relativity/time dilation

firefly08

I'm trying to get my head around time dilation, but I keep hearing this explanation that sounds very bogus to me.

People keep using this "light clock" to explain it. So you have 2 mirrors, with light bouncing back and forth between them, and a clock that ticks for each complete cycle. Now if you put one of those clocks on a plane, and keep another one on the earth, an observer on the earth would see the one on the plane ticking more slowly (assuming he could actually see it). The trouble is, I think this is trivial and doesn't require time dilation to explain:

When the light bounces off the top mirror it reflects off it, and the location where the light hits the mirror is the source of light for this half-cycle of the clock. That does not change within this time period. But the location of the bottom mirror does change, relative to this light source - it gets further away, so it therefore takes longer for the light to reach the lower mirror. So the clock ticks less frequently. This is simply because the distance between the light source and the target mirror has increased. So with the speed of light remaining the same, there is no need whatsoever for time to slow down.

Interestingly, this means that the clock would slow down for all observers, including the guy on the plane - it is the relative motion between the components of the clock (the light and the mirrors) that causes the clock to actually slow down. The one left on earth would not appear to have slowed down from anyone's point of view because the mirrors are in the same place at the end of the cycle as they were at the beginning. (IWO the light strikes both mirrors at the same angle each time, 90 degrees. )

Of course I'm assured that these observations are not what actually happens when they test the theory so that tells me either the analogy is wrong or I am missing something. What am I missing here? I see this represented in pretty much every video, documentary, and online article that claims to explain time dilation. They always show animations of it and you can see the distance increasing.

Kohl

firefly08 wrote: »

I'm trying to get my head around time dilation, but I keep hearing this explanation that sounds very bogus to me.

People keep using this "light clock" to explain it. So you have 2 mirrors, with light bouncing back and forth between them, and a clock that ticks for each complete cycle. Now if you put one of those clocks on a plane, and keep another one on the earth, an observer on the earth would see the one on the plane ticking more slowly (assuming he could actually see it). The trouble is, I think this is trivial and doesn't require time dilation to explain:

When the light bounces off the top mirror it reflects off it, and the location where the light hits the mirror is the source of light for this half-cycle of the clock. That does not change within this time period. But the location of the bottom mirror does change, relative to this light source - it gets further away, so it therefore takes longer for the light to reach the lower mirror. So the clock ticks less frequently. This is simply because the distance between the light source and the target mirror has increased. So with the speed of light remaining the same, there is no need whatsoever for time to slow down.

Interestingly, this means that the clock would slow down for all observers, including the guy on the plane - it is the relative motion between the components of the clock (the light and the mirrors) that causes the clock to actually slow down. The one left on earth would not appear to have slowed down from anyone's point of view because the mirrors are in the same place at the end of the cycle as they were at the beginning. (IWO the light strikes both mirrors at the same angle each time, 90 degrees. )

Of course I'm assured that these observations are not what actually happens when they test the theory so that tells me either the analogy is wrong or I am missing something. What am I missing here? I see this represented in pretty much every video, documentary, and online article that claims to explain time dilation. They always show animations of it and you can see the distance increasing.

I think you have to see this in terms of the specific frame of reference for each observer. In the reference frame of the observer on the plane, his clock is stationary, yet in the reference frame of the observer on the ground the clock of the observer on the plane is moving. Don't forget that the observer on the ground is measuring with a different clock, a clock that's stationary in his frame of reference.

I learned about this concept with an example of an observer on a train (moving frame of reference), and an observer on the platform watching (stationary frame of reference). There was a cross section cut in the train and you can see a shot of the light beam at the bottom of the light clock, then a shot of the light beam at the top of the light clock, and the a further shot of the light beam at the bottom of the mirror again. The train has moved forward in each of those cases and you can see that the light is travelling at an angle from the frame of reference of the observer on the platform (remember, this observer is measuring the time with a different clock, that's stationary). This light path was described by Pythagoras' theorem and thats how the time dilation formulas are derived.

Here's a diagram of what i mean

http://en.wikipedia.org/wiki/File:Time-dilation-002.svg

firefly08

ok...I'm going to have to think it over for a while! My problem is that it doesn't seem unexpected at all for the plane-clock to be slower. It's slower because it's dimensions have been physically stretched. It's mirrors are further apart than the ones in the ground-clock. I realize it appears the opposite way to the people in the plane, and that's something I'm trying to get my head around now. But even so, this seems to be due to the fact that the clock works by shooting light between two moving mirrors. I don't see why a clockwork device, or the human body, or anything else, would actually slow down relative to the other reference frame. There's nothing in the experiment that indicates that to me.

Morbert

firefly08 wrote: »

ok...I'm going to have to think it over for a while! My problem is that it doesn't seem unexpected at all for the plane-clock to be slower. It's slower because it's dimensions have been physically stretched. It's mirrors are further apart than the ones in the ground-clock. I realize it appears the opposite way to the people in the plane, and that's something I'm trying to get my head around now. But even so, this seems to be due to the fact that the clock works by shooting light between two moving mirrors. I don't see why a clockwork device, or the human body, or anything else, would actually slow down relative to the other reference frame. There's nothing in the experiment that indicates that to me.

What you must remember is the speed of light is the same for all observers. If the person on the plane observes stationary mirrors (I.e. The mirrors do not move with respect to the observer), and he sees the photon move at speed c, how could he observe a slower tick?

firefly08

What you must remember is the speed of light is the same for all observers. If the person on the plane observes stationary mirrors (I.e. The mirrors do not move with respect to the observer), and he sees the photon move at speed c, how could he observe a slower tick?

The mirrors move with respect to the source of light (the source of light being the other mirror at a time in the recent past, when it was somewhere else). In my mind, that is what makes the clock tick more slowly!

Morbert

firefly08 wrote: »

The mirrors move with respect to the source of light (the source of light being the other mirror at a time in the recent past, when it was somewhere else). In my mind, that is what makes the clock tick more slowly!

Not according to the observer on the plane. He sees the mirrors stationary, and the speed of light as c, and hence sees the clock tick at a "proper" speed. The observer on the ground sees the mirrors as moving, and the speed of light as c, and hence sees the clock tick more slowly.

Similarly, if we give the clock to the person on earth, he will see the mirrors as stationary and the speed of light as c, hence the clock will tick properly, while the person in the plane will see the mirrors moving and the speed of light to be c, hence he will see the clock ticking slowly.

firefly08

Not according to the observer on the plane. He sees the mirrors stationary, and the speed of light as c, and hence sees the clock tick at a "proper" speed.

Stationary with respect to what? Himself? That I understand. But the components of the clock are moving with respect to each other - surely that can be observed by anyone anywhere!?

Otherwise, it seems that you're saying that the light behaves like a ball bounced by someone standing on a moving train - the ball always comes up under their hand and so to them it appears there is no horizontal movement. But isn't that because the movement of the train and the person imparts horizontal momentum to the ball? I didn't think that could happen with light. When light shines vertically from a source that's moving horizontally, does the light get horizontal momentum too?

Thanks for being patient with me btw!

Morbert

firefly08 wrote: »

Stationary with respect to what? Himself?

Yes.

That I understand. But the components of the clock are moving with respect to each other - surely that can be observed by anyone anywhere!?

Otherwise, it seems that you're saying that the light behaves like a ball bounced by someone standing on a moving train - the ball always comes up under their hand and so to them it appears there is no horizontal movement. But isn't that because the movement of the train and the person imparts horizontal momentum to the ball? I didn't think that could happen with light. When light shines vertically from a source that's moving horizontally, does the light get horizontal momentum too?

Thanks for being patient with me btw!

A ball is a good way to highlight the consequences of the speed of light being the same for all observers. A person on the train will see the ball bounce up and down at a speed v. But a person on the ground will see the ball move up and down at speed v, but also along the track at the speed of the train, u. Hence, he will observe the speed of the ball to be the square root of v^2 + u^2. In otherwords, the person on the ground sees the ball move faster than the person on the train. Hence, under Newtonian physics, both people will see the ball bounce at the same rate, because although the person on the ground observes the ball travel a greater distance, they also observe the ball travel at a greater speed. But this is not the case with light. The person on the ground sees the light travel a greater distance, but the same speed c. Hence, they see a slower "bounce".

firefly08

OK, I get that difference between the ball and the light. But that doesn't address the issue I have with the light-clock; that the light does not move as a consequence of the movement of the airplane (and hence the clock) and therefore the plane, observer and mirrors all move relative to the light source.

Here is how I visualize it: the light hits the top mirror, and begins to shine from that point. I think of the lightwaves as concentric circles expanding from a particular point. Of course the light does not continue to emanate from that point, since the source was only there for the briefest of moments. Let's just look at one wave, the outermost circle in my visualization. This "circle" of light (really a sphere I suppose) will continue to expand until it hits something and is absorbed, right? In my mind, the centre of this circle does not move, ever. Therefore mirror moves relative to the centre of the circle.

Morbert

firefly08 wrote: »

OK, I get that difference between the ball and the light. But that doesn't address the issue I have with the light-clock; that the light does not move as a consequence of the movement of the airplane (and hence the clock) and therefore the plane, observer and mirrors all move relative to the light source.

Here is how I visualize it: the light hits the top mirror, and begins to shine from that point. I think of the lightwaves as concentric circles expanding from a particular point. Of course the light does not continue to emanate from that point, since the source was only there for the briefest of moments. Let's just look at one wave, the outermost circle in my visualization. This "circle" of light (really a sphere I suppose) will continue to expand until it hits something and is absorbed, right? In my mind, the centre of this circle does not move, ever. Therefore mirror moves relative to the centre of the circle.

The centre of the circle remains on the mirror from the perspective of the person on the train, as the observer on the train sees the circle expand at speed c (I.e. propagate at speed c equally in all directions).

firefly08

The centre of the circle remains on the mirror from the perspective of the person on the train, as the observer on the train sees the circle expand at speed c (I.e. propagate at speed c equally in all directions).

I think we've zeroed in on the key point that I'm struggling with. I don't see how the centre of this circle can stay with the observer. This means that an observer on the ground would see the centre of the circle moving relative to himself. But that can't be, since that would result in him observing light at a higher speed (i.e. the speed of the light wave relative to earth, plus the speed of the plane).

Whereas if the observer on the plane sees the centre of the circle moving relative to himself, that's fine. He's not going to see a different speed of light. Just a larger distance that the light has to travel before his clock registers a tick!

Morbert

firefly08 wrote: »

I think we've zeroed in on the key point that I'm struggling with. I don't see how the centre of this circle can stay with the observer. This means that an observer on the ground would see the centre of the circle moving relative to himself. But that can't be, since that would result in him observing light at a higher speed (i.e. the speed of the light wave relative to earth, plus the speed of the plane).

Whereas if the observer on the plane sees the centre of the circle moving relative to himself, that's fine. He's not going to see a different speed of light. Just a larger distance that the light has to travel before his clock registers a tick!

That is indeed the crux of the issue. The answer is that all observers see the centre stationary with respect to themselves. Observers will therefore not agree where the centre of the circle is. The observer in the plane will say it is at the mirror. The observer on the ground will say it is at some point the mirror has passed through. This leads to contradictions unless we employ relativistic co-ordinate transformations (Lorentz transformations) to understand how different observers are related.

firefly08

OK...so I have started to read up on this Lorentz transformation stuff.


It seemed very complicated until I stumbled across Einstein's actual book, that is clearing up the maths for me a bit.

I'm still having trouble with the intuition side of things, but I suppose it's like trying to explain to a blind person that stuff gets smaller as you get further away. They'd think you were nuts.

Morbert

firefly08 wrote: »

OK...so I have started to read up on this Lorentz transformation stuff.


It seemed very complicated until I stumbled across Einstein's actual book, that is clearing up the maths for me a bit.

I'm still having trouble with the intuition side of things, but I suppose it's like trying to explain to a blind person that stuff gets smaller as you get further away. They'd think you were nuts.

Be warned, Einstein was a great physicist, but presented his theory in a confusing manner (primarily because the theory was new and there were competing mathematical frameworks at the time). Relativity is most intuitive when it is described with Minkowski spacetime, developed by Hermann Minkowski. He is the one who famoulsy said the concept of time is an illusion and the concept of space is an illusion, and only a unification of the two concepts will endure.

So I would not recommend Einstein's book. There are some great books out there.

http://math.ucr.edu/home/baez/physics/Administrivia/rel_booklist.html

himnextdoor

Concerning the light-clock.

It seems to me that any horizontal component of motion 'imbued' to a photon (I have a problem with this too) is irrelevant to the rate at which the clock 'ticks'.

If the two mirrors of the light-clock are arranged parallel to the direction of the train's motion and the photons are emitted perpendicular to the mirror's surface then the distance, 'd', between the mirrors can remain constant.

Now, suppose that the photon arriving at a mirror were represented on an oscilloscope; mirror 'A' and mirror 'B' are represented as two points along the y-axis. And the clock begins to tick at a rate 'f'.

The x-axis represents the motion of the train.

Considering first that the train is at rest then:

A photon is emitted and subsequently detected by mirror 'A' and a 'spot' appears on the scope at the top of the y-axis; the photon is reflected, detected by mirror 'B'' and the 'spot' moves to the bottom of the y-axis; the photon is reflected back to 'A', the 'spot' returns to the top and one 'clock-cycle' is completed.

The distance between the spots, the length of the y-axis is related to 'd', the distance between the mirrors.

Essentially, in an electronic equivalence, I am describing an 'astable multivibrator' whose mark-to-space ratio is represented along the y-axis.

Since we know the speed of light, 'c', and we know the distance between the mirrors, 'd', we also know the frequency, 'f', of the clock. We simply count the number of times the 'spot' appears at 'A' and when we count to c/2d, one second has passed. We have effectively defined one second as being c/2d cycles.

All of this can be represented by the y-axis.

Now consider the train in motion. And that we are using the same photon.

On the oscilloscope, the x-axis represents the velocity, 'v', of the train. As the train accelerates, the 'spots' at 'A' and 'B' become displaced and the scope traces out a 'square-wave'. The distance between the pulses is a function of 'v'.

If the photon were to maintain a perpendicular path between the mirrors then as the train speeds up the photon would start to lag behind the mirrors due to the relative motion of the photon to the mirror it is to be detected by. Eventually, the photon would fall off the back end of the mirror and be lost to the system.

But 'd' would remain constant and therefore the length of the second would not be affected. The clock would tick at a rate of c/2d Hz for a few cycles and then stop. The scope would briefly trace a few cycles of a square-wave and then go blank as no photon would be detected.

Let us modify the apparatus in three ways.

1) The detection of one photon stimulates the emission of another,
2) The entire surfaces of the mirrors perform as detectors and
3) The length of the mirrors is twice the distance between them in order to ensure that every photon that is emitted will be detected even if the train travels at the speed of light.

This will allow the oscilloscope to maintain a constant trace of what is happening at 'A' and 'B'.

Provided that the photons travel perpendicular to the surfaces of the mirrors then the frequency, 'f', will remain constant regardless of the speed of the train. (As long as it travels in a straight line.)

The only way that 'f' can change is through a change in 'd' since 'c' is constant. But 'd' is constant too, isn't it? The distance between the two mirrors doesn't change.

However, we could define 'd' as the distance that the photons travel between the mirrors and that may not be constant. It follows then that the only way for 'd' and therefore 'f' to change is if the photons travel along a path that is not perpendicular to the mirror's surface.

How can this happen without changing the angle of propogation? What is the mechanism by which the speed of the train can alter the angle of propogation of photons?

Even if photons can be 'flung' by an 'imbued motion due to the train', the photons are still travelling from 'A' to 'B' at speed 'c'.

Or is it the case that the forward component of motion provided by the train to the photons reduces the velocity of the photons in a lateral direction?