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Posted

I've just watched a SR video on youtube

It is a typical one showing a clock being 2 mirrors in a vertical tube of length C. The clock ticks when light bounces of each mirror, i.e every second.

It goes on to explain that when the clock is moving horizontally, a stationary observer would see the light travel further, ie indicating time dilation for an observer moving with the clock.

 

What seems wrong with that explanation is that if you had 2 identical clocks at right angles to each other, then would the stationary observer see the clock parallel to the motion have a longer period for when the light was travelling in the same direction, and shorter when at 180 deg.

 

It seems obvious that an observer with the clock would see both clocks tick in sync, but according to SR would a stationary observer really see both clock ticking at different times and the horizontal clock having asymmetrical pulses?

Posted (edited)

What seems wrong with that explanation is that if you had 2 identical clocks at right angles to each other, then would the stationary observer see the clock parallel to the motion have a longer period for when the light was travelling in the same direction, and shorter when at 180 deg.

 

It seems obvious that an observer with the clock would see both clocks tick in sync, but according to SR would a stationary observer really see both clock ticking at different times and the horizontal clock having asymmetrical pulses?

 

You're reasoning is good, you're just missing a piece of the puzzle.

For the horizontal clock, the stationary observer would indeed see asymmetrical pulses.

This is because the time an event happens in one frame is related to both the time and place it happens in another.

 

[math] t' = \gamma\left(t - \frac{v}{c^2}x\right)[/math]

 

This is the best explanation of the concept I've seen:

 

If you look carefully at the rotating-switcheroo you'll also see the vertical distance between the time lines get's further apart (moving clocks are slow) and the horizontal distance decreases (length contraction).

 

The vertical moving clock would be like light bouncing straight into and out of the page, so the ticks just get further apart (a zig-zag, but we can only see a straight line because it's zigging in and out of the page).

The horizontal moving clock would be like a symmetric zig-zag going up the page before the switcheroo, and an asymmetric zig-zag after.

Edited by Schrödinger's hat
Posted

If the 2 clocks were fixed in a cross with flashing lamps at the centre, wired to the sensors on the mirrors, the observer with the clocks would see both lamps flash in sync. I can't then see how a stationary obeserver would see them flash out of sync and with one lamp having asymmetrical pulses.

Posted

If the 2 clocks were fixed in a cross with flashing lamps at the centre, wired to the sensors on the mirrors, the observer with the clocks would see both lamps flash in sync. I can't then see how a stationary obeserver would see them flash out of sync and with one lamp having asymmetrical pulses.

 

Asymmetrical ≠ asynchronous

The orientation of the clock can't, and won't, matter. It's asymmetrical because the paths aren't the same length: when the pulse is emitted, it has to catch up to the mirror, and will a travel longer path than the return pulse, when the detector is moving toward the photon.

Posted

If the 2 clocks were fixed in a cross with flashing lamps at the centre, wired to the sensors on the mirrors, the observer with the clocks would see both lamps flash in sync. I can't then see how a stationary obeserver would see them flash out of sync and with one lamp having asymmetrical pulses.

 

There are two other effects of Relativity to consider here: Length contraction and the Relativity of Simultaneity.

 

Basically, this is what would happen as seen by the stationary observer comparing the moving clocks to his own:

 

length_con2.gif

 

The stationary observer will also see the horizontal clock as being length contracted, which results in the clocks remaining in sync for every round trip of the photons.

 

The fact that he sees asymmetry in the horizontal clock's "half-ticks" is due to the Relativity of Simultaneity. Put simply, it means that events judged as simultaneous according to one observer, will not be judged so by one moving relative to the other, if those event are separated along a line parallel to the direction of relative motion.

Posted

There are two other effects of Relativity to consider here: Length contraction and the Relativity of Simultaneity.

 

Basically, this is what would happen as seen by the stationary observer comparing the moving clocks to his own:

 

length_con2.gif

 

The stationary observer will also see the horizontal clock as being length contracted, which results in the clocks remaining in sync for every round trip of the photons.

 

The fact that he sees asymmetry in the horizontal clock's "half-ticks" is due to the Relativity of Simultaneity. Put simply, it means that events judged as simultaneous according to one observer, will not be judged so by one moving relative to the other, if those event are separated along a line parallel to the direction of relative motion.

 

Excellent. I am going to try to add that to my 3d simulation program.

Posted

There are two other effects of Relativity to consider here: Length contraction and the Relativity of Simultaneity.

 

Basically, this is what would happen as seen by the stationary observer comparing the moving clocks to his own:

 

length_con2.gif

 

The stationary observer will also see the horizontal clock as being length contracted, which results in the clocks remaining in sync for every round trip of the photons.

 

The fact that he sees asymmetry in the horizontal clock's "half-ticks" is due to the Relativity of Simultaneity. Put simply, it means that events judged as simultaneous according to one observer, will not be judged so by one moving relative to the other, if those event are separated along a line parallel to the direction of relative motion.

 

Great graphics.

 

In your system, if there was a lamp on each clock, located at the intersection, that was wired to flash when the photons hit either mirror, then if an observer local to the clocks sees both lamps flashing together, how can those light beams from the lamp, travel to a moving observer and make him see them flashing out of sync?

Posted

Great graphics.

 

In your system, if there was a lamp on each clock, located at the intersection, that was wired to flash when the photons hit either mirror, then if an observer local to the clocks sees both lamps flashing together, how can those light beams from the lamp, travel to a moving observer and make him see them flashing out of sync?

 

In order for your intersection light to know when the far mirror is reached by the photon, the detector at the far mirror has to send a signal back to it. Since this signal can, at most travel at the speed of light, it cannot return to the intersection light any faster than the returning pulse does. If the signal travels at the speed of light, then it arrives at the same time and the returning pulse and the intersection light will not flash at the same time as the pulses reaches the far mirrors even for an observer local to the clocks. There is no way for the light at the intersection to instantly detect when a pulse reaches a far mirror.

 

 

SO instead let's try this:

 

We know the distance between intersection and far mirrors and we know the speed of light so we know how long after the pulses leave the intersection that they will arrive at the far mirror according to someone local with the clocks. In my example, this happens when the clock numbers read 0.5. So will just set the intersection lights to flash when the clock reads 0.5. This way according to the local observer, they flash at exactly the half point of the round trip and when the pulse reach the far mirror.

 

What does the Moving observer see? Here's where the relativity of simultaneity comes in. He also sees the intersection lights flash when the clock reads .05, however, according him, while this occurs when the vertical pulses reach the mirrors, it is not when the horizontal pulses reach the mirror. Again just because the intersection light flash and light pulse reaching the mirror happens simultaneously for the local observer, does not mean it does so according t he moving observer. So, what he sees is that both light pulses leave the intersection, the intersection lights flash at the 0.5 mark (just like for the local observer), and the pulses return at the 1.00 mark(just like for the local observer). On this he agree with the local observer, what he does not agree upon is whether the intersection light flash and the light pulse reaching mirror for the horizontal clock happen simultaneously.

Posted

If the lamps were wired to the mirrors with the same length of cable, then there would be a delay after the photon strikes the mirror before the lamp flashes (same delay for each mirror). The lamp would then flash at regular intervals (albeit delayed after the event) for a local observer. Would then an observer with relative motion see the flashes with 2 different flash periods?

 

I know i'm not explaining this very well, but this experiment could be set up so that we have 2 of these clocks at 90deg, with sensors at each end wired back to lamps at the center with cable of the same length. Then for an observer in the same reference frame as the clocks he would see both lamps flashing in sync and with regular periods.

 

I cannot understand how an observer moving close to C along the axis of one of the clocks could see one of these lamps flash differently, because he should be seeing the same 'light cones' of the lamps that the local observer saw?

Posted (edited)

Lowemack: I can't quite figure out the scenario you're explaining, but SR says:

Two events, different places, same time in one frame -> Two events, different places, possibly different times in other frame (depending on direction of separation)

 

Two events, same place, same time in one frame -> Two events, same place, same time in all frames (ie. actually same event).

 

Four events, two pairs, two places (one for each pair), two durations (difference between times of pair of events) which are the same, two start times that are the same in one frame -> Four events, two pairs, two places (one for each pair), two durations (difference between times of pair of events) which are the same as each other but possibly different from the original, two start times that can change depending on frame

 

So you can have two clocks that go out of synch, or two parts of one clock that go out of synch, but each individual clock or part of the clock will continue to have the same period as the other parts providing the whole thing is moving inertially.

 

There's a stickied thread explaining the lorentz transforms. If you can understand it, try setting up some situations and seeing what they say.

Edited by Schrödinger's hat
Posted

I think my point is that the local observer sees the lamps flash in sync, because the light beams hit the mirrors at the same time.

 

A moving observer would 'see' the light hit the mirrors along the axis of travel, at different times. Yet, as you just stated he would see the lamps flash together..... so for him does the light actually hit the mirrors at different times, or just 'look' that way because of how we see or measure things using light?

Posted

I think my point is that the local observer sees the lamps flash in sync, because the light beams hit the mirrors at the same time.

 

A moving observer would 'see' the light hit the mirrors along the axis of travel, at different times. Yet, as you just stated he would see the lamps flash together..... so for him does the light actually hit the mirrors at different times, or just 'look' that way because of how we see or measure things using light?

 

Which lamps? I think it's best to look at one situation and concentrate on that, rather than have three or four different. It's far too confusing. You can use the animation that Janus provided, or come up with a diagram explaining another setup, but it's best to pick one and stick to it.

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