Do Twins Age Differently in Space?

[Chris Miller]

Twins leave Earth in opposite directions, accelerate at the same rate until their relative v = ~c, hold this v for 20 years (or however long), then decelerate at the same rate to v=0, and accelerate at the same rate back towards Earth until their relative v again =~c, hold for same amount of time, then decelerate at the same rate until they reunite where they started. For the entire journey, wouldn't each have seen the other as aging much more slowly? Are they the same age now? How much time has passed on earth?

 

[Ibix]

They'd be the same age. A triplet at home would be older. Look up Orodruin's Insight on the geometric resolution of the twin paradox.

Edit: one of the learning points of the twin paradox is that time dilation isn't anywhere near the whole story.

 

[Chris Miller]

Thanks, that's what I thought. So even though each twin "saw" the other as aging more slowly for the entire trip, they are the same age when they reunite. It's like their triplet's/earth's frame or reference retroactively reverses their in-trip observations.

 

[Orodruin]

To boil it down: The time dilation formula is based on the assumption of the simultaneity in a particular frame. This notion of simultaneity will differ from frame to frame and will therefore change as an observer accelerates.

Note that time dilation does not describe what an observer actually sees, but what it can deduce happened. In order to find out how it would actually look you would need to take the finite travel time of light into account.

 

[Ibix]

Thanks, that's what I thought. So even though each twin "saw" the other as aging more slowly for the entire trip, they are the same age when they reunite. It's like their triplet's/earth's frame or reference retroactively reverses their in-trip observations.

No. Their observations are always consistent with the notion that the travellers will be the same age when they return. The Earth frame does nothing. It's just a choice of coordinates.

 

[Orodruin]

Look up Orodruin's Insight on the geometric resolution of the twin paradox.

Oh, and the easiest way to find this text is by following the "My Insights" link in my signature.

 

[rede96]

even though each twin "saw" the other as aging more slowly for the entire trip

If it were possible for each twin to observe the other for the entire trip then they couldn't see each other as ageing slower for the entire duration. That would be like Twin A watching Twin B's clock running slower for the whole trip and then suddenly at the end of the journey the clock jumps forward to the same time as Twin A

I'm not too sure what twin A would observe if he could watch Twin B's clock for the entire journey but what ever he sees it must symmetrical (e.g. if he sees twin B's clock running slower then at some point he must see it running equally faster.) as the two clocks have to read the same time again at the end of their journeys.

 

[Bandersnatch]

Have a look here:
http://www.einsteins-theory-of-relativity-4engineers.com/twin-paradox-2.html
It includes diagrams with 'messages' being sent between twins. The short story is, during the outbound trip the messages arrive in longer intervals than they are sent (equivalent to 'seeing time slow down'), while during the return trip, the intervals are shorter.

 

[Chris Miller]

To boil it down: The time dilation formula is based on the assumption of the simultaneity in a particular frame. This notion of simultaneity will differ from frame to frame and will therefore change as an observer accelerates.

Note that time dilation does not describe what an observer actually sees, but what it can deduce happened. In order to find out how it would actually look you would need to take the finite travel time of light into account.

Thanks, Orodruin. I get that acceleration impacts t dilation, which is why I kept it symmetrical. I also get that neither can really observe in "real" time the other's clocks (biological or mechanical). But, for the purposes of this thought experiment, can I not assume some sort of instantaneous (say entanglement based) method of observation? In any case, what both deduced was occurring, via SR, clearly was not, or was retroactively undone?

 

[PeroK]

Thanks, that's what I thought. So even though each twin "saw" the other as aging more slowly for the entire trip, they are the same age when they reunite. It's like their triplet's/earth's frame or reference retroactively reverses their in-trip observations.

If you are serious about learning SR, you need to knuckle down and study the relativity of simultaneity and the so-called leading clocks lag rule, which lies at the heart of these problems.

Coming up with a pseudo explanation like this is not the real understanding.

 

[Orodruin]

If it were possible for each twin to observe the other for the entire trip then they couldn't see each other as ageing slower for the entire duration. That would be like Twin A watching Twin B's clock running slower for the whole trip and then suddenly at the end of the journey the clock jumps forward to the same time as Twin A

I'm not too sure what twin A would observe if he could watch Twin B's clock for the entire journey but what ever he sees it must symmetrical (e.g. if he sees twin B's clock running slower then at some point he must see it running equally faster.) as the two clocks have to read the same time again at the end of their journeys.

This is exactly what you will find if you compute what the observers will actually see, as mentioned in my previous post. This is not what time dilation is about. Time dilation is about what time coordinates are assigned to different events in a particular frame and its comparison to the proper time.

This is based on the notion of simultaneity in the particular frame and changes when you change reference frame by accelerating.

 

[Chris Miller]

If it were possible for each twin to observe the other for the entire trip then they couldn't see each other as ageing slower for the entire duration. That would be like Twin A watching Twin B's clock running slower for the whole trip and then suddenly at the end of the journey the clock jumps forward to the same time as Twin A

I'm not too sure what twin A would observe if he could watch Twin B's clock for the entire journey but what ever he sees it must symmetrical (e.g. if he sees twin B's clock running slower then at some point he must see it running equally faster.) as the two clocks have to read the same time again at the end of their journeys.

And yet this (each seeing the other's clocks running slower for the entire trip) is exactly what SR predicts they would each observe, which is why it's called a paradox, I guess.

 

[PeroK]

Thanks, that's what I thought. So even though each twin "saw" the other as aging more slowly for the entire trip, they are the same age when they reunite. It's like their triplet's/earth's frame or reference retroactively reverses their in-trip observations.

If you are serious about learning SR, you need to knuckle down and study the relativity of simultaneity and the so-called leading clocks lag rule, which lies at the heart of these problems.

Coming up with a pseudo explanation like this is not the real understanding.

 

[Orodruin]

can I not assume some sort of instantaneous

No

Even if you could it would depend on which frame you want it to be instantaneous in. If it is instantaneous in one frame it will not be in another (it will be an FTL communication that could a priori go back in time). This is at the very core of relativity and is called the relativity of simultaneity: what is "at the same time" in one frame is not "at the same time" in another.

Failing to understand the relativity of simultaneity is likely responsible for more than 90 % of the misconceptions beginners have of relativity. Understanding it is crucial if you want to have any chance of understanding SR at a deeper level than popular science.

 

[PeroK]

And yet this (each seeing the other's clocks running slower for the entire trip) is exactly what SR predicts they would each observe, which is why it's called a paradox, I guess.

It's what you think SR predicts, because you only know about time dilation. SR is more than just time dilation.

 

[jbriggs444]

I get that acceleration impacts t dilation

Acceleration does not affect time dilation. Acceleration results in a change of synchronization convention.

 

[Chris Miller]

Acceleration does not affect time dilation. Acceleration results in a change of synchronization convention.

so acceleration is not the same as a gravity (feels the same though), been wondering

 

[Chris Miller]

No

Even if you could it would depend on which frame you want it to be instantaneous in. If it is instantaneous in one frame it will not be in another (it will be an FTL communication that could a priori go back in time). This is at the very core of relativity and is called the relativity of simultaneity: what is "at the same time" in one frame is not "at the same time" in another.

Failing to understand the relativity of simultaneity is likely responsible for more than 90 % of the misconceptions beginners have of relativity. Understanding it is crucial if you want to have any chance of understanding SR at a deeper level than popular science.

I'm not sure I have the grey matter or mathematical chops to understand SR well. It'd be nice not to totally embarrass myself writing SF, though. And, so far, this site's been helpful in that regard.

PS

Aren't entanglement's changes simultaneous across any distance? And so FTL?

 

[jbriggs444]

so acceleration is not the same as a gravity (feels the same though), been wondering

No. You continue to misunderstand.

Gravity is the same as an acceleration. That's the equivalence principle. But gravitational acceleration is NOT associated with time dilation. Gravitational potential is. The distinction is that potential is a combination of an acceleration and a distance.

Accelerations in special relativity can be interpreted as an incremental change of reference frame and an associated incremental change of clock synchronization. The amount of clock change scales with distance. A mere acceleration is not enough. You need an acceleration and a remote clock some distance away.

 

[Mister T]

And yet this (each seeing the other's clocks running slower for the entire trip) is exactly what SR predicts they would each observe, which is why it's called a paradox, I guess.

It's not a real paradox, it's an apparent paradox. This is why you often see it referred to as the Twin Trip or some such, as it really doesn't deserve the name Twin Paradox. A less complex apparent paradox is the symmetry of time dilation, which really ought to be resolved before tackling the twin paradox as glossing over it means you'll forever find the twin paradox baffling.

But to address the issue you raise, imagine each twin with a flashing strobe light. Let's call these strobe lights clocks, as they send out the flashes at regular intervals, say once per minute. When each is at rest relative to the other, the rate at which the flashes are seen by one twin is equal to the rate at which they are sent by the other. But if there is relative motion between the twins, that will not be the case. When moving apart each will see the other's flashes as slow, but when they approach each other, each will see the other's as fast. Now this speeding up and slowing down of clock rates is due only partially to time dilation, the other part being due to light travel time. So each will see the other's clock as running fast or slow depending on whether they are approaching or receding, but if you subtract off the part of the effect due to light travel time, then each will observe that the other's clock is running slow, regardless of whether they are approaching or receding.

So what you see is different from what you observe.

Anyway, if you go through the details you will find that after the twins reunite to compare notes, the number of flashes that each sent will equal the number of flashes that the other received. But they may not agree on the time that elapsed between the flashes, and when the total time between flashes is added up, they may get different sums.

Now, if the journeys are symmetrical in the way you propose, the sums will match. But a triplet that stayed home will get a larger sum.

There's a hokey old cartoon that can you find by searching YouTube for "Paul Hewitt Twin Trip". The physics is solid.

 

[Dale]

And yet this (each seeing the other's clocks running slower for the entire trip) is exactly what SR predicts they would each observe

No, this is not at all what SR predicts. Not only is it not what they visually observe, there is also no reference frame where that is what they calculate to be true.

What they would observe is the other twins clock being redshifted during the first part, normal in the middle, then blueshifted during the last part. They end with the same elapsed time.

In the Earth's frame they are always equal. They end with the same elapsed time.

In an inertial frame where one twin is initially at rest then the other will start slow, but the first will end slow. They end with the same elapsed time.

In a non inertial frame the math is complicated. They end with the same elapsed time.

No matter what frame you pick, if you actually do the math... They end with the same time.

It's like their triplet's/earth's frame or reference retroactively reverses their in-trip observations.

No, it is nothing like that at all.

 

[Chris Miller]

It's not a real paradox, it's an apparent paradox.

That's why I quoted it in my question.

...but if you subtract off the part of the effect due to light travel time, then each will observe that the other's clock is running slow, regardless of whether they are approaching or receding.

This, and your entire explanation was extremely helpful/interesting (even the cartoon!). Although I still don't understand how, if each (after discounting light travel time) sees the other's clock running slow for the entire journey (as SR would predict) how their (discounted) sums match at the end.

 

[jbriggs444]

This, and your entire explanation was extremely helpful/interesting (even the cartoon!). Although I still don't understand how, if each (after discounting light travel time) sees the other's clock running slow for the entire journey (as SR would predict) how their (discounted) sums match at the end.

Read up on the twin's paradox. The explanation that I gravitate to is that the accounting from the traveling twin's point of view skips part of the aging process of the stay-at-home twin. At turnaround his notion of what age his twin is "right now" changes. He matches up the first bit of his twin's aging to his outbound trip. He matches up the last bit of his twin's aging to his return trip and never accounts for the part in between.

 

[robphy]

If it were possible for each twin to observe the other for the entire trip then they couldn't see each other as ageing slower for the entire duration. That would be like Twin A watching Twin B's clock running slower for the whole trip and then suddenly at the end of the journey the clock jumps forward to the same time as Twin A

I'm not too sure what twin A would observe if he could watch Twin B's clock for the entire journey but what ever he sees it must symmetrical (e.g. if he sees twin B's clock running slower then at some point he must see it running equally faster.) as the two clocks have to read the same time again at the end of their journeys.

Here's a diagram based on my Relativity on Rotated Graph Paper Insight.
(You can use https://www.geogebra.org/m/HYD7hB9v to draw parts of the diagram below.)

In the frame of the stay-at-home twin (on which the gridlines of the rotated graph paper are based),
we draw the ticks for each "traveling" twin (each with speed (3/5)c).
Then, I show the light signals sent by the "positive-x" twin... Think of it as the "negative-x" twin watching an 8 hour tv show broadcast by the "positive-x" twin.
Due to their relative motions, the viewer sees that show with irregular timing.
(You can imagine that each has the same 8-hr movie started at separation...and that one twin is comparing the received broadcast with her own local playback of the movie.)

The ticks of the stay-at-home twin are not shaded in... but you can shade them into realize that
at reunion, 10 ticks elapse for the stay-at-home twin while 8 ticks elapsed for each of these symmetrically-traveling traveling-twins.

You could also analyze what each (traveling or stay-at-home) twin sees from the other two twins.
You could also try asymetrical twins, as well as trips with asymmetrical there and back legs.

(One could try to interpret the situation using light-travel time corrections and change of lines of simultaneity, etc... but I feel that this presentation is direct and to the point.)

 

[Nugatory]

Although I still don't understand how, if each (after discounting light travel time) sees the other's clock running slow for the entire journey (as SR would predict) how their (discounted) sums match at the end.

The quick answer is that special relativity does not predict that each one SEES the other's clock running slow . We've already discussed what the twins SEE at some length, and there's also a good explanation of what they do SEE in in the "Doppler analysis" section of the twin paradox FAQ.

If you haven't already read that FAQ in its entirety, do so now. It covers the asymmetric case in which one twin stays on Earth while the other flies out and back, but until you clearly understand that case you won't be ready to take on the symmetric case.

 

[Chris Miller]

The quick answer is that special relativity does not predict that each one SEES the other's clock running slow . We've already discussed what the twins SEE at some length, and there's also a good explanation of what they do SEE in in the "Doppler analysis" section of the twin paradox FAQ.

If you haven't already read that FAQ in its entirety, do so now. It covers the asymmetric case in which one twin stays on Earth while the other flies out and back, but until you clearly understand that case you won't be ready to take on the symmetric case.

I've read the Twin paradox and get EM Doppler effect and that acceleration (GR) muddies the waters. "See" is clearly a bad word to use. SM doesn't predict what they would literally "see." But does it predict the rate at which each would expect the other's clock to be running?

 

[Ibix]

Special relativity, as normally presented, provides a way to relate the tick rate of someone else's clock after lightspeed delay is corrected for, yes. However, there is some flexibility in what "correcting for the lightspeed delay" means, and the "natural" way of doing it leads to different answers for different people, and different ideas about what "at the same time" means. Accounting for the latter is one way to resolve the twin paradox, as @jbriggs444 says above.

 

[Dale]

if each (after discounting light travel time) sees the other's clock running slow for the entire journey (as SR would predict)

SR does not predict this. This is not predicted as a visual observation, and it is not predicted (after discounting light travel time) in any inertial frame nor in any valid non-inertial frame.

Here is an example of a valid non-inertial frame, with the analysis for the standard twins scenario. It also explains why the naïve approach is not a valid non inertial frame.

https://arxiv.org/abs/gr-qc/0104077

 

[Dale]

But does it predict the rate at which each would expect the other's clock to be running?

SR predicts the rate of change of proper time with respect to coordinate time for any clock and for any valid coordinate system. You must specify both the clock and also the coordinate system in order to get such a rate.

 

[PeterDonis]

does it predict the rate at which each would expect the other's clock to be running?

It predicts this given the assumption that each twin is at rest in a fixed inertial frame. But if the twins separate and then meet up again, this assumption must be false for at least one of them. In the standard twin paradox, it's false for the traveling twin. The "time gap" page of the Usenet Physics FAQ article that Nugatory linked to discusses this.

 

[DrGreg]

It's not a real paradox, it's an apparent paradox.

To be pedantic, it is a paradox, because the word "paradox" has more than one meaning:

Paradoxically, the word "paradox" has (amongst others) two meanings that are almost opposites:

1. an argument that comes to a false conclusion (e.g. contradicts itself), via steps that appear, at first, to be valid
   
2. an argument whose conclusion may appear, at first, to be false, but is actually true

The "twins paradox", like some other paradoxes in maths and physics, is a paradox of the second type.

In this post I used "paradoxically" with a third meaning, "having apparently contradictory characteristics".

 

[Ibix]

I've argued that it is a paradox by definition 1 if one misunderstands relativity in a particular way common among beginners. It's not a paradox under a correct understanding of relativity. Hence the resolution is to realize that "time runs slowly at high speed" is not really true. Or at least, is rather incomplete.

 

[Mister T]

This, and your entire explanation was extremely helpful/interesting (even the cartoon!). Although I still don't understand how, if each (after discounting light travel time) sees the other's clock running slow for the entire journey (as SR would predict) how their (discounted) sums match at the end.

Thanks, but let's sort something out here. The cartoon uses the Doppler effect to analyze the usual twin paradox, where one twin stays home and the other travels. In this scenario it is not appropriate to say each sees the other's clock running slow, because sometimes they see them running fast. When you do the sums at the end there is no need to worry about any delays due to light travel time because each twin is simply taking a sum of the times elapsed between flashes at his own location.

If you want instead to analyze things a different way and focus on that oft-repeated phrase that each observes the other's clocks to be running slow during both the outbound and inbound phases, then you have to account for the fact that when the traveling twin turns around his entire notion of what's happening "simultaneously" back home gets shifted. It's an understanding of that shift in the notion of what's simultaneous that's needed to understand how the symmetry of time dilation can account for the twins' different ages.

 

[Jeronimus]

And yet this (each seeing the other's clocks running slower for the entire trip) is exactly what SR predicts they would each observe, which is why it's called a paradox, I guess.

They don't see but measure/calculate each others' clocks to go slower. More precise, they calculate the clock count of the instances of each others' clocks which cross the simultaneity axis to be lagging behind the clock count of a stationary clock local to them.

It is also not true that they measure each others' clocks to be running slower for the ENTIRE trip. The stay at home twin will measure/calculate the traveling twin's clock instance that lies on the simultaneity axis( where the worldline of the clock crosses the simultaneity axis) to be running slower by the same factor as the traveling twin measures the stay at home twin's clock to be going slower, with the exception of the acceleration phase.

At the acceleration phase/turn around phase, the stay at home twin will measure the travellings twin's clock to be running slower still while the traveling twin "breaks" to a halt. At the halt point, logically their clocks would be running at the same pace again for a very brief moment of time, followed by further acceleration towards the stay at home twin where the stay at home twin measures the traveling twin's clock to start ticking slower again until it ticks slower by the same factor as before, once max relative velocity is reached.The traveling twin measures something different in the acceleration phase. Whole accelerating back, the traveling twin will measure/calculate the stay at home twin's clock to be ticking much faster than his. Faster the higher the magnitude of the acceleration. If the acceleration was to be near instantaneous, he would see the clock count of the stay at home twin's clock to "jump" up a considerable amount. After the acceleration, back to the same relative velocity as before, he would again measure the stay at home twin's clock to be ticking slower by the same factor as before.

You can see what happens exactly in the video here, where the lorentz transformation formulas have been used to map events that happen at x,t measured by the stay at home twin (left diagram) to x', t' in the right diagram, which represents the traveling twin's perspective.



On the left diagram, the cyan coloured clock represents the stay at home twin's clock measured from the stay at home twin's perspective, while the white clock is is the what we _interpret_ at the traveling twin's clock.

In the right diagram, the white clock represents the traveling twin's clock from the traveling twin's perspective, while the blue clock is what we _interpret_ as the stay at home twin's clock.

What are the numbers and what are the moving circles/dishes in the diagrams? Generally speaking, those are all events which in the left diagram happen at x,t and are then mapped to the right diagram where they are measured at x',t', using the Lorentz transformation formulas.

More detailed, the numbers represent clock counts. In the left diagram, all but the traveling twin's clock are at rest seen from the stay at home twin's perspective, which is why you see the instances of the clocks, displaying different clock counts, all being on an (imagined) straight, vertical worldine.

A clock that is measured to be at rest from the perspective of the stay at home twin, would be measured to be moving from the perspective of the traveling twin, and therefore the instances of a certain clock which is at rest relative to the stay at home twin and are on a (imagined) vertical line on the left diagram, will be on a angled line in the right diagram(between 0 and 45° for this type of diagrams).
The reason why i am pointing out that those instances of the clocks on the simultaneity axis are merely what we interpret as moving clocks which are simultaneous to us, is because this is just a physical definition we agreed upon.

If you look at the video, particularly at stage 3 and 4, you see how the blue clock in the right diagram (the filled blue circle), ticks much faster in phase 3 and 4 when the traveling twin accelerates. "Its count goes up much faster" relative to the traveling twin's clock local to him.

This means, the traveling twin will measure a future instance of the blue clock to be on the simultaneity axis post acceleration. However, he could decide to accelerate in the opposite direction again, and then the instance of the blue clock which lies on the simultaneity axis as measured by the traveling twin would be one of the past compared to the one before accelerating into the opposite direction.

The traveling twin could keep doing this "acceleration dance" and the instance of the blue clock which is measured by the traveling twin to be on the simultaneity axis, would seemingly be "moving forwards and backwards in time" on repeat.

So one has to be careful in what the simultaneity axis really is. It is an axis which has been defined in physics accurately, but it NOT the axis where events happen "at the same time" to us when by "at the same time" we are asking "what is my friend doing/feeling right now". They happen at the same time only in the sense of having the same t or t' coordinate.

Unfortunately, consciousness or subjective experience is beyond the scope of physics but it is nevertheless important to understand that when we talk about events happening at the "same time" in relation to the twin paradox, as physicists, we merely mean they have the same t or t' coordinates and therefore lie on a specific axis we defined as the simultaneity axis precisely.

Physical time has been defined precisely, but it completely ignores the "present" or "now (subjective)experience". Hence, physicists do not care how consciousness travels through the block universe on a worldline and or when two worldlines cross, the two consciousnesses traveling those worldlines would actually meet at the cross-points or not at all.
Yet, unless we are ok with meeting zombies at the worldline crossing points, we would have to come up with a "meta-physics" which takes this into account as well. (I will be starred at for typing this, i know... but someone had to say it)

It would be absurd to assume that events happening at the same physical time as in having the same t or t', actually happen at the same time as in what two people experience at the same time, shown by the example with the "acceleration dance" above.

 

[Dale]

then the instance of the blue clock which lies on the simultaneity axis as measured by the traveling twin would be one of the past compared to the one before accelerating into the opposite direction.

The traveling twin could keep doing this "acceleration dance" and the instance of the blue clock which is measured by the traveling twin to be on the simultaneity axis, would seemingly be "moving forwards and backwards in time"

Note that what you describe here is not a valid coordinate system. A coordinate chart on spacetime is a one to one mapping between events and coordinates.