Solving Einstein's Twin Paradox

Many solutions have been proposed to Einstein's twin paradox, but many of them miss the vital reasons why the Earth twin is correct and the Spaceship twin is wrong. Here we condense the solution of the twin paradox to its essentials, and also discuss why applying general relativity to the problem is unnecessary.

CHAPTERS
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What is the Twin Paradox? 00:00
Time Dilation 00:43
The "Paradox" 01:17
The "General Relativity School" 02:09
Twin Paradox Without Physical Acceleration 03:31
Bob's Two Reference Frames 05:04
The Counterargument 06:06
Why the Counterargument is Wrong 07:08

If you're interested in more special relativity content, check out the series below!

SPECIAL RELATIVITY SERIES
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[TingleCowboy]

I'm sorry to say it, but you haven't even begun to understand the solution to the paradox. You only see time dilation, but completely ignore length contraction and the resulting relativity of simultaneity.
You get caught up in the fact that the twin travels back and forth. But that is not necessary. Even if the route is only flown once, the traveling twin ages less. Even acceleration phases are superfluous; it is sufficient for the twin to send a light signal back to earth with his age when he reaches his destination. The traveler does not have to change his frame of reference, accelerate or do anything else, so the time dilation is absolutely symmetrical, yet he has aged less than the twin on Earth when he reaches his destination. And as long as you don't understand this, the twin paradox is far from being solved.

[A_GoogIe_User]

Since we all move through spacetime at the same rate and Bob travels the longest distance (and not Alex because Bob is the one that had the acelleration (which is absolute)). Therefore Bob travelled more quickly through space and hence less through time.
Why make it difficult when it really is this simple ?

[the-karabin]

Thank you! Finally after all those years of being unsatisfied with answers given for the twin paradox the kind of video I'd been waiting for!
I just wish at 5:37 the calculations to "prove" that Bob indeed aged less than Alex (in that frame of reference, Bob's inital one) were on screen since it's not very intuitive, but then again, none of this really is^^

[paulomanuelsendimairespere]

The very reason for the assimtry has nothing to do with changing frame or acceleration. We can see it by only considering the going to the star. In fact if the twin stopped a clock at the arrival, it would show half of its aging when he met his brother.

Both formulas (see below) are right:

t'=t/g (for x'=0) and
t=t'/g (for x=0) .

But the first is only valid when x'=0 and the second only x=0.

What happens is that the end conditions are compatible only with the first formula but not with the second one. In fact at the end=

x'=0, x=L. Because the second formula is for x=0 we cannot apply it.

Then the very reason for the assimetry is that one twin is moving "inside" the space of the other (seeing the path shortening).

[Music_Creativity_Science]

Sorry, the thought experiment is made in a clear and interesting way, but imo the equivalence principle must be used to solve the twin paradox, physically.

Initial statement (mine): A relative motion (or position) between objects (any objects in the universe) can not come into existence without acceleration (a force).

You seem to use this logic, initially:

Premise 1. "I assume that I can solve the paradox, without accounting for all acceleration processes in my thought experiment". Disregarding Carols acceleration. But, she can not just "be moving". Doing so can be called the "cosmic magic hands" - error, moving (or placing) other observers relative to the twins with pure magic. 4:00, what you do here is neglect/disregard her physical ageing when she accelerated (which is the same added ageing that Bob would have experienced if he had returned normally from Betelgeuse, instead of Carol). The twin experiment is about physical ageing of the TWINS, not measuring clocks/time handed over in different ways with external experiment participants.

Conclusion. "I perform my thought experiment, do not include all accelerations in it, and have showed that acceleration is not the (only) cause for physical time dilation".

This is called "assuming the conclusion" - error in a premise, in a logical reasoning.


4:25 you state: "In Bob's reference frame, the situation is the reverse, Alex's clock will have ticked less by the time Bob reaches Betelgeuse". No, time dilation is a physical process (clocks and other matter), and in reality Bob did use a force to accelerate also here. His clock ticked less also here, going to Betelgeuse.

You can not avoid a real physical solution without the equivalence principle, with only acceleration phases affecting matter, and there is mathematical proof of that. The time dilation equation in GR is equivalent with the time dilation equation in SR. They just have a different set of variables in them (include the escape velocity equation in the GR equation and you get the SR-equation). v^2 is a velocity after an acceleration phase (v^2 = 2 • acceleration • distance),
not an average velocity or an instantaneous velocity when coasting.

Which means:

- The two equations can not physcally affect matter in different ways (an atom must react in the same way, affected by gravitation or by an accelerating rocket). It has experimentally been proven in a lab that time dilation is the decrease of certain frequencies in atoms, both in a gravitational environment and during mechanical acceleration.

- Only acceleration/deceleration phases in relative movement affect clocks/matter.

- The SR time dilation equation is an acceleration based equation, it can not be used calculating time dilation between objects during coasting phases (inertial objects). Nothing physically happens to a coasting clock (coasting matter), relative to another object (inertial frames). This is often misunderstood in thought experiments and calculations with the SR time dilation equation.

[stewiesaidthat]

What you are overlooking is the fact that space and time are separate frames of reference. The caesium-133 atom is chilled to absolute zero to prevent it from being accelerated in time when a force is applied. Are either of the twins in cryostasis?
Both twins experience the same amount of time. One just experiences more space.

[khushalsharma]

Hello can you explain what happen when two twin go in opposite direction and come back. My answer will be there age will be same but they are moving near speed of light they should feel time dilation and one one of them get older but which one? Can you explain

[atchjay]

The paradox is in the final outcome. Before the final outcome, is Alex aging faster near uniformly relative to Bob's aging if the turn around by Bob is very rapid? That to me is the paradox. If Alex goes and catches up to Bob before the turn around, Alex will be younger. If Alex goes and catches up to Bob after the turn around, they can be the same age or Alex can be older or younger depending on where they meet. That is the real paradox. Alex can make himself relatively younger by going out to meet Bob and Bob can employ tactics to ensure that does not happen.

[alexjohnward]

Alex and Carol are not twins, they don't resolve anything. Talking about multiple inertial reference frames isn't really helpful either. Lets just consider Alice and Bob, because the special thing about twins is that they start in the same location, with the same velocity, and same acceleration. Therefore when they start, their clocks tick at the same rate. If one Twin accelerates, the clocks immediately fall out of sync. If the clocks ever come back together to allow a comparison, it's the spacetime travel distance that always determines the discrepancy.

[michaelccopelandsr]

Time is fascinating. I worked the subway stations for nearly 10 years. From one end of the city to the other. Every so often I would notice the city would be saying that, "Today just flew by" or "The day was just dragging along."  How can an entire city, with no interaction with each other until they used the subway, complain about the same time paradox unless it was effected by it? Maybe a time distorted bubble the earth passes through in its revolution around the sun. Maybe random waves of time distortion hitting the earth? Maybe they're given off by the sun. Maybe they're from outside our Terran system and reach us in intervals. ???? Ti-i-i-ime, is on my side. Yes, it is

[philmann]

I don't see how this solution materially differs from others that recognize the lack of symmetry between Alex and Bob and ultimately rely on acceleration/gravitation and General Relativity. Bob very definitely feels acceleration that Alex does not and that has very noticeable consequences in the real world. (If you don't believe this, calculate the forces generated if Bob, travelling at 0.98c in one direction, slows down and accelerates to 0.98c in the opposite direction in, say, one second. Guess whether a human body can survive that. For grins, try it over a period of a month.)

Your statements that, this is Physics and we can tell who is right and who is wrong, and that "it's down to some elementary physical principles" to make that determination are correct. But if I may, I'd like to expand and modify them slightly to point out that, in Physics (and, indeed, all of science) it is actual observation that is the ultimate arbiter of scientific truth, and that even "elementary physical principles" must give way if they prove to differ from what is actually observed.

The appeal of the Twin Paradox over what is now more than one-hundred years comes from asking, "If my twin brother actually does go off on a high-speed trip and comes back years later, will he really remain a young man, while I've grown old and gray?" Until and unless that experiment can actually be performed, we cannot know for certain. Theory and experimentation to date certainly suggest that's the case. But until and unless we actually see it with our own eyes, who really knows?

[tahmidislamtasen]

Finally thats the counterargument that came to my mind

[chocopappy]

Nothing is stationary, nothing is ever in the same place for more than an instant. Time seeks its end, that all matter ends up in the same place. The more matter you have in one "place" the slower time flows. Enough matter in one place, time stops.

[stewiesaidthat]

Clocks in motion run slower than stationary clocks due to the simple fact that the frame of the clock is accelerated and not its power source.
The easiest wave to visualize it is two objects traveling in space, one accelerates, and the other one doesn't. You are an observer only. The cells of your body are in a different frame, being accelerated in time by the action of the heart and lungs.
You are trying to apply the workings of a mechanical clock to those governing biological processes. There is no correlation other than the 24-hour day/night cycle in which plants and animals have evolved. Have you actually changed how much force is being applied to each cell in your body simply by traveling faster in space?

[PierreIsmail]

You can resolve the “paradox” without regard to acceleration. All you have to do is add a 3rd observer at a distant point. Imagine a straight line from left to right with Earth>Rocket>3rd Observer. From the Earth’s pov, it’s the rocket that is going away, but the 3rd observer is stationary relative to the Earth. From the rocket’s pov, it’s the earth that’s going away, but the 3rd observer is getting closer.  From the 3rd observer’s pov, the earth is stationary, but the rocket is coming closer.

Therefore the Earth & 3rd observer agree that the rocket is the one that is moving, it’s the rocket that breaks the symmetry.

Forget acceleration, just imagine you have a ship that can instantly go 99% the speed of light.

Btw, the rocket does NOT need to return to earth to experience the slowing of time.

Here's another way to think about it: imagine a very large sphere with many observers positioned on the shell of the sphere. A spaceship is traveling inside the sphere from one side to the other. All observers will agree that they are stationary relative to other observers on the sphere AND they will also agree that it's the spaceship that's moving.

A person inside the spaceship looking at multiple observers on the sphere can no longer claim that the ship is stationary because in effect there are now many reference points (some moving away, while others are moving closer).

[michaelccopelandsr]

My idea so I get to name it! What I mean is, no one has claimed it so I'm officially calling, "Dibs."  Voyager 1 is now in the, "Milky Way's interstellar time" or "Mikey's Time."
"V-ger's" message has sped up now that it's outside our Sun's, "Time Bubble, " or, "Terran Time."  It will be faster, still, when "V-ger" sends a message from beyond the Milky Way's time bubble. Then there's Outside the Local Group time bubble.  So on and so on until we get outside any influence and into the, "True Interstellar Time Standard." Or, "T.I..." ;-P
Now that "V-ger" is outside our Sun's reach, in interstellar space, it's now in the Milky Way's faster moving, Interstellar Time or "Mikey's Time."  This can be proven by turning off everything except its clock and transmitter.  Have "V-ger" read time for as long as possible.  They WILL show the flow of time speeds up the further away you get from any celestial bodies.  Until you reach the Milky Way's time standard or "Mikey's Time."
•Our sun's time bubble: "Terran Time" we know and have measured.  In a lifetime, our head is one second younger than our feet.
•Milky Way's time bubble or "Mikey's Time." The rate/flow of TIME outside any influence but within the Milky Way: We just got there and are still figuring what the difference is. Wild guess I'd say time will increase in speed, now and until V-ger is outside the Ort cloud.
•Local Group's time bubble or the rate/flow of time outside of any influence but within the Local Group: Name still open and unknown. Wild guess .08 P-22% to a couple seconds faster, maybe. Used just for reference.
•Outside any influence in the, "True Interstellar Time Standard." (or T.I...) ;-P  This name is NOT up for grabs. The rate/flow of time is fastest here.  (Time flows fastest here so it's best to use a motor boat and hold tight.  Always applies when you're in T.I....) ;-P
A minute is a minute in all. It's the rate/flow I'm talking about.  Heck, rivers of time flowing differently might explain dark energy and dark matter.
The Milky Way's Interstellar Time Standard will be known as, "Mikey's Time."
Pass it on, please and thank you!

[lulufrumusica]

If Carol moves relative to Bob, they cannot agree on the simultaneity of the moment when they sync their clocks. You are assuming that Carol syncs her clock with Bob's at the same time Bob meets her at Betelgeuse. This is not the same moment Bob measures on his own clock.
Syncing clocks is not possible unless the observers are at rest relative to each other. That is the reason why both twins are needed to be at rest on Earth at the start of the experiment.
For the same reason why you cannot measure the one-way speed of light, you cannot solve twin's paradox in special relativity.

[surfraider]

Let's say all these space cadets are physically identical, including a convenient anatomical appendage that works just like a pendulum. Set them loose on their various journeys through space and gather them together after their journeys. Whoever's pendulum swung the most is youngest.

[stewiesaidthat]

Mechanical clocks don't measure time. They measure motion in space. A slower running running clock just means it is experiencing more space.
They neophyte Einstein combined space and time and has you all confused.
Riddle me thus. Why, when you shine a light on a solar sale, is it accelerated in space. And yet that same force accelerates a plant in time.
Why do synchronized clocks, one mobile, the other stationary, use the same amount of energy. One is experiencing more space/gravity than the other.
The ONLY way to age less in space for humans is cryostasis. For plants, if you don't allow for the redshifting of electromagnetic waves when in motion, the plant will receive less sunlight and thus have less growth. But that's not relativity. That's elementary physics. Which the majority of you don't understand because you live in Einstein’s fantasy universe.

[massimilianodellaguzzo]

I believe that the twin on Earth is younger, if we consider the motion of the Earth in the frame of the spaceship. (round trip)
And this is not a defeat, the motion of the spaceship (in the frame of the Earth) is different from the motion of the Earth. (in the frame of the spaceship)
I understand that we can disagree on this, but time dilation is symmetrical.
In my opinion the acceleration is not important, accelerating means moving at a constant speed during infinitesimal instants of time dt.
You did a great job though, I enjoyed your video!😊