# What causes people to age differently?

1. Oct 29, 2013

### spaced-out

What causes people to age differently?
Here is a simple example:
A man moves inertially between two clocks in inertial coordinate
system A. He is age 20 when he starts.

Man
(20) -->
[0]-------------Frame A-----------[?]
ClockClock

Man
---------------------------------(23.67) -->
[?]-------------Frame A----------[3.80]
Clock Clock

The A-frame observers note that his aging rate is 96.47 percent
compared to the observers' clock times.

A second man moves faster but still inertially between the same two
clocks in inertial coordinate system A. He is also age 20 when he
starts.

Man
(20) -->
[0]-------------Frame A-----------[?]
ClockClock

Man
---------------------------------(21.37) -->
[?]-------------Frame A----------[1.70]
ClockClock

The A-frame observers note that his aging rate is only 80.87 percent
compared to the observers' clock times.

The question is What causes the men age differently? I know that
the math gives it, but what is the physics behind the math?
(Remember the epicycles!)

2. Oct 29, 2013

### Staff: Mentor

The men have taken different paths through space-time, and a different amount of time passes on these paths, just as a different numbers of miles would pass if they had taken different paths through ordinary space.

3. Oct 30, 2013

### spaced-out

To Nugatory: Yes, I realize that the times are different, but I was asking about the different aging rates. Could you please address this? (In case you are saying that merely taking different path in space-time causes the two men to age differently, then I ask how.)

4. Oct 30, 2013

### Staff: Mentor

They age differently because the time is different, just a car that drives a longer distance experiences more wear and tear because it's covered more miles.

Time is defined (google for the Einstein quote "Time is what a clock measures") by observing the progressive change of physical systems: Sand falling through an hourglass, the movement of the hands of a clock, the graying of my hair, the rate of spoilage of food or decay of atoms in a sample of radioactive material, they're all measuring the passage of time. And so is the aging of a biological organism - you'll age more on ten-year journey than on a five-year journey.

So your question comes down to asking why, other than that the math says so, should different paths through space-time have different "lengths" in time. There's really no deeper answer than that that's how the universe we live in works.

That sounds like a non-answer, but it's what you find at the bottom of any scientific explanation of "why" something happens. The math can explain how things makes sense and predict the results of experiments, but it doesn't really answer the "why?" question. We chose the math (in this case, the definition of the space-time interval that we use to calculate the time passing on different paths through spacetime) to match what the universe was doing long before we started constructing mathematical descriptions.

Last edited: Oct 30, 2013
5. Oct 30, 2013

### dauto

Your question is akin to asking: Yes, I know that apples fall because of gravity but what causes apples to fall? I know that the math gives us that apples fall but what causes them to fall? (Remember the epicycles!)

6. Oct 30, 2013

### nitsuj

As he and others said the answer is what it is, note there are different perspectives for "why" this differential aging happens.

Consider this is all about geometry, and the "tools" for geometric measurements are not just rulers and protractors, but also clocks.

7. Oct 30, 2013

### stevendaryl

Staff Emeritus
Here's a different way of thinking about it that is possibly helpful.

Your original question involved thinking of proper time $\tau$ (the amount of aging) as a function of coordinate time $t$. It's mysterious why velocity should affect $\tau$.

A different way of thinking about it reverses the dependent versus independent variable. Pick a coordinate system. A coordinate system associates four numbers: $x, y, z, t$ with each event (point in space and time). If you're traveling, then you can describe your path by 4 functions $x(\tau), y(\tau), z(\tau), t(\tau)$, which together give your coordinates as a function of the proper time $\tau$ showing on your watch. If you start at $\tau = 0$ and travel until $\tau = 100$ seconds, then clearly where you end up $\langle x(100), y(100), z(100), t(100)\rangle$ depends on the "velocity" $\langle\frac{dx}{d\tau}, \frac{dy}{d\tau}, \frac{dz}{d\tau}, \frac{dt}{d\tau}\rangle$

So in these terms, your question amounts to: Why is $\frac{dt}{d\tau} > 1$?

Coordinate time in special relativity is treated in much the same way that any other spatial coordinate is. There is no particular reason to think that $\frac{dt}{d\tau}$ should always be the same, for all travelers, any more than $\frac{dx}{d\tau}$ is.

8. Oct 30, 2013

### Staff: Mentor

I like to look at it the other way:
The men don't age differently. Using the car analogy, it is just as incorrect to say/ask why the men aged differently as why their cars traveled at different speeds when they were instead going the same speed for different distances. In fact, in both examples, they behave exactly the same, they just do it for different times/distances.

The wording of the question is a reflection of not accepting what time dilation is.

9. Oct 30, 2013

### spaced-out

To Russ: Just a quick question: What exactly, in yoiur opinion, is "time dilation" physically speaking? Thanks!

10. Oct 30, 2013

### Staff: Mentor

Time dilation is the differing rates of the passage of time that exist between different reference frames.

Last edited: Oct 30, 2013
11. Oct 30, 2013

### stevendaryl

Staff Emeritus
No, I don't agree with that wording. There is no difference between "the rates of passage of time" in different frames. All inertial frames are equivalent in Special Relativity.

12. Oct 30, 2013

### Staff: Mentor

Poor word choice: I've swapped "in" for "between".

13. Oct 30, 2013

### spaced-out

I am aware of 2 sorts of time dilation, one physical, the other a mere point of view. The physical is when people born at the same time end up having different ages. The pt-of-view is when observers see each other's clocks "running slow" - this cannot be physical because 2 clocks cannot both run slower. Which one, if either, are you guys talking about? (I will have to reply in the am) Thanks!

14. Oct 30, 2013

### Staff: Mentor

There is only one time dilation(unless you separate SR and GR), but those are two different implications: both very real. And the only significant difference between the cases is that if the two clocks are in different reference frames, there may be disagreement about how to compare them.

15. Oct 30, 2013

### PAllen

No clock 'runs slow'. This point has been emphasized for you several times. It is possible for two observers to each see another's clock running slow, and this is a 'real' observation, that is not paradoxical precisely because no clocks run slow. What differential aging (twin scenario shows) is not that one clock ran slow, but that total time along different histories (world lines) between a pair of events can be different - just as two curves connecting points on a paper can be different lengths.

What you can say about time dilation is that it is observer dependent (not that isn't 'real'). For example, the fact that a muon created in the upper atmosphere usually reaches the ground is a fact that everyone agrees on. However, for an earth frame, the reason is time dilation of the muon 'decay clock'. For a muon observer, it is the earth clock that is seen to run slow, and the reason the muon reaches the ground is extreme contraction of the thickness of the atmosphere. Thus, you can say that (in contrast to differential aging), that time dilation is a frame or observer dependent explanation of a particular phenomenon. But the phenomenon associated with time dilation in one frame is 'real' and agreed on by other frames.

[edit: In the case of differential aging (twins), because two clocks begin and end co-located, the explanation in all frames involves time dilation. However, different frames will disagree on the details; they only agree on the final result.]

Last edited: Oct 30, 2013
16. Oct 30, 2013

### Staff: Mentor

On the contrary, it is possible for both clocks to run slower, and this time dilation is physical.

As for how this apparent impossibility can come about... You have to consider very carefully exactly what it means to say that a clock "is running slow", and also remember the relativity of simultaneity.

Let's say that A flies past B at .6c, and as they pass one another they both zero their clocks and start them running. At some later time, A looks at his stopwatch and sees that it reads ten seconds. A knows that at that moment B is six light-seconds away, and therefore that light leaving B at that moment will reach A's eyes when his watch reads 16 seconds. Thus, when A sees his clock read 16 seconds and at the same time sees B's clock reading 8 seconds, he correctly concludes that B's clock is running 20% slow - at the same time that his clock read 10 seconds B's clock read 8 seconds.

But we also have to consider the relativity of simultaneity. The two events "A's clock reads 10 seconds" and "B's clock reads 8 seconds" only happen at the same time in a frame in which A is at rest. In a frame in which B is at rest, the event "B's clock reads 8 seconds" happens at the same time as the event "A's clock reads 6.4 seconds", and B will correctly conclude that A's clock is running 20% slow.

There is nothing illusory about this effect - you might want to look up the cosmic ray muon lifetime measurements in the FAQ at the top of this subforum.

17. Oct 30, 2013

### robphy

Maybe this helps....

Consider an odometer (a wheel with a counter, counting the number of rotations).
On a plane, it functions the same way (turning once for traveling one circumference of the wheel)... no matter which path on the plane you take from point A to point B. The reading of the elapsed distance depends on the path taken from A to B.

Consider a clock (a light clock [my video below]). In Minkowski spacetime, it functions the same way (ticking once for an inertial timelike-displacement of 1 second)... no matter which worldline in spacetime you take from event A to event B. The reading of the elapsed time depends on the worldline taken between A and B.

So, follow the ticking of a light-clock,
as in my old video [ http://physics.syr.edu/courses/modules/LIGHTCONE/LightClock/#twins [Broken] ],
gives you a mechanism for how time elapses along each worldline.

(Motivation for why this light-clock works as it does...
http://physics.syr.edu/courses/modules/LIGHTCONE/LightClock/#circularlightclocks [Broken]
from here, scroll upwards to see the development of these light-clocks [with reference to Michelson-Morley].)
(The bottom of that page has links to a paper describing the light-clocks.)

Last edited by a moderator: May 6, 2017
18. Oct 31, 2013

### Staff: Mentor

Why not?

"Physical" means "of or pertaining to physics". So time dilation is certainly physical. It is also experimentally measurable, but it is frame variant meaning that different frames will disagree.

Btw, I agree completely with Nugatory's answer. They age differently because the take different paths through spacetime. It is no different than accumulating more mileage when taking different paths in space. Hopefully you understand intuitively that different paths through space accumulate different distances? Why should it be different with spacetime?

Last edited: Oct 31, 2013
19. Oct 31, 2013

### spaced-out

This odometer case is not a proper analogy. An odometer relates to tires which
constantly contact a road. What do the Triplets contact that affects
their ages? They merely move inertially through space. And who
cares if they move different distances or in different directions;
how can that cause people to age differently?
(Triplets = No Accelerations)

Triplet Case: When Mary & Bill meet in passing, both are the same age, and Bill goes on to meet Barry when they are the same age. Barry then catches up with Mary, and they have different ages. This is a direct comparison of aging and shows that people who move differently age differently. Barry's and Bill's paths relative to Mary are the same - same speeds - same distances traveled - same space-time paths.

Odometer: How long tires contact a road
(distance is all that counts, direction is irrelevant)

Triplets: How fast each person moves through space
(speed is relevant, distance not as much, direction none)

20. Oct 31, 2013

### robphy

The light-clock's mechanism is determined by the light-rays which make contact with ("reflect off") the inertial mirrors... which follow the geodesics of Minkowski spacetime. (There is a presumption that a standard unit of time has been established... that is, the directions on how to build an identical light-clock for another inertial observer. That's part of the development.) [I restricted the discussion of the light-clock to "piecewise-inertial" for simplicity... or else one should make the displacements infinitesimal (as one would do for an arc-length in space for an arbitrary curve) and then take a limit.]

The construction does match the calculation using the formulas from special relativity.