# Special Relativity and Biological Clocks.

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1. May 30, 2014

### siddharth5129

Hi.
So the whole premise of special relativity seems to me to be hinged on the immutability of the speed of light, the fact that it is the same for every inertial frame of reference, and the fact that information and energy cannot travel faster than this.
What really puzzles me is this whole traveling forward in time thing. While I can appreciate the use of the twin paradox as a pedagogical device, would a moving frame of reference at a comparable to light speed actually affect how fast a biological system in that frame ages? Has this ever been observed ? Would the living system's biological clock actually slow down relative to an observer on the earth ? Would his sense of time perception alter to make it feel as if he's spending say 2 years on the shuttlecraft, while his twin back home feels like he's spent 50 waiting for him ?
Special relativity made perfect sense to me until this came along.
From the derivation of the time dilation equation that my textbook shows, the crucial argument seems to me to hinge on the fact that the light ray follows different paths when viewed from one frames of reference or another, and because of the fact that it's speed remains the same, the time measurements must be different. So, if you used a signal other than light, would you even have time dilation ? Why must all clocks be based on light ? A biological clock surely doesn't use light to keep time, does it ?

2. May 30, 2014

### tom.stoer

I think the pedagocial problem is that time dilation, twin paradox and diffential aging is introduced in terms of reference frames and coordinate times. In my opinion one should better start with the proper times of the two observers.

The measuring device for proper time is a co-moving clock, e.g. a wristwatch, or the biological system itself. Starting at the same point in spacetime two observers follow different paths through spacetime and eventuelly meet "some time later" to compare their proper times (wristwatches, greyed hairs, face wrinkles, ...). In this description we avoid the introduction of a "globally valid time", "exchanged light signals" and all that stuff. We do never compare times - unless the two observers meet at the same spacetime point after their journeys.

The question "would the living system's biological clock actually slow down relative to an observer on the earth ?" becomes irrelevant. Each observer feels his aging as usual. There is no measurable effect. Only after comparing their proper times both agree that something strange happened to them.

The effect can be (and has been!) measured with high accuracy - but unfortunately it's so tiny that it's not observable for biological systems.

3. May 30, 2014

### siddharth5129

Why does light have to be this 'ultimate' signal then ? What if we use sound for all our timekeeping ? Do the postulates of relativity not hold if the signal is mechanical rather than electromagnetic ?
And i'll make my other question more specific then. Would a person who travels for 20 years at light speed, finally arrive at his starting location (assuming that there's no acceleration or deceleration anywhere ) and see that the earth has aged 448 years ? This would imply that his biological clock has, in some real way, slowed down. What if the timekeeping mechanism in his body is something other than electromagnetic ?
Thanks for all your time :)

4. May 30, 2014

### Simon Bridge

Yes.

I don't think anyone has done the long-term experiment described no.
But can you think of any reason a tick on a biological clock should be any different from a tick of an atomic clock? Is biology not subject to physics?

This was actually an historical objection to relativity.
Vitalists etc argued that biological processes are fundamentally different so whatever your wristwatch says, your body has it's own notions of time.

The reason a light signal is used in the thought experiment is to make the physics simple and the concepts clear.

The current state of knowledge is that biological organisms are subject to the same physical laws in the same way as anything else. If it holds for the light-clock, it must hold for all clocks - including biological ones.

5. May 30, 2014

### siddharth5129

But it doesn't hold for sound clocks does it ? If the speed of sound is different in different inertial frames of reference, then sound clocks wouldn't display time dilation ? I say this because the argument in my textbook that derives the time-dilation relation seems to hinge on using a light clock and the fact that the speed of light is the same in both the earth frame of reference and the train frame of reference. Am i mistaken in saying that that speed of sound is indeed different in both frames of reference because sound is a mechanical wave ? In that case, 'sound' clocks shouldn't display time dilation at all, right? What if the signal is merely a transverse wave on an infinitely long string? If the timekeeping mechanism in the body is electromagnetic, then I have no problem with this argument, but is it ?
It seems to me that not using light would fundamentally alter the physics of the whole problem ? So light must be fundamental in some way (Is it because of the invariance of maxwell's equations under lorentz transformations or something ?) and not just to make the physics simple.
Appreciate all the help. Thanks a ton.

6. May 30, 2014

### tom.stoer

You have to distinguish between aging and exchange of light signals.

Think about the following: instead of exchanging light signals you could exchange the wirstwatches themselves. Unfortunately during the journey of the watch the watch itself ages. So when twin A receives the watch of twin B and compares the two times she can not distinguish between the time interval attributed to her twin's journey and the time interval for the watch after having been sent from B to A.

With light signals this is different: the proper time along a light-like path is always zero!!

So in a sense there is no aging of light and one can use it to compare proper times w/o distorting them. That's why one is using light signals when explaining special relativity. But please keep in mind that the effect does not depend on the exchange of light signals. It's a purely geometrical effect, and there's no need to exchange light signals at all.

Aging itself is governed by other physical processes (human cells) and for each macroscopic physical system there are typical time scales w/o any direct reference to speed of light.

You mean near speed of light, not at speed of light.

Yes, this is what could happen (and it's of course possible to take accelerated motion into account)

They do not slow down from the local perspective of one twin observing herself in a mirror during the journey.

7. May 30, 2014

### siddharth5129

I'm sorry. I'm still very confused. What if the twin in the space shuttle bounces a ball to keep time (say there's no air friction ). Since this is a periodic phenomenon, it's a valid way to keep time. But an observer on earth will record the same time interval for any two events that the observer in the space shuttle records if time is kept in this manner. Hence no time dilation, and no length contraction. This makes absolutely no sense, so what am I missing here ?

8. May 30, 2014

### siddharth5129

I'm sorry, I don't understand at all what you mean by 'aging of light' .

9. May 30, 2014

### Simon Bridge

This is not correct - time dilation applies to the bouncy ball method too.
It gets a bit more complicated that the ball's speed is not invariant.

10. May 30, 2014

### tom.stoer

It doesn't matter whether you use a light clock, a bouncing ball, a watch or the biological system itself. During the journey no twin will observe anything special. After the journey they can compare the number of bounces of their balls and will find that they differ - as predicted by special relativity.

What do you mean by "recording a time interval" for these far distant events? How are these time intervals measured? Are you now talking about observing them via light signals?

11. May 30, 2014

### siddharth5129

the shuttle carrying the ball moves at a speed v relative to the earth observers frame, so after every bounce, the observer on earth sees the ball moving at a horizontal speed v in addition to the vertical speed it has. So Though the ball follows a longer path as seen from the observer on earth, it also has an additional speed to compensate. So they should both measure the same time interval between bounces. This doesn't happen with light because light has the same speed in both reference frames, and since light follows a longer path when seen from the earth observer's frame of reference, it should give him a larger time interval between the events registering on a counter. So shouldn't the bouncy ball method give you no time dilation ? Where has my reasoning gone wrong ?

12. May 30, 2014

### tom.stoer

Suppose there's something like a massless wristwatch which could move along a light-like path of a photon. The proper time measured by this watch is always zero. Objects moving at the speed of light have zero proper time.

Attention: please make sure that you understand the difference between proper time (which is a purely local concept and which is exactly the time measured by clocks) and coordinate time (which is a global concept but requires additional assumptions like synchronized clocks located at every point of space). The twin paradox can be described w/o referring to coordinate time at all.

13. May 30, 2014

### siddharth5129

By 'recording a time interval' I mean counting the number of ball bounces.

14. May 30, 2014

### siddharth5129

So you're saying you could derive the time dilation equation by using the bouncy ball method too ? Has this been done anywhere ?

15. May 30, 2014

### tom.stoer

This is not true. In relativistic kinematics it's no longer allowed to add velocities as usual.

Let's say the shuttle moves at speed v in horizontal direction w.r.t. to earth. And let's assume the ball moves at speed w in vertical direction w.r.t. the shuttle. Then you would conclude that the velocity of the ball w.r.t. earth is described by the vector (v,w). This is wrong! The exact formulas for relativistic addition of velocities can be found in the Wikipedia article.

16. May 30, 2014

### siddharth5129

Thanks. But this assumes that time dilation is true. My concern is with showing that it is true. So, why exactly would the vector quantities not add vectorially as in the galilean sense ? Can we show that they shouldn't add vectorially near light speeds without invoking light clocks ? Can we use regular household pendulum clocks and show that the galilean addition of velocities near light speeds doesn't hold ?
Thanks for all the replies. Really appreciate it.

17. May 30, 2014

### tom.stoer

But that's not the same thing.

Counting the number of bounces certainly measures something invariant. The number of bounces of the ball in the shuttle is the same when observed in the shuttle or when observed from earth via light signals.

Recording the time interval means that you measure the time between two bounces using an additional watch. You don't need a watch to count bounces.

The time between two bounces of two identical balls (one on earth and one in the shuttle) is identical - provided that the first ball on earth is observed by a observer on earth on a watch located on earth, and provided that the second ball in the shuttle is observed by an observer in the shuttle on a watch located in the shuttle.

The time interval between two bounces of the ball in the shuttle differs when observed a) by an observer on earth and a watch located on the earth and b) by an observer in the shuttle on a watch located in the shuttle.

18. May 30, 2014

### tom.stoer

Where' your problem? There's a formal derivation of time dilation which has been confirmed experimentally. At which step do you see problems?

19. May 30, 2014

### siddharth5129

Thanks. That clears up a lot of things for me. I'm just confused about why use light to derive lorentz transformations. Does it have to do with the fact that we 'see' everything? Isn't information available to us via sound as well? Why not use sound to derive everything ? In that case would you conclude that time dilation must happen? I don't see how.

20. May 30, 2014

### siddharth5129

Does this derivation use light clocks? I would just like to see an argument that isn't hinged on the use of light clocks. Could you send me a link where they derive it formally without the use of light clocks ?

21. May 30, 2014

### siddharth5129

The bouncing of a ball is a periodic event. So counting the number of bounces is the same as using a watch is it not? A watch essentially counts a recurring periodic event. So if you say that the number of bounces is invariant, then I have in fact devised a clock which is invariant at near light speeds, have i not ? This is exactly my point, the way i see it, all these arguments seem to be predicated on the mechanism used to measure a time interval. If my mechanism is mechanical ( counting the number of ball bounces ) then time dilation doesn't seem to hold. It seems to hold only when you count light reflections to measure time. I still feel like i'm missing something.

22. May 30, 2014

### m4r35n357

Time dilation is routinely computed via the Lorentz transformation. Here is a link to a derivation of the Lorentz Transform without using light clocks. http://mathpages.com/rr/s1-07/1-07.htm. It is a little more mathematical, you need to know about the determinant of a 2x2 matrix, but not much more than that.

The derivation proper begins about 75% of the way down, starting at the paragraph beginning: "For a typical derivation of the Lorentz transformation in this axiomatic spirit, . . .".

23. May 30, 2014

### nearlynothing

But remember no experiment at all can be used to distinguish an inertial frame from any other, this ball bouncing is an experiment, a mechanical one.
If both obsrvers agreed on the time, you could say which one of them is moving 'absolutely'.

Edit: you can also add that a biological system of course is a physical entity which can be regarded as an experiment, in the same sense the ball bouncing is one.

Last edited: May 30, 2014
24. May 30, 2014

### pervect

Staff Emeritus
You might want to think how you'd model "a biological clock".

Is this something that you can measure experimentally, or is it something philosophical, like "do humans experience time in the same way that a clock does" that can'b be decded by experience.

I will say that there isn't any known difference in the measurement of rates of clocks that can be measured (for instance by comparing one clock to a different sort of clock). They all appear to keep the same time, though some are more precise than others. So it would be odd if biological systems were "special" in their notion of time from any known physical phenomenon.

As far as your other questions go, someone in a moving rocketship wouldn't notice anything out of the normal (in any way that could be measured at least), this is one of the principles of relativity - the laws of physics aren't any different in motion, all motion is relative.

If you have a pair of clocks, part of the twin paradox is that which clock is running fast and which is slow depends on how you compare them.

Have you read anything about the relativity of simultaneity? From your questions, I would suspect that perhaps you have not, or have missed something if you have.

I would recommend http://www.aapt.org/doorway/TGRU/articles/Vokos-Simultaneity.pdf, though I'm not sure its necessarily at the right level, hard for me to tell. It's notoriously hard though to communicate the idea of the relativity of simultaneity, and the authors have studied the issue, so I'm hoping their approach will help. The main issue is that the paper is aimed more at instructors, than students.

Last edited: May 30, 2014
25. May 30, 2014

### tom.stoer

Lorenz tranformation, time dilation and SR do in no way depend on light, observations using light or anything like that. SR is a purely geometric framework.

Suppose there are no massless photons at all. Suppose we do not have eyes to register photons. Suppose we do not have wristwatches. Suppose we do not even have a concept called "time". Suppose we make the same experiment with two identical bouncing balls, one on earth and one in the spaceship. Suppose neither twin does ever observe the other twin's ball. All what they are doing is counting bounces. When the spaceship leaves they start counting, when it returnes they stop counting. The twin on earth counted N bounces during the absence of of the second twin; the twin in the spaceship counted N' bounces during the journey. All what they are doing relies on local facts (bounces, which could be registered acustically, sensors, ...). From N and N' they can derive a concept called proper time: τ and τ', respectively. The number of bounces N and N' differ, and so do the (derived) proper times. The difference τ - τ' agrees with the formula derived from SR. That's time dilation in it's bare form.