B Time Dilation: How Does Speed Affect Aging?

[Tristan1607]

TL;DR Summary

I am trying to understand relativity and time dilation, but I am having trouble understanding how it works.

Hello everyone,

I wanted to know how speed can dilate time. For example, if there is a star 100 light years away from Earth and I started traveling at light speed, how long would it take for me to get there? I understand that the time differs from the point of reference (ie time from Earth's perspective, vs traveling at light speed).

More specifically, why would I experience time going faster and age slower than people on Earth? And how does this affect my biological health? I am struggling to see how traveling faster would slow my aging process. I can't seem to find the link between speed of light and the speed of which my human cells die.

Thanks for the insight!

 

[PeroK]

Summary:: I am trying to understand relativity and time dilation, but I am having trouble understanding how it works.

Hello everyone,

I wanted to know how speed can dilate time. For example, if there is a star 100 light years away from Earth and I started traveling at light speed, how long would it take for me to get there? I understand that the time differs from the point of reference (ie time from Earth's perspective, vs traveling at light speed).

More specifically, why would I experience time going faster and age slower than people on Earth? And how does this affect my biological health? I am struggling to see how traveling faster would slow my aging process. I can't seem to find the link between speed of light and the speed of which my human cells die.

Thanks for the insight!

SR, in general, is a theory of space and time. The first postulate of SR says that there is no sense in which absolute motion may be determined. If you are in your rocket ship traveling to a faraway star, cruising at constant speed close to the speed of light relative to Earth, then your reference frame is completely equivalent to the Earth's. There is no sense in which you are physically any different from a person on Earth.

Your time will be dilated, as measured on Earth; but, also, Earth's time will be equally dilated as measured by you. In this respect, velocity-based time dilation is symmetric: neither you in the rocket nor someone on Earth can say that the other is "really" moving and you are "really" at rest.

It's often said that "time slows down if you move close to the speed of light". But, for the reasons given above that is at best misleading and to some extent dead wrong.

 

[Drakkith]

For example, if there is a star 100 light years away from Earth and I started traveling at light speed, how long would it take for me to get there?

You can't travel at light speed, so we have to adjust your question to any significant velocity just under c (c represents the speed of light). If we say you're traveling 99.9% of c, relative to the star, then your own clock on board your spacecraft will measure a time interval of about 4.47 years, while a clock stationary with respect to the star will measure just over 100 years instead.

Note that, for you, the distance to the star has contracted from 100 light years to just 4.47. That's how you can get there in less than 100 years even though you can't travel faster than light.

More specifically, why would I experience time going faster and age slower than people on Earth?

That's just the way the laws of nature work.

And how does this affect my biological health?

Your health is unaffected, but you will only experience 4.47 years worth of time.

I am struggling to see how traveling faster would slow my aging process. I can't seem to find the link between speed of light and the speed of which my human cells die.

The link is time dilation. Clocks in two different reference frames that are moving relative to each other will see the other as ticking at different rates. These clocks could be be mechanical clocks, bouncing light pulses, or the chemical reactions that take place in your cells. You are, indeed, aging at a different rate if you are moving relative to someone else.

 

[PeroK]

You are, indeed, aging at a different rate if you are moving relative to someone else.

This is not true. Time dilation is symmetric. If we look at a full round trip for the rocket, then there will be differential aging, but that's a different matter.

 

[Drakkith]

This is not true. Time dilation is symmetric. If we look at a full round trip for the rocket, then there will be differential aging, but that's a different matter.

I was trying to keep it simple for the op, but you are correct. You won't see the differential aging until one of you accelerates and comes back to the other.

 

[Nugatory]

I am struggling to see how traveling faster would slow my aging process.

Your cells age at exactly the same rate as the cells of someone who stays at home on earth, and likewise with all other biological, chemical, physical, mechanical processes - time is still passing at a rate of one second per second for both you.

To understand what's going on we have to dig deeper than just "speed dilates time". There are four important points in spacetime here:
a) You leave earth, as both you and the person left behind zero your wristwatches.
b) You arrive at the distant star and look at your wristwatch.
c) The person back on Earth looks at their wristwatch at the exact same time that you arrive at the distant star, using the frame in which the Earth is at rest and you are moving to define “same time”.
d) The person back on Earth looks at their wristwatch at the exact same time that you arrive at the distant star, using the frame in which you are at rest while the Earth and the star are moving in the opposite direction to define "same time".

Because of the relativity of simultaneity (an essential concept in understanding relativity) #c and #d are different events that happen at different times. DO NOT MOVE ON until you are comfortable with the notion that #b and #c happen at the same time in one frame while #b and #d happen at the same time in the other. This is what most confuses most people when they first encounter special relativity, and it is a consequence of the fact that the speed of light is the same in all frames.

There are fewer seconds along the path in spacetime between #a and #b than between #a and #c, so even though everybody’s cells are aging at the same rate and obeying the same laws of nature the Earth person will conclude that time is running slow for you. Same rate of aging for fewer seconds means less aging.

However, there are also fewer seconds between #a and #d than between #a and #b so you might equally reasonably conclude that the Earth person is the one with the slower clock. This is how we get the apparently paradoxical fact that time dilation is symmetric - if you and I are moving relative to one another we both will correctly find that the other clock is slower than our own if we consider ourselves to be at rest and the other to be moving relative to us.

And finally, since @Drakkith and @PeroK introduced differential aging (which is not time dilation, but often confused with it) we can consider what happens if when you reach the distant star you turn around and return to earth.
This gives us a fifth relevant event, #e: You arrive back at Earth and compare your age and wristwatch time with the person who remained behind.

It turns out that there are more seconds between #a and #e (their path through spacetime) than along your path from #a to #b to #e. That's what a comparison of the wristwatches shows, and it's what a comparison of your biological ages shows: cells aging at the same rate, but yours had fewer seconds in which to age.

 

[cianfa72]

I would like to propose a process/procedure to 'implement' what @Nugatory said in previous post.
Let me know if it makes sense.

Suppose the person left on Earth has got two wristwatches: the first reads the (coordinate) time of the frame in which he and the Earth are at rest while the second reads the (coordinate) time of the frame in which you are at rest while the person left on Earth is moving relative to you. Zero these wristwatches when you leave earth.

Now consider event a) and in particular event d) of the post #6. For the latter the person on Earth reads the time $t_0$ as shown from its first wristwatch when its second wristwatch shows a time value exactly the same as the time $t'_0$ shown from your wristwatch when you arrive at distant star (i.e. basically the coordinate time of the frame you are at rest in when you arrive at distant star).

Since speed of light is finite, to physically realize the above you can do the following: when you arrive at distant star send a message back to the person on Earth with the time value $t'_0$ read from your wristwatch (the coordinate time of the frame you are at rest in when you arrive at distant star).

Eventually the message will be received by the person on Earth and then he will be able to calculate back the value of time shown from its first wristwatch (i.e. $t_0$) when its second wristwatch showed the time value $t'_0$.

 

[PeroK]

Let me know if it makes sense ...

Alternatively, consider a row of clocks at regular intervals between Earth and the distant star. All at rest and syncronised in the Earth frame. Then consider a long line of rockets at regular intervals, all at rest relative to each other, with syncronised clocks in the common rest frame and the same proper distance apart as the clocks in the Earth's frame.

We find there is complete symmetry (as there must be):

The rockets are closer together, their clocks run slow and are not synchronised, as measured in the Earth frame. Likewise, the Earth frame clocks are closer together, run slow and are not synchronised, as measured in the rocket frame.

Any asymmetries are created by changes in the rest frame - often by the rockets' initial accceleration and final deceleration phases. But, if we have these phases as happening outside the experiment (e.g. we accelerate the rockets to full speed before they reach Earth and alow them to overshoot the distant star without slowing down), then we have complete symmetry between two inertial frames.

 

[cianfa72]

Then consider a long line of rockets at regular intervals, all at rest relative to each other, with synchronized clocks in the common rest frame and the same proper distance apart as the clocks in the Earth's frame.

That long line of rockets at regular intervals (all at rest each other with clocks Einstein synchronized in their rest frame) are moving at constant velocity w.r.t. the Earth and the star, right ?

 

[PeroK]

That long line of rockets (all at rest each other with clocks Einstein synchronized in their rest frame) are moving at constant velocity w.r.t. the Earth and the star, right ?

Yes.

 

[Jonathan Scott]

A basic rule of Special Relativity is that everyone measures the speed of light in a vacuum to be the same. So imagine a clock that works by reflecting light (or radio waves) between two mirrors a fixed distance apart and counting the number of reflections. Now align it so that the light path is perpendicular to the direction of motion as seen by an external observer. The light now has a zig-zag path, making it longer, so according to the external observer the clock runs more slowly because of the extra path length. This is just one simple example; all other methods of determining time locally are subject to the same effect.