Relativity: Twin Paradox - Is Age Determinable?

[JArnold]

I'm just joining this long discussion, and it may be inevitable that my contribution will only be annoying. But there are basic and well-established principles that should guide the discussion: Uniform motion is relative; inertial acceleration and gravitational effects are absolute. In the former case, observers will mirror each other's experience of retarded clock speeds; they will each say the other's clock is moving more slowly. In the latter case (and our GPS system relies on actual time dilation): clocks move more slowly according to the intensity of their location in a gravitational field and according to their subjection to a force (as can be experimentally confirmed).

 

[SiennaTheGr8]

... Uniform motion is relative; inertial acceleration and gravitational effects are absolute. ...

I'd rephrase that: your velocity is relative, but whether you're moving inertially isn't.

 

[Ibix]

actual time dilation

"Actual" isn't a sensible word here. No time dilation is any more actual than any other. Some circumstances lead to symmetric time dilation and others lead to asymmetric time dilation (and some to differential aging) , that's all.

clocks move more slowly according to the intensity of their location in a gravitational field and according to their subjection to a force

Location in a gravitational field yes (more precisely, the gravitational potential difference between two clocks governs their rate). But force does not cause any time dilation.

 

[1977ub]

re: acceleration "causing" aging.

Here is a scenario with no acceleration. It involves 2 travelers and one stationary observer. One traveler passes Earth moving toward a distant star 4 light years distant, synchronizing clocks with Earth observer as it passes very closely. Another traveler leaves the distant star toward earth. Both outgoing & incoming travelers are traveling near to c as measured by the Earth observer. For Earth observer the first traveler moves away for 2 years and then passes the other traveler closely - information is swapped between the travelers so that the toward-earth traveler finds that all observers and instruments on the outward-traveling ship have aged less than one second since they passed earth. Less than a second later, the earthward ship arrives at earth.

 

[hutchphd]

Less than a second later, the earthward ship arrives at earth.

I'll save everybody else the trouble: whose clock are you referring to?

 

[1977ub]

I'll save everybody else the trouble: whose clock are you referring to?

inward ship - experiences almost no time after passing the outward ship.

 

[hutchphd]

re: acceleration "causing" aging.

I'm sorry but I don't see how this recitation relates to the intro. Nobody is questioning time dilation.

 

[JArnold]

I'd rephrase that: your velocity is relative, but whether you're moving inertially isn't.

Velocity is just motion in a particular direction. Inertial motion isn't relative? Don't tell Einstein.

 

[JArnold]

"Actual" isn't a sensible word here. No time dilation is any more actual than any other. Some circumstances lead to symmetric time dilation and others lead to asymmetric time dilation (and some to differential aging) , that's all.

Location in a gravitational field yes (more precisely, the gravitational potential difference between two clocks governs their rate). But force does not cause any time dilation.

Actual time dilation is "actual" when A observers the clock of B moving more slowly, while B observers the clock of A to be moving more quickly. It is not actual when each observes the other's clock to be moving more slowly.
Force causes time dilation because it causes acceleration, and time dilation corresponds with acceleration.

 

[SiennaTheGr8]

Velocity is just motion in a particular direction.

I'd rephrase that: velocity is the derivative of position with respect to coordinate time.

Inertial motion isn't relative? Don't tell Einstein.

If by "inertial motion" you mean "velocity," then yes, it's relative. If by "inertial motion" you mean "whether one's motion is inertial," then no, it's not relative. Agreed?

 

[SiennaTheGr8]

Actual time dilation is "actual" when A observers the clock of B moving more slowly, while B observers the clock of A to be moving more quickly. It is not actual when each observes the other's clock to be moving more slowly.
Force causes time dilation because it causes acceleration, and time dilation corresponds with acceleration.

This is incorrect. I suggest brushing up on time dilation.

 

[SiennaTheGr8]

To elaborate, @JArnold :

At the very least your terminology is off. What you've described sounds more like "differential aging" than "time dilation," and when you say "actual" perhaps you mean "invariant." (But even so, there are still problems with the post.)

 

[JArnold]

I'd rephrase that: velocity is the derivative of position with respect to coordinate time.
If by "inertial motion" you mean "velocity," then yes, it's relative. If by "inertial motion" you mean "whether one's motion is inertial," then no, it's not relative. Agreed?

I think I agree. Uniform velocity, speed, and rest are relative. Whether a body is inertial or accelerating is not. Yes?

 

[SiennaTheGr8]

I think I agree. Uniform velocity, speed, and rest are relative. Whether a body is inertial or accelerating is not. Yes?

Yes, although you can drop the word "uniform," and you needn't mention "speed" or "rest" (they're both covered by "velocity").

 

[JArnold]

To elaborate, @JArnold :

At the very least your terminology is off. What you've described sounds more like "differential aging" than "time dilation," and when you say "actual" perhaps you mean "invariant." (But even so, there are still problems with the post.)

To elaborate, @JArnold :

At the very least your terminology is off. What you've described sounds more like "differential aging" than "time dilation," and when you say "actual" perhaps you mean "invariant." (But even so, there are still problems with the post.)

"Time dilation" is a standard term. "Actual" is not-relative, and can be measured variously from different reference frames.

 

[SiennaTheGr8]

"Time dilation" is a standard term.

Yes, but you're using it incorrectly.

"Actual" is not-relative, and can be measured variously from different reference frames.

The word you're looking for is invariant.

 

[JArnold]

Yes, but you're using it incorrectly.
The word you're looking for is invariant.

You seem to have your own dictionary. "Velocity" doesn't substitute or include "speed" and "rest"; velocity is speed in a particular direction, and a body that is considered to be at-rest thereby has neither speed nor velocity. A clock-speed that can be considered more-or-less dilated from other reference frames isn't invariant, it is very much variant.

 

[Ibix]

Actual time dilation is "actual" when A observers the clock of B moving more slowly, while B observers the clock of A to be moving more quickly. It is not actual when each observes the other's clock to be moving more slowly.

You seem to be inventing your own term here. The underlying reason for time dilation, always, is that the interval along a given worldline between planes of simultaneity in a particular coordinate system depends on the chosen worldline. I would not use "actual" to describe this in any case. "Symmetric" and "asymmetric" is better since it describes what's happening without taking a position on whether one coordinate-dependent effect is more "actual" than another.

Force causes time dilation because it causes acceleration, and time dilation corresponds with acceleration.

It most certainly does not. Time dilation in special relativity depends purely on the velocity of a clock compared to your choice of "at rest". In general relativity you can, in some spacetimes, divide the effect into one depending on relative velocity and one depending on gravitational potential. In general spacetimes I think the only available definition relates to the angle between the clock's worldline and the worldline of constant spatial coordinates, and the result may be nonsensical since the latter needn't be timelike.

Note that "acceleration" appears nowhere in any of that.

 

[Ibix]

"Velocity" doesn't substitute or include "speed" and "rest"; velocity is speed in a particular direction, and a body that is considered to be at-rest thereby has neither speed nor velocity.

It doesn't substitute, but it does cover. If you know the velocity you know the speed and you know whether or not the object is at rest. I'd suggest that regarding an object at rest as having zero velocity is better than it not having a velocity since it is more consistent with the mathematical description (for example, an object with velocity $\vec v$, when transformed into a frame with velocity $\vec v$, has velocity $\vec v-\vec v=0$, not "doesn't have velocity"), but either is unambiguous.

A clock-speed that can be considered more-or-less dilated from other reference frames isn't invariant, it is very much variant.

Agreed. I believe @SiennaTheGr8 was proposing "invariant" in place of your "actual", but I don't think it covers what you mean by "actual", which is indeed coordinate dependent. Which is why "actual" is a bad word to use.

 

[JArnold]

Time dilation in special relativity depends purely on the velocity of a clock compared to your choice of "at rest". In general relativity you can, in some spacetimes, divide the effect into one depending on relative velocity and one depending on gravitational potential. In general spacetimes I think the only available definition relates to the angle between the clock's worldline and the worldline of constant spatial coordinates, and the result may be nonsensical since the latter needn't be timelike.

The underlying reason for time dilation is real-world physics. With relative uniform motion it is observer-dependent, and yes, there is no “actual.” With gravitation and inertial acceleration different clocks actually move at different speeds, and one twin will actually age more than another.

When results become “nonsensical” it may be because one’s formalisms have lost contact with physics — physical effects like “acceleration”, for example. An observer, in uniform motion (or “at rest”), and at an infinite distance from two clocks, can observe one clock actually moving more slowly than the other if one of the clocks is more affected by a gravitational field and/or the application of a force. (Note that “infinite” and “uniform” or “at rest” means sufficiently free of objective influences, as can be determined by a test-particle floating freely in a vessel in the observer’s lab.)

 

[Ibix]

The underlying reason for time dilation is real-world physic

Actually, no (edit: Dale, below, prefers to call your statement "meaningless" rather than saying "no" - I don't have a problem with his wording, although I - obviously - wouldn't have picked it). Time dilation isn't a direct observable and depends on the choices you make in your interpretation of things you actually can observe.

With gravitation and inertial acceleration different clocks actually move at different speeds, and one twin will actually age more than another.

This isn't correct. It's trivial to construct variants on the twin paradox scenario in which both twins undergo acceleration and either do or do not age differently. And it's possible to do the same in a gravitational field, although the maths needed to determine the course is more complicated.

When results become “nonsensical” it may be because one’s formalisms have lost contact with physics

Or it may be because an interpretation of results that works ok in flat spacetime does not generalise well to curved spacetime.

An observer, in uniform motion (or “at rest”), and at an infinite distance from two clocks, can observe one clock actually moving more slowly than the other if one of the clocks is more affected by a gravitational field

No. They will observe the two Doppler shifted. To what extent they attribute this to the clock "actually" ticking slowly and how much to effects on the light of its passage through the curved spacetime (edit: or, indeed, different coordinate velocities) is an interpretation. In a static gravitational field there's an obvious way to do this, but not in general. And you are not obligated to use the obvious interpretation even when it's available

the application of a force

A force does not have any effect on the tick rate of a clock except inasmuch as it changes the path of a particle. The elapsed time is $\int\sqrt{|g_{ab}dx^adx^b|}$ (and this has been experimentally tested), which depends only on the first derivative of coordinates, not the second. Velocity, not acceleration.

 

[Dale]

The underlying reason for time dilation is real-world physics.

While true, this statement is so broad that it is meaningless. What specifically in the real-world physics does it depend on?

In general time dilation is given by $\frac{d\tau}{dt}$. In an inertial frame that simplifies to $\sqrt{1-v^2}$, but that is not a general rule for all situations. Note that $d\tau$ is invariant but $dt$ is not.

 

[Bruce Wallman]

All that matters is the relative speed of the twins. And the speed need not be anywhere near $c$. Modern clocks are precise enough to see the effect when the speed is a very tiny fraction of $c$.

Yes, we see slight effects at micro levels in current astronauts. I was thinking about a more noticeable age difference. To answer two replies at once, the twin staying on Earth is still moving relative to the universe or cosmos. We know it is in the thousands of km/s range. This reduces all of our aging by a slight amount over 100 years. The faster moving twin might save 10 days of lifetime while the one on Earth saves 1 second. The age difference would then be 9 days, 23 hours, 59 minutes, and 59 seconds. The thing that we move relative to is the universe or cosmos - this is an easier way to understand the twin paradox than our motion relative to one another. When reduced to movement relative to one another, then both twins are always moving at the same velocity and acceleration relative to one another, so there would be no difference in aging. There needs to be a common ground to measure against. I look at that as the gravitational center for all things and call it the universe. This is a hard concept to point at since the big bang or bounce happened everywhere relative to us, but such is life.

 

[Ibix]

The thing that we move relative to is the universe or cosmos - this is an easier way to understand the twin paradox than our motion relative to one another.

Easier or not, it's wrong.

When reduced to movement relative to one another, then both twins are always moving at the same velocity and acceleration relative to one another, so there would be no difference in aging.

The whole point of this scenario is to make students realize that this analysis is naive and, ultimately, incorrect.

 

[Dale]

The thing that we move relative to is the universe or cosmos - this is an easier way to understand the twin paradox than our motion relative to one another.

Easier or not, it's wrong.

Well, I wouldn’t say it is wrong, but it is certainly not easier. While you can choose any reference frame, the velocity wrt the local frame where the CMB is isotropic is irrelevant. It drops out of the equations, so determining it has no bearing on the result and simply adds additional and unnecessary complication. The local CMB frame is as superfluous to this problem as the aether.

 

[Ibix]

Well, I wouldn’t say it is wrong

Taken on its own I agree. Leading into the next bit I quoted (edit: and the following bits about the "gravitational centre for all things"), however, I think it is actually wrong.

 

[Dale]

Taken on its own I agree. Leading into the next bit I quoted (edit: and the following bits about the "gravitational centre for all things"), however, I think it is actually wrong.

Excellent point!

 

[Bruce Wallman]

Easier or not, it's wrong.

The whole point of this scenario is to make students realize that this analysis is naive and, ultimately, incorrect.

Naive and simple yes. General relativity is about acceleration and gravity. Special relativity was written as being about velocity and the velocity of electromagnetic waves. What if I update my thinking about SR to GR standards and make it about velocity and the velocity of gravity? Then all velocities in the universe are measured against a gravitational frame and things like time dilation and mass increase become more intuitive.

 

[Ibix]

Naive and simple yes. General relativity is about acceleration and gravity. Special relativity was written as being about velocity and the velocity of electromagnetic waves. What if I update my thinking about SR to GR standards and make it about velocity and the velocity of gravity? Then all velocities in the universe are measured against a gravitational frame and things like time dilation and mass increase become more intuitive.

This is just nonsense.

If you don't understand special relativity well enough to be able to resolve the twin paradox without inventing reference to some illusory absolute reference frame then you aren't ready to try to understand general relativity.

 

[Mister T]

When reduced to movement relative to one another, then both twins are always moving at the same velocity and acceleration relative to one another, so there would be no difference in aging.

Neither your premise nor your conclusion is correct. In the typical presentation of the twin paradox only one twin has an acceleration. They do indeed have equal but opposite velocities relative to each other. And there is a difference in aging.

 

[Mister T]

Yes, we see slight effects at micro levels in current astronauts.

I don't understand. Micro levels of what?

I was thinking about a more noticeable age difference.

I'm not sure what you mean by noticeable. We can start with two identical clocks in the same location, and synchronize them. If the two clocks separate, take different paths through spacetime, and then reunite, it is as noticeable as it can possibly get when we observe that the clocks are no long synchronized.

This is a fact of life. We have observed it!

What physics does is provide an explanation. In this case, we can use it to calculate the path length of each clock, and compare it to the elapsed time on each clock. In all cases they match!

That's as noticeable as possible.

 

[Ibix]

Here are correct Minkowski diagrams (albeit for a slightly longer journey than Earth-Mars). First, in the rest frame of the planets (marked as blue worldlines):

The ship (red worldline) does 0.8c. I've marked black crosses, joined by a fine grey line, when the same proper time has elapsed since departure for both the traveller and stay-at-home. In this frame, the stay-at-home is older when the traveller arrives. Note that I have only drawn the traveller's worldline in transit - you may extend it inertially or treat it as taking off and landing. It makes no differece to the only thing that matters - the positions of those crosses.

We can also draw the same scenario in the frame where the ship and planets have equal and opposite velocities:

In this frame, the traveller and stay-at-home are the same age when the traveller arrives. And finally, we can consider the rest frame of the ship:

Here, it is the traveller who is older.

The point is that all of these diagrams are valid, and there is no reason to prefer one over another. So there is no unique answer to the question.

 

[PeterDonis]

@Elroch, you have now been banned from further posting in this thread. All you are doing is confusing the issue and repeating erroneous claims.

 

[PeterDonis]

Moderator's note: A number of confusing and erroneous posts and responses to them have been deleted.