Do We Need General Relativity To Solve The Twin Paradox?

There seems to be still a disagreement whether the General Relativity is required to solve the famous Twin Paradox. In this video I will talk about why are people divided about this topic and hopefully bring more light on the whole issue.

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[dialectphilosophy]

Really appreciated two things about this video: 1) Your clarification that SR treats inertial frames as given — something you’re likely to get pushback on from commenters (as we once did) but about which you’re absolutely correct. 2) Your noting that proper acceleration as a solution doesn’t generalize to GR — something almost everyone who treats on the topic of the twin paradox overlooks.

In our long study of the twin paradox, we learned that, within the context of the current theories of relativity, there is only one “resolution” to who is younger — and that is whichever twin traveled the shorter spacetime path. In flat spacetime, this will always be the accelerating twin, while in curved spacetime considerations of the metric will determine who travels the shorter spacetime path.

But of course, if one asks, what is the physical meaning of spacetime distance — the only answer the theory can give is that it is the amount of proper time which elapses on a co-moving clock. So the “resolution” to the twin paradox is precisely this: the twin who comes back younger is the twin who experiences less elapsed proper time. Quite tautological.

The problem you may or may not be grasping is that Relativity is not a theory of causes, it is a mathematical description of correlations between measuring instruments/coordinate systems. And the paradox of the twins is essentially not asking what breaks the symmetry, but asking what causes time dilation in the first place. And as both we know, Relativity can’t answer that question.

Indeed it seems you still have not grasped the full significance of the one-way-speed-of-light problem. If nothing requires observers to choose epsilon = 1/2, then the twins can choose appropriate epsilon values such that they both agree that it is the traveling twins clocks that are running slower — and so there is no paradox in the first place. Of course, everyone’s understanding progresses at its own pace, and there was a time when we too still believed relativity to be correct, and dismissed all those who told us that only an ether could explain time dilation as essentially crackpots. Sometimes one must taste the medicine they dish.

[helifynoe]

Changing the direction of travel of your spaceship, such as going in circles, is said to be "Acceleration", in the world of physics. That sounds a bit confusing. Meanwhile, if your spaceship travels in a straight spatial line, but constantly accelerates while in the process of doing so, it too in truth is also constantly changing its direction of travel. All this goes on, while the magnitude of the motion of the spaceship, NEVER actually changes. All that can be changed, is its direction of travel. Within the 4D space-time environment, the more your spaceships ongoing motion is directed to being across space, the less of your ongoing motion is now directed across the dimension of time. Taking this 4D perspective into account, throws the paradoxes out the window.

[BlueMoonshine]

General Relativity is not required, as Special Relativity is perfectly capable of dealing with accelerated frames of reference, as proven in the tutorial.

[asherweinerman]

I've really enjoyed this video and the one about whether or not falling charges radiate. My opinion is that in the framework of Special Relativity we are allowed to make a measurement to decide if we are accelerating. It could be an accelerometer, or just letting go of a golf ball in front of our eyes and seeing whether it changes speed. I think we are allowed to interpret the result of such an experiment within the framework of SR and measure our acceleration that way. The falling charge is fascinating, and after looking into it for some time I have to agree with Feynman. It solves all the paradoxes and preserves the equivalence principle if only a charge whose acceleration is changing produces radiation.

[Physicslover]

Bro is Length contraction Really An effect of superposition or Quantum wave mechanics ?As Dialect proposed in his interpretation of Relativity and Length contraction can You make a video about it

[rebeljackbrewingco]

SR doesn't say anything about acceleration.

Each observer is given identical clocks and measuring rods. One moves at constant velocity, the other doesn't. In SR it doesn't matter who is A and who is B. They both measure the same values within their respective inertial frames, for example, they measure the same value for the speed of light. Time dilation and length contraction falls from a comparison of A to B or B to A. Without the comparison there is no time dilation nor length contraction. Both will experience time dilation and length contraction depending on the point of view. A says B is moving. But B says A is moving. Swap your perspective and you get the same answers.

The twin paradox arises because we compare the twins (thru observation of clocks) and say one is older than the other (time dilation). We define a point of view and define 'who' is 'moving'. We interpret that time dilation to be persistent once both twins return to the same inertial frame. Is it real? Perhaps neutrino decay is the best evidence for this?

But, isn't there a larger concern here? If it is real, then can't we claim there is a preferred inertial frame. Wouldn't such a preferred inertial frame justify the ether? Wouldn't an ether change physics completely? Suppose that the ether could be explained as a series of coupled mechanical pendula.

Special Relativity Hidden in a Series of Coupled Mechanical Pendula

[cai_o]

It's simpler than we all imagine, you don't always see things in slow motion when you move, sometimes you see things in fast motion, things in the direction of motion move in fast motion, if you hover above a gravitational field, the universe above you is in fast motion.

If you were to move very fast in the direction of Proxima Centauri, you would see it in fast motion, because you are moving in relation to it. When you get there, your're younger.

When you reach it, it's older than it would've been if its aging were only determined by the time light takes to reach you, and you catching the light rays faster as you get close to it.

You don't need acceleration, you don't need to go back to "compare clocks" and you don't need to be close to it beforehand.

[DrDeuteron]

So when I think about measurements in internal frames and use the verb "see", I never think about light reaching the observer. I think about his infinite lattice of graduate students with synchronized clocks and calibrated rulers, and "see" means what does the grad student who is at the distant event "now", at the time of seeing, measure.
Right before turn around, the space twins grad student (bob) sees a younger earth twin. Then bam, turn around happens. Bob still sees a younger twin on earth, but bob is no longer synchronized with his adviser space twin. Space twin needs a whole new lattice of grad students, and the one he needs on Earth is a much older bob (if bob waits). This new grad student is now standing next to a much older Earth twin, who ages more slowly on space twins return trip.

[juliavixen]

Didn't you mention in a previous video that you can rotate your accelerometer by 90° and know that if there's no change then you are in an inertial reference frame? (Proper acceleration will make your accelerometer different in each orientation.)

[DrDeuteron]

The answer is a firm NO. In SR, you can work in Minkowski space and integrate proper time along a world line and get the answer without contradiction. Thus SR is enough, because it is a self-consistent theory.

The reason you get a paradox is when you leave Minkowski space and work in 3 + 1 frames. The paradox is not the asymmetry, its that each twin sees the other's clock tick less time on each leg, so the sum of elapsed times disagree,

Ofc the paradox is resolved when you remember a line takes the form: y = mx + b, and we're just looking at "m" (time dilation), you need to include "b" (clock bias), and that changes at turn around.
It's not time dilation---you can make b "run" forward or backward--it's just clock bias (see Andromeda paradox).
Now you can invoke GR, and ofc it gives you the correct results, but it is absolutely not necessary.

If you want to describe it in apparent physical terms, it really is paradoxical, in the limit of zero turns around (TA) time: Space twin ages zero TA, Earth Twin sees space twin age zero during TA, Earth twin sees Earth twin age zero during TA, but Space twin just picks a whole new "now" on Earth that is much later. It's not aging, it's just a new now. You know it's not aging, because if he turns around again, boom Earth twin is young again.
This is the Andromeda paradox, where "now" at distant locations depended on which way you drive your car here on Earth, and ofc, the ppl living in Andromeda don't care.

[robdev]

Great video. Just one minor thing to add. Those who argue that the Twin Paradox can be resolved by simply considering inertial frames and use the Triplet example to show this to be the case, miss the obvious; The ‘Triplet Paradox’ is not the ‘Twin Paradox'! The Twin Paradox requires the twin to return to Earth, and hence accelerate. The Triplet example leads to a different paradox; Namely, when B and C pass each other they both agree they are the same age. A also agrees that B and C are the same age. But B and C disagree on the age of A.

[hpeterh]

I think it is easy to proof that relative velocity difference does not necessarily cause relative time dilation.
Instead of twins consider triplets. L travels to left, E remains on earth, R travels to right with exactly same, but exactly opposite acceleration as L.

There will be no time dilation between L and R, despite the HUGE difference velocity, but both will have time dilation against E.

Also, if we only use SRT with straight lines then infinite acceleration within zero time at the starting, ending and turning point must be assumed. This is impossible to calculate. When it is neglected, we get an error.

[sakismpalatsias]

Out of curiosity, though I completely understand the physical manifestation of the measurements, of two Reference frams.

What is occurring in the space of two different frames. Ie. At the quantum level, what is occurring in the interactions, especially in different gradients of a gravitational field.

Ie not simply the passage of time but the physical mechanics of the gradient in time dilation. Like... Is there an adjustment (phase change) to renormalization. I'm curious if there is research on the subject that you may provide links too.

[Buzz_Purr]

The difference in age of the twins doesn't come from time dilation, time dilation is symmetrical.
However, length contraction is not symmetrical.
While the stationary twin sees the rocket shorter, the traveling twin sees the entire length of the trip shorter.
So the traveler needs less time to complete the journey.

What exactly happens during the acceleration phases doesn't really matter for the twin paradox.
As Lukas said, it can be made arbitrarily short.

[dave_m]

Very clear, as usual. Interesting "fact": in a not so popularly known formulation of the paradox, one twin is on earth, subject to earth's gravitational acceleration (ok, the floor imparted acceleration upwards... of 9, 81 m/s^2) while the travelling twin starts from a high tower. Bear with me; the final makes one reflect on the nature of 3D-space.

Well: Since he's starting from a high tower, with lesser gravitational strength, he can "use" the difference (say he's subject to 9, 80 m/s^2, not 9, 81) of 0, 1 m/s^2 to move further up. As he gets away, the gravitational strength diminishes, so, in order to maintain his acceleration equal to the other twin's (=9, 81 m/s^2) more and more "moving" acceleration becomes available.

When the earth's gravitation becomes negligible, due to the *inverse square law*, the 9, 81 m/s^2 are used practically only to increase his velocity. Then, to invert the motion he takes on a speed higher than orbital velocity around the - now far away - earth, so that he must maintain himself centripetally accelerated at 9, 81 m/s2 while turning around, and finally heads back home, where he then decelerates, always maintaining his "perceived weight" at 9, 81 m/s^2 against the spaceshift's floor.

And, when he returns, he's younger. But the difference is only one: earth's gravitational field is spatially limited, whereas the "apparent" gravitational field arising from the (absolute) acceleration is not.

So when the "fictitious", spatially infinite gravitational field acts, the one making time go faster on earth (therefore making the earthbound twin age faster) *from the travelling twin's perspective*, it acts at the *distance* between "orbital" (not really) motion and the earth. We call it "Radius", obviously.

Now: different journeys with combinations of parameters: acceleration, journey duration, distance reached, etc... will result in different experiences, and different age offsets between twins.

For example:

A- if you decide to "orbit" (not really: you have to maintain centripetal acceleration of around 9, 81 m/s^2 = 1 g) *very far away*, you'll experience 1g centripetally only to sustain circular motion; but here, far from earth, the circle is very wide: much time is needed to complete at least 1 circle to head back home. The circumference is = 2*pi*Radius.

B- decide for a lower "orbit"? but then you've got to accelerate less - and for a shorter duration, as you're not so far away and the circumference isn't big - to invert the motion, because there's still a non negligible earth's gravitational field _helping_ you turn without accelerating. Being - "nearby" means that the "fictitious" gravitational field that you feel acts at a lesser distance and makes the earthbound twin age faster (from your perspective) at a much much lesser rate during that phase of accelerated motion, than in the previous (earth far away) example! Also, your proper time offset from pure SR isn't big, because the whole experience takes less time, distance, etc...

Now, maintaining the relation between radius and circumference (2*pi), suppose we ask for the *gravitational strength <-> distance relation* that has to be in place for a traveller that stays in the loop for a certain fixed duration and ends up experiencing a certain *fixed* age offset between stationary and travelling twins.

The result is NEWTON's INVERSE SQUARE law for the gravitational

(the initial "tower" is only a kickstarter, a "trick" and can be reduced to zero at the limit)

[jeffguarino]

Leo Moser posed the problem of the largest sofa you can move down a hallway and around a 90 degree turn. I just wonder if you could use length contraction to move a very long object down this hallway and around the turn as along as it maintains its high speed in the straight portions of the hallway and accelerates around the turn maintaining its speed? I don't understand how to do the math and if it could actually make the turn in the hallway. I know the car that is too long for the garage can fit from the stationary observers frame but how would this apply to an object too long to make a turn in a hallway ?
Could you look at this problem, it might make an interesting video. I already asked this question on the stack exchange and pretty well got brushed off. They told me length contraction was not real and was just apparent. Also got a bunch of other non answers that it was off topic.

[chrimony]

@10:50: "Whereas the observer accelerated in a rocket detects a uniform gravitational field spanning the entire universe."

[pawegawe]

9:06
I disagree. Special relativity tells us why you should be younger if you change inertial frames. The twin that turns around jumps to an inertial frame for which events on Earth occurred earlier than for the frame it jumps from.

[juliavixen]

For everyone who keeps saying that "we don't know the one-way speed of light" as someone kind of "gotcha!" (as if it actually matters in this case at all) (and, as if the Compton Edge Experiment hasn't measured the speed of light to be isotropic to within one part in 10⁻¹⁴) (and, you know, Maxwell's Equations, etc.)

​Here's a really good argument that the speed of light would violate the conservation of energy if it did not propagate at the same velocity in all directions:

[sdutta]

I am confused by something I thought you said: my clock will tick slower if I am moving at uniform velocity wrt another, external Observer. I thought that wrt to my own inertial frame of reference, there is NO time dilation. So my clock would APPEAR to tick slower to the Observer but not to ME. I hope you agree so far. In your example, my elapsed time would be 5.75 years, from my perspective, before I turned around, although to the Observer it would seem like 2.84 years. When Observer and I meet again, after I turned around, my clock would have recorded MY time, which would be 11.5 years, not the time (5.75 years) that Observer thought I had clocked. The Observer looking at my clock when we are “sitting across a table and wondering who is older”, is no longer the scenario where we were moving relative to each other at near-light speed. My point simply is: my clock recoded my time, not the time perceived by Observer. So the so called “paradox” may be a “red herring”. Am I missing something?