[abacus9900 (OP)]

We have been told many times that two observers, one moving at a large fraction of the speed of light in a spaceship and the other one on earth (say), will each see the other's clock as moving much more slowly than their own clock and that this is somehow tied up with the constancy of the speed of light, but why? How does light decide how quickly or slowly clocks, either mechanical or biological, run?


[MOD EDIT - PLEASE PHRASE YOUR POST TITLES AS QUESTIONS, IN LINE WITH OUR FORM POLICY. THANKS. CHRIS.]

[JP]

Basically, it comes from enforcing two requirements in inertial reference frames.  These are frames moving at a constant velocity, so that acceleration isn't important.
1) The speed of light is constant no matter how fast you're moving.
2) The laws of physics are the same within your own reference frame no matter how fast you're moving. 

If you assume those two are true, then it turns out that observers in different frames don't end up agreeing on time or distance measurements.

The famous example would be a train passing a station.  There are two observers here: Tony is at the back of the train, and Paula is on the platform.  When Tony and Paula are right next to each other, a flash goes off at the front of the train.  Let's say they both have special watches that have been set so that one "tick" equals the time it takes for light to go from the front of the train to back. 

Tony on the train measures that it takes 1 tick for the light to reach him.  By the time the light has reached him, he's already moved past Paula, so he knows that the light will take longer than 1 tick to reach Paula.

Meanwhile, Paula is on the platform.  Since the light originated from 1 train length in front of her and appears to her to be moving at the speed of light, it only takes 1 tick of her clock for the light to reach her.  Since Tony is further ahead of her, she deduces that the light passed Tony in under 1 tick.

So Tony observes: It took 1 tick to reach Tony, and more than 1 tick to reach Paula,
while Paula observes: It took less than 1 tick to reach Tony and more than one tick to reach Paula


This disagreement happens because of point (1)--that light appears to move at the same speed to all inertial observers, regardless of how fast they're moving.  If we didn't require that, and the light came towards tony faster than it did towards Paula (because he was moving towards it), they could both agree that it took less than 1 tick to reach Tony and 1 tick to reach Paula.  However, there's overwhelming evidence that relativity is true and that the speed of light is constant for all observers, which requires that time measurements can disagree between observers.

Once you accept that time measurements disagree between observers, then point (2) tells you that the laws of physics for each observer within their reference frame seem to work according to their personal clock.  This includes biological processes, such as aging.  According to their own points of view, Tony and Paula would appear to age normally and time would appear to flow normally for them.  But if they compared their clocks, they'd find disagreement.

[abacus9900 (OP)]

Once you accept that time measurements disagree between observers, then point (2) tells you that the laws of physics for each observer within their reference frame seem to work according to their personal clock.  This includes biological processes, such as aging.  According to their own points of view, Tony and Paula would appear to age normally and time would appear to flow normally for them.  But if they compared their clocks, they'd find disagreement.

Thank you very much for that extensive reply JP, much appreciated.

I was wondering, though, if we knew why all physical processes (such as ageing) slow down at greater speeds. I know it's because time 'slows down', but what does this really imply?

[JP]

I think it implies that our intuitive belief that time is constant for everyone isn't true.  Different observers won't agree on the time between events, and physical processes rely on a series of events to happen, so different observers say that the processes happen faster or slower...

[Bill S]

Hi, abacus9900, we meet again.

Since the light originated from 1 train length in front of her and appears to her to be moving at the speed of light, it only takes 1 tick of her clock for the light to reach her.  Since Tony is further ahead of her, she deduces that the light passed Tony in under 1 tick.

No problem with this, but I do run into a problem with another observer. I'll work through it.


Let’s stick with Tony and Paula, and with their special clocks, but let’s alter the ticks slightly to simplify things.  I need simplicity.  Say the light takes 2 ticks to travel from source to Tony, then, in Tony’s F of R, a further tick to reach Paula. 
Tony observes: The light takes 2 ticks to reach him, then 1 tick to reach Paula.  However, Paula’s clock registers just 2 ticks for the light to reach her.  Thus, in Tony’s F of R, Paula’s clock takes 2 ticks while his takes 3.  Paula’s is running slower.

Paula observes: The light takes 2 ticks to reach her, so it must have reached Tony in 1 tick.  Thus, in Paula’s F of R, Tony’s clock takes 1 tick while hers takes 2. Tony’s is running slower.

What does an outside observer, who perceives himself as being stationary relative Paula, observe?  Assuming the light is a single, very brief flash he does not observe the source as moving, but he does see Tony moving towards the source.  He sees light travelling at “c” and Tony travelling at half that speed. Therefore, he sees the light as reaching Tony in 1 tick, but Tony’s clock took 2 ticks, so in the F of R of the outside observer, Tony’s clock is running faster, but he perceives Tony as moving relative to him.

There must be something wrong here, but I can’t see it.

[Bill S]

There must be something wrong here, but I can’t see it.

Someone must be able to see it!

[maffsolo]

I found this in under Time dilation in wikipedia if it might shead some light on the subject  [?]

"Time dilation: special vs. general theories of relativity
In Albert Einstein's theories of relativity, time dilation in these two circumstances can be summarized:

In special relativity (or, hypothetically far from all gravitational mass), clocks that are moving with respect to an inertial system of observation are measured to be running slower. This effect is described precisely by the Lorentz transformation.
 
In general relativity, clocks at lower potentials in a gravitational field—such as in closer proximity to a planet—are found to be running slower. The articles Gravitational time dilation and Gravitational red shift give a more detailed discussion. Special and general relativistic effects can combine, for example in some time-scale applications mentioned below.

Thus, in special relativity, the time dilation effect is reciprocal: as observed from the point of view of either of two clocks which are in motion with respect to each other, it will be the other clock that is time dilated. (This presumes that the relative motion of both parties is uniform; that is, they do not accelerate with respect to one another during the course of the observations.)

In contrast, gravitational time dilation (as treated in general relativity) is not reciprocal: an observer at the top of a tower will observe that clocks at ground level tick slower, and observers on the ground will agree about that, i.e. about the direction and the ratio of the difference. There is not full agreement, all the observers make their own local clocks out to be correct, but the direction and ratio of gravitational time dilation is agreed by all observers, independent of their altitude."

[JP]

What does an outside observer, who perceives himself as being stationary relative Paula, observe?  Assuming the light is a single, very brief flash he does not observe the source as moving, but he does see Tony moving towards the source.  He sees light travelling at “c” and Tony travelling at half that speed. Therefore, he sees the light as reaching Tony in 1 tick, but Tony’s clock took 2 ticks, so in the F of R of the outside observer, Tony’s clock is running faster, but he perceives Tony as moving relative to him.

Sorry--I didn't see this earlier.  I think it goes like this: If he sees Tony's clock take one tick, but Tony's clock actually took 2 clicks according to Tony, then the clock is ticking more slowly for the moving observer than it is for Tony, and therefore, appeared to slow down.

[Bill S]

Still struggling! Let's split it into bite sized bits.


1.  Paula’s clock takes 2 ticks while Tony’s takes 3: Paula’s is running slower.

2.  Tony’s clock takes 1 tick while Paula’s takes 2:   Tony’s is running slower.

3.  Observer sees 1 tick while Tony sees 2 ticks. Is this equivalent to saying that the observer’s clock takes 1 tick while Tony’s clock takes 2?  If it is, then to keep our reasoning in line with points 1 & 2, we have to say that the observer’s clock is running slower than tony’s, but this is in the observer's F of R, in which we are regarding him as stationary, (relatively, of course).

[Ron Hughes]

abacus, doesn't look like you are going to get an answer just a run around.

[maffsolo]

Tony is traveling in a train, near light speed.
Tony looks out the window everything is passing by near light speed.
Anything he views as an individual motion of the things he pasts, are moving slow, a wheel spinning, a person blinking etc…

Tony’s frame of reference within, to Tony, it is normal.
 It takes a person (4) ticks to blink.
Same goes for Paula’s frame of reference.

At a flash his train pasts Paula, as she begins to blink:
According to Tony’s clock… it takes her ( ticks to blink.
He reads Paul’s clock from his frame as being (4) ticks. Her clock is referenced to her blink and its image is also paused at that number tick..

Paula observes Tony as he speeds by or view it as if Tony is at rest and Paula is speeding by in the opposite direction.
According to Paula’s Clock… it takes Tony ( ticks to blink.
She reads Tony’s clock from her frame as being (4) ticks.

If distance were introduced, let’s say Tony’s train traveled a certain distance.
To Tony the round trip time would be shorter when compared to the time Paula observed, when both clocks are held side by side in the same frame of reference.

[Geezer]

Abacus,

Just in case you are not aware of an experiment that appears to confirm the theory, here's some information on it.

http://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment

[jartza]

How does light decide how quickly or slowly clocks, either mechanical or biological, run?

Nobody knows, I guess.

But why does a "light clock" slow down when pushed? In other words, why does the spreading of
a beam of light get _slower_ when a spotlight pushed?

Well, for the light that is inside the reflector, when the reflector starts to move, the reflector appears to proceed farther.

Now we have explained one case of slowing down.

Next thing to explain might be: Why does a fast moving light bulb without any reflector
produce a beam of light, that spreads very slowly, if the speed is very high?
 

[jartza]

Here is something interesting:
When a long compressed spring spinning along its long axis starts to vibrate, when the adhesive tape that keeps the spring compressed breaks, the spinning does not slow down.

This kind of contradicts the law of time dilation we have learned at the college, but slowing down of the spinning would contradict the law of conservation of angular momentum that we have learned at the college.

Now some might say the increase of mass of the spring allows the spin to slow down while angular momentum stays the same, but that would be very erroneous thing to say, because objects do not change their mass spontaneously.

So could you readers accept that the spinning does not slow down?

 

[imatfaal]

Jartza - I have trouble linking the the spinning spring with time dilation.  I presume that spin and expansion are all at non-relativistic speeds and there is something in the combination of motions that triggers a similarity in your thoughts - I cannot see that similarity, perhaps you could explain.

[jartza]

Jartza - I have trouble linking the the spinning spring with time dilation.  I presume that spin and expansion are all at non-relativistic speeds and there is something in the combination of motions that triggers a similarity in your thoughts - I cannot see that similarity, perhaps you could explain.

Well, a spinning particle in a particle accelerator slows down its spinning,
while accelerated, because of time dilation, doesn't it? This particle
could be an ion, a charged molecule, or a charged dust particle, if elementary
particles do not spin. So here we have a spin that slows down when linear speed
increases.

[Bill S]

why does the spreading of a beam of light get _slower_ when a spotlight pushed?

I'm not sure that I have grasped this. The speed of light does not change, so in what sense does the "spreading" slow down; and in which F of R does this happen?

[imatfaal]

Jartza - I think I will have to think about that.  But I find it difficult to make a judgment on a relativity question through a non-relativistic example that only provides insight because of its similarity to a different relativistic event (and one I am not convinced about). 

Particles travelling at relativistic speed need to be very carefully handled - when you say it slows down its rotation, as measured by whom? in which reference frame?  what sort of spin?

[jartza]

why does the spreading of a beam of light get _slower_ when a spotlight pushed?

I'm not sure that I have grasped this. The speed of light does not change, so in what sense does the "spreading" slow down; and in which F of R does this happen?

The spotlight stands on a slippery table. We pick two random photons in the light beam.
The distance between the photons might grow at speed 0.2 c, for example.

Now we push the spot light, direction of the push is the direction of the light beam. When the spotlight is moving the distance between two randomly chosen photons grows slower, on the average, because the beam is a narrower beam now, in the F of R of the table.

[jartza]

Jartza - I have trouble linking the the spinning spring with time dilation.  I presume that spin and expansion are all at non-relativistic speeds and there is something in the combination of motions that triggers a similarity in your thoughts - I cannot see that similarity, perhaps you could explain.

When a clock moves it is slow. (this is from a physics book),
so therefore:
When a clock is shot from a cannon it slows down. (this my own reasoning)

Also when a gyroscope is shot from a cannon, it slows down. (also my own reasoning)

But when a spinning cannon shoots a cannon ball, the cannon ball's spinning does not change. (this is what I claim)
 

(if you want you can replace "slows down" with "slows down or speeds up depending on frame of reference", or "changes")