Twin paradox explained for laymen

[Tony Wright]

As a layman I also have conceptual difficulties with the twin paradox. It would allow me to move on if some one could quickly answer the rather obvious question: would there be any time dilation if the Earth was removed entirely from the thought experiment so that the twins are in a symmetrical relationship of inertia or relative motion. I cannot see how there could be but would then have to look to gravity to explain it.

 

[PeroK]

As a layman I also have conceptual difficulties with the twin paradox. It would allow me to move on if some one could quickly answer the rather obvious question: would there be any time dilation if the Earth was removed entirely from the thought experiment so that the twins are in a symmetrical relationship of inertia or relative motion. I cannot see how there could be but would then have to look to gravity to explain it.

The Earth is irrelevant to the twin paradox. It's just a way of making one of the twins have (approximately) inertial motion throughout the experiment. It works just the same in deep space. Gravity has nothing to do with it.

 

[Ibix]

would there be any time dilation if the Earth was removed entirely from the thought experiment so that the twins are in a symmetrical relationship of inertia or relative motion.

You mean, before the turnaround? Yes, both calculate that the other's clock runs slow. Gravitational time dilation is a separate phenomenon and not relevant here.

One of the twins turns around, which means that their experiences aren't identical over the whole journey. It also means that if you wish to apply the time dilation formula from the traveller's perspective you need to explicitly account for the effects of the relativity of simultaneity at the turnaround.

 

[A.T.]

... so that the twins are in a symmetrical relationship of inertia or relative motion

They have a symmetrical relationship of relative motion, but not of inertia. Only one of them moves inertially all the time.

See this recent thread:

https://www.physicsforums.com/threa...idered-to-be-accelerating.991333/post-6366469

https://www.physicsforums.com/threa...idered-to-be-accelerating.991333/post-6366866

 

[Dale]

would there be any time dilation if the Earth was removed entirely from the thought experiment

Yes. In fact, that would make the experiment much “cleaner” in my opinion.

the twins are in a symmetrical relationship of inertia or relative motion

It is not as symmetrical as you might think. Here are a list of several asymmetries:

1) the traveller’s accelerometer reads non-zero during the turnaround

2) for the traveller there is a Doppler blueshift for half the journey but for the home twin the Doppler blueshift is only briefly at the end

3) using radar coordinates for the home twin shows the moving twin making one turn, but using radar coordinates for the moving twin shows the home twin making two turns

I am sure there are others, but anyone of these is an asymmetry that uniquely identifies the traveller

 

[etotheipi]

In our model the rest frame of the lazy twin floating in space with no means of providing thrust will always be an inertial frame; this can be verified by means of an accelerometer. So we will do the analysis using the rest frame of this twin. Now you draw the trajectories of both twins w.r.t. the lazy twin's coordinate system, between the start and end events where their worldlines meet.

The amount by which either twin ages biologically is determined by the proper time elapsed along their respective trajectories (that which is measured by their respective wristwatches), both of which will be frame invariant quantities, which means that our analysis in this chosen frame will be fully general. The proper time over the "longer" trajectory on paper of the traveling twin is less than that of the "shorter" trajectory on paper of the lazy twin, because of how the Minkowski metric is defined. ☺

 

[anuttarasammyak]

As a layman I also have conceptual difficulties with the twin paradox. It would allow me to move on if some one could quickly answer the rather obvious question: would there be any time dilation if the Earth was removed entirely from the thought experiment so that the twins are in a symmetrical relationship of inertia or relative motion. I cannot see how there could be but would then have to look to gravity to explain it.

Prepare a triplet, A,B,E. A is a pilot to make a go-return trip. B is also a pilot of go-return trip but reverse direction. E stays on the Earth. After trips, their ages are
$$A=B<E$$ E stays in an IFR.
If E builds a huge engine on the Earth and thrust it so that the Earth travels along with B, then their ages are
$$A=B=E$$ Nobody stays in IFRs.

 

[Tony Wright]

As a layman I find resolution of the twin paradox in terms of physics difficult. Given the observation of time dilation by astronauts on their return to Earth I can only approach it by means of the thought experiment In which the Earth is removed and the twins perform the same relative movements outside of any gravitational fields apart from their own. Because their motions, including acceleration, constant motion or inertial motion and deceleration away and then towards each other are mutual, or reciprocal, I cannot envisage any time dilation. I can replace the twins by objects of much greater mass, equal to that of the earth, but then I am seeing just the final moment of a much larger experiment before they collide and again there is no dilation. I can therefore only conclude that the time dilation that is observed in the real situation is due the huge difference in mass between the Earth and the orbiter, or more precisely the mutual acceleration, inertial motion and deceleration away and towards of the two objects in an asymmetrical gravitational field in which only that of the Earth is significant.
i would be very grateful for any comments on my analysis so that I can move on and start to understand other concepts of relativity.

 

[Drakkith]

Gravity has nothing to do with time dilation due to relative motion, nor with the twin paradox scenario.
You will get time dilation with objects of any mass, whether they are equal or widely different.

I am uncertain how to correct your analysis, as you don't appear to have invoked any math or physics. If you do the math the results are unquestionable and are verified by millions or billions of people every day who use GPS technology.

 

[A.T.]

Because their motions, including acceleration, constant motion or inertial motion and deceleration away and then towards each other are mutual, or reciprocal, ...

Their proper accelerations are not reciprocal. Have your read the posts I linked to in the other thread you just started?

See this recent thread:

https://www.physicsforums.com/threa...idered-to-be-accelerating.991333/post-6366469

https://www.physicsforums.com/threa...idered-to-be-accelerating.991333/post-6366866

Why do you start a second thread on the same topic?

 

[Ibix]

As a layman I find resolution of the twin paradox in terms of physics difficult.

The twins' movements are not the same. One of them turns round and comes back - that one will feel proper acceleration and the other one will not. The reciprocal nature of time dilation only applies between clocks at rest in inertial frames and the twin that turns around was not at rest in a single inertial frame for the entire journey. Thus your analysis is based on an incorrect statement.

There are a great many ways to understand what is actually happening. The first would be to look up relativity of simultaneity. This is an important aspect of relativity that's frequently overlooked in popsci sources. The traveling twin's inbound and outbound inertial frames have different definitions of what "on Earth at the same time as the turnaround event" means. Thus your naive analysis fails to account for the chunk of the stay-at-home's proper time between "on Earth at the same time as the turnaround according to the outbound frame" and "on Earth at the same time as the turnaround according to the inbound frame".

Possibly the simplest correct analysis is to look up the Lorentz transforms, write down the x and t coordinates of all of the interesting events, and work out the description of the experiment in all three frames. This doesn't require maths more complicated than a square root and is well worth doing - we are happy to help if you find yourself struggling.

There is a far simpler analysis, but it requires a larger conceptual leap. That leap is this: the twins follow paths through four dimensional spacetime, and those paths have "lengths" which turn out to be directly proportional to the elapsed times according to their wristwatches (or any other clock traveling with them). The twin paradox is trivial if you can accept that - they followed different paths through spacetime and those paths had different "lengths", just as two paths through space can have different lengths. Note that I'm writing "length" in scare quotes - that's because the quantity is actually called interval and does not act quite the same way as normal length. Nevertheless the analogy to length is extremely close.

Note that gravity does not appear in this analysis anywhere. Gravitational time dilation is a real phenomenon, but it is completely irrelevant to this experiment.

 

[Ibix]

Why do you start a second thread on the same topic?

To be fair, he didn't start the first thread. He posted in an older thread and a mentor has spun that off into another thread. I would expect he has notifications telling him this, but its possible he's not familiar with the forum software and hasn't used them.

 

[Sagittarius A-Star]

... would there be any time dilation if the Earth was removed entirely from the thought experiment so that the twins are in a symmetrical relationship of inertia or relative motion. I cannot see how there could be but would then have to look to gravity to explain it.

Gravity is not needed for time dilation to occur. The "twin paradox" scenario exists also, if both twins stay in the same gravitational potential on earth. That is confirmed by real experiments, for example:

Bailey et al. (1977) measured the lifetime of positive and negative muons sent around a loop in the CERN Muon storage ring. This experiment confirmed both time dilation and the twin paradox, i.e. the hypothesis that clocks sent away and coming back to their initial position are slowed with respect to a resting clock.

Source:
https://en.wikipedia.org/wiki/Experimental_testing_of_time_dilation#Twin_paradox_and_moving_clocks

The "twin paradox" is symmetrically only from a kinematical viewpoint, but not from a dynamical viewpoint. Only one twin is accelerated by an interaction force (for example electric field or rocket motor) relative to an inertial frame (=proper acceleration).

The turnaround changes the rest frame of the traveling twin to another inertial frame than before, with a different simultaneity relation to the inertial rest frame of the non-travelling twin.

 

[Tony Wright]

Thank you for all your replies; just what I’d hoped for. I will read them thoroughly before coming back. Yes, sorry about the other post; I didn’t see it when I logged in and thought it had failed.

 

[Tony Wright]

I can say that my first conceptual difficulty is that for the twins in my scenario to experience the motion ie acceleration, differently implies that their motion is measured with respect to an external definition; ie there are fixed points in space even though motion of objects is relative. Can we therefore say For example that the Earth has an absolute motion?

 

[Ibix]

Can we therefore say For example that the Earth has an absolute motion?

No. There is no absolute motion. However, proper acceleration is absolute in the sense that you can detect it in a closed box - the sensation of added weight in an accelerating lift is one example.

So there is a physically meaningful distinction between being inertial and being non-inertial. One of the twins is inertial for the whole trip and one is not. This isn't the cause of their differential aging, but it does show that they didn't do the same thing for the whole experiment.

 

[anuttarasammyak]

I can therefore only conclude that the time dilation that is observed in the real situation is due the huge difference in mass between the Earth and the orbiter, or more precisely the mutual acceleration, inertial motion and deceleration away and towards of the two objects in an asymmetrical gravitational field in which only that of the Earth is significant.

Special relativity assures a kind of EQUALITY among IFRs. But IFRs and non IFRs are not relative and have a kind of ABSOLUTE DIFFERENCE, in the sense of special relativity, e.g. absolute, I mean the both sides agree with it, time difference is observed and shared between the twins one is in IFR and the other is in Non IFR. Relativity in GR is another story.

I agree that we have to make troublesome labors to accelerate heavy bodies but Mass is not a player to dominate generating IFR.

 

[PeroK]

I can say that my first conceptual difficulty is that for the twins in my scenario to experience the motion ie acceleration, differently implies that their motion is measured with respect to an external definition; ie there are fixed points in space even though motion of objects is relative. Can we therefore say For example that the Earth has an absolute motion?

Suppose you get into your car, which is parked next to a lamppost. As you accelerate away, the lamppost (in your accelerating reference frame) accelerates away from you.

Now, there is a difference in this scenario between the acceleration of your car (in the reference frame of the Earth) and the acceleration of the lamppost in your reference frame. The first is real "proper" acceleration, which requires a force, which itself can be felt and measured. The second is not real and the lamppost feels no force when you accelerate away from it.

Motion is relative, but real (proper) acceleration is not.

Another important point is you might say that your car is speeding up and the lamppost is stationary. But, let's look at this from a reference frame where the Earth is spinning and imagine you drive off west, against the Earth's spin. In this reference frame, the lamppost moves at constant speed, but you slow down! It's impossible for you to say, therefore, whether you are absolutely speeding up or slowing down. You're definitely accelerating (and the acceleration has the same magnitude in all inertial reference frames), but you cannot say absolutely what speed you are moving, nor whether you are speeding up or slowing down.

 

[Sagittarius A-Star]

I can move on and start to understand other concepts of relativity.

I think, for laymen, the "twin paradox" is a bad starting point for understanding relatvity, because it is complicated to understand.

A better starting point would be to think about, relative to which object light moves in vacuum with 30 cm/ns and then try to understand the 2nd postulate of special relativity. The vacuum speed of light is in every inertial reference frame 30 cm/ns. That can only be, if Newton's assumption of an "absolute time" is dropped.

See for example an animation of a thought experiment with a "light clock", moving relative to the observer:
https://www.pitt.edu/~jdnorton/teac...cial_relativity_clocks_rods/index.html#Light2

 

[PeroK]

I think, for laymen, the "twin paradox" is a bad starting point for understanding relatvity, because it is complicated to understand.

Absolutely. Instead of using the twin paradox to try to understand SR, one should learn SR to try to understand the twin paradox!

 

[f todd baker]

There is a simple way to understand the twin paradox which does not have to get into the complications which are rife throughout this thread. It requires the acceptance of length contraction and time dilation is unnecessary to explicitly include. Think of the distance between the Earth and the distant goal as a stick of length L. The traveling twin, with speed v relative to the stick, sees that stick moving with with speed v. He therefore sees the distance to the goal as L' =L√(1-(v/c)^2). The time for the trip, measured by the traveler, is 2L'/v ; the earth-bound twin measures 2L/v who is therefore older.

 

[phinds]

... there are fixed points in space

No, there are not. That would imply an absolute frame of reference for the universe and there is not such thing. Points are "fixed" only relative to other points, not "fixed in space".

 

[Ibix]

There is a simple way to understand the twin paradox which does not have to get into the complications which are rife throughout this thread. It requires the acceptance of length contraction and time dilation is unnecessary to explicitly include. Think of the distance between the Earth and the distant goal as a stick of length L. The traveling twin, with speed v relative to the stick, sees that stick moving with with speed v. He therefore sees the distance to the goal as L' =L√(1-(v/c)^2). The time for the trip, measured by the traveler, is 2L'/v ; the earth-bound twin measures 2L/v who is therefore older.

Neat. Although the relativity of simultaneity rears its ugly head anyway if you try to understand a ruler co-moving with the ship instead of with the planets.

 

[f todd baker]

Neat. Although the relativity of simultaneity rears its ugly head anyway if you try to understand a ruler co-moving with the ship instead of with the planets.

I just put a "stick" in there to make it more "laymanish". I could have said that there is a length L in the Earth frame which contracts in the moving frame.

 

[danb]

for the twins in my scenario to experience the motion ie acceleration, differently implies that their motion is measured with respect to an external definition; ie there are fixed points in space even though motion of objects is relative. Can we therefore say For example that the Earth has an absolute motion?

There was a lot of disagreement about this question a hundred years ago, when the subject had just been discovered. H.A. Lorentz is the guy who figured out the formulas called the "Lorentz transformations", and his opinion was yes, every object has an absolute velocity relative to the "ether".

The problem is that no-one has ever been able to detect any sign of an ether. That's what the Michelson-Morley experiment was about, and its result was negative: no visible sign of an ether. Lorentz's theory was that time dilation and length contraction combine in such a way as to hide the existence of the ether, but his view was considered unrealistic and has been lost to history. Einstein's view, that all motion is relative, has prevailed ever since, and hardly anyone takes the ether seriously any more.

Einstein's view has never been conclusively proved. Absolute velocity would explain why the spaceship's clocks run more slowly than Earth's. But don't be too insistent about that on a physics forum. Many physicists believe the principle of relativity is a proven fact, and it's been accepted as mainstream physics for over a century.

 

[Nugatory]

Absolute velocity would explain why the spaceship's clocks run more slowly than Earth's.

However, it is unnecessary - we have a satisfactory (internally consistent, mathematically elegant, excellent fit with observation, excellent predictive power) explanation that does not require that we introduce this notion of absolute velocity.

 

[danb]

we have a satisfactory explanation that does not require that we introduce this notion of absolute velocity.

As I said a while ago in another thread, the relativistic "explanation" of time dilation is derived from the Lorentz transformations, which are based on experimental evidence of time dilation, so ... take that however you like.

 

[danb]

the relativistic effects ... I thought was a consequence of speed of light being same for all observrs...

Yes, that's right. You can derive the Lorentz transformations from the constant speed of light, and most physicists believe the speed of light is a fundamental principle of causality.

 

[Ibix]

As I said a while ago in another thread, the relativistic "explanation" of time dilation is derived from the Lorentz transformations, which are based on experimental evidence of time dilation, so ... take that however you like.

No - the Lorentz transforms were initially deduced from study of Maxwell's equations. Time dilation was a consequence of Einstein showing that they are more generally applicable. The modern view is simply to start from the principle of relativity and deduce that the Galilean and Lorentz transforms are consistent with that. Then you simply test any of a number of predictions to see which is consistent with reality. Thus you can deduce time dilation from the prinnciple of relativity and something like Bertozzi's experiment on velocity versus energy of electrons.

 

[Ibix]

I just put a "stick" in there to make it more "laymanish". I could have said that there is a length L in the Earth frame which contracts in the moving frame.

That was fine - there was nothing wrong with your approach. My point was about the next step some people will take. If they consider the mirror image case - the ship uses a stick of length $L'$ at rest with respect to itself to measure the distance between the planets - then the planets will measure the stick to be $L'/\gamma=L/\gamma^2$ long. They need the relativity of simultaneity to make sense of that.