have a single frame of reference for a rocket, where there is "gravitational field" during its acceleration.
Your explanation is certainly more fundamental than that of Sabine, That can be seen clearly if we calculate the elapsed proper time t1 of then traveling twin. ti= integral from t=0 to T of sqrt(1-v^2)*dt, and the proper of the stationary twin t2: t2 = integral from t=0 to T of dt, where T is the time the stationary twin spent beterrn the departure and arrival of the moving twin. We don't even need to do that calculation in the frame of the travelling twin because proper time is an invariant in relativity. Moreover, there is no acceleration in this calculation of proper times, only v appears. Of course the velocity changes only if there is acceleration and we can say that acceleration has on effect. But actually acceleration never causes anything in mechanics and/or special relativity because acceleration itself is caused by net force acting on a body, not the other way round. So Sabine could equally well have said that the key to the twin paradox is force.
The phrase I learned in school and have seen used is "in an accelerated frame of reference". I think you are right about English causing problems - this is so easily misinterpreted.
Don, My first visit to Fermi-lab was in 1983. The math is just a likely story not that actual story, over emphasizing it is why we have not made any real progress in theory. Math has become a lab bottle on ideas, where all we do is wash bottles and sort buttons.
The best explanation is the one that enables new ideas to precipitate, aka create space for predictions.
Frame 3 wouldn't be twice the velocity from frame 2 would it, you need to add velocities relativistically? The key understanding for me is that the earth clock moves forward rapidly from thr rocket's perspective when it turns around. Brian Greene does a good explanation of the concept of now that helps in this regard.
I'll start again here, in the hope of keeping this point separate from all the others. It is written in response to the suggestion that it is the frame-switching that explains the asymmetry.
Could someone kindly let me know what I am doing wrong, here? In my situation, B travels to another star at near-light speed, reads his clock on arrival, and sends the information back to A on Earth by radio. B experiences and measures the trip duration as 0.5xT, and A learns this fact. However, it is not permissible to reverse the story, putting B as the stationary observer and A as the traveller. In that instance, A's time will be T, and B will be told this.
No 2-frames in this setup, just one for each observer, but the asymmetry is still there. Therefore, A is in a privileged frame, in which time dilation does not occur. What makes his frame privileged?
" _No 2-frames in this setup, just one for each observer, but the asymmetry is still there. Therefore, A is in a privileged frame, in which time dilation does not occur. What makes his frame privileged_ "
A's frame is not privileged. It is however slightly different than B's frame.
Because in A's frame the earth-star distance is not length contracted .
But in B's frame, earth and star are moving , so earth-star distance is length contracted.
Time slows for moving object within its boundary limits. Mercury's orbital motion is faster than Mars. Time at Mercury runs slower than Mars. Twin on fast space trip will age slower than the one on Earth. Motion of twin on space trip has no effect on flow of time for Earth bound twin.
Sabine Hossefelder disturbed for example the gravitational redshift and the redshift based on the Doppler-effect (published in a German version of "Scientific American"). Furthermore she couldn't agree with the preservation law of energy in the gravitational field etc.
Two neighbors were fighting over a financial dispute. They couldn’t reach an agreement, so they took their case to the local rabbi. The rabbi heard the first litigant’s case, nodded his head and said, “You’re right.”
The second litigant then stated his case. The rabbi heard him out, nodded again and said, “You’re also right.”
The rabbi’s attendant, who had been standing by this whole time, was justifiably confused. “But, rebbe,” he asked, “how can they both be right?”
The rabbi thought about this for a moment before responding, “You’re right, too!”