# A quick question about observations in different frames

1. Jun 12, 2015

### rede96

There was a post made here https://www.physicsforums.com/threa...the-speed-of-light.818301/page-2#post-5138063 by PAllen that describes a way of measuring length contraction of a moving body as seen in the rest frame.

I thought this was a great way to visualise length contraction but it got me thinking…

If I was to make similar experiment where there was an arbitrary large piece of photographic film on the floor and I passed the same 2 meter ruler (rest length) over the film, about 1 cm above it and travelling at 0.968c. But also with a 2 meter flash bulb attached to the ruler directly above it, parallel to its length and pointing down towards the ruler.

The flash is activated at some point as the ruler passes over the film in such a way that it leaves a shadow on the film as per the original experiment.

My questions is would the experiment sill leave a ½ meter shadow as per the first time, or as the light originated in the frame of the ruler travelling at 0.968c relative the film, would the shadow left be 2 meters long? (Or some length other than ½ meters)

2. Jun 12, 2015

### Orodruin

Staff Emeritus
The light is a flash and originates at one event only. As it is a single event, it does not have a rest-frame associated with it.

3. Jun 12, 2015

### rede96

Ok, thanks. But that doesn't help me understand what the outcome would be? Are you saying it does matter where the light originates from, the result will still be the same e.g. a 1/2 meter shadow left in the film?

4. Jun 12, 2015

### Orodruin

Staff Emeritus
The light in this example is from an idealised light source. As such its origin is a single event in space time. It does not matter which frame the lamp is at rest in when it is not on. As the only interesting part of the lamp is when it is on and it is only on for a negligible amount of time, the concept of a rest frame does not apply.

5. Jun 12, 2015

### rede96

So is the answer 1/2 meter or 2 metes?

Sorry but is just the way my brain works, seek the correct answer then try and understand the principles that give it.

6. Jun 12, 2015

### Orodruin

Staff Emeritus
I just told you that it cannot depend on where the light is when it is not doing the flash. It must then obviously be the same.

7. Jun 12, 2015

### rede96

Ah ok. Thank you. Hope you didn't mind me asking but I do struggle initially to get my head around things as I am just an interested layman.

But from what you say it doesn't matter where the light flash originates from. The imprint left on the photographic film by the ruler would always be 1/2 meter for the above sample.

I sort of thought it might be, but I was struggling to understand it. The reason is I imagined a similar scenario where I have say a 12inch ruler which I hold out at arms length about 1 cm from a wall. With my other arm a shine a light on the ruler so it casts a shadow on the wall. The shadow will of course be measured by me to be the same length as the ruler.

Now if this was a special wall that was extremely long and could move past me at 0.968c I would still see the shadow cast by the ruler as 12 inches. (I think) Even if I was to move along the wall at 0.968c I would still see the shadow of the ruler measuring the same as the ruler.

So I just replaced the wall with photographic film and as I move along the film at 0.968c I quickly turn the light on and off to make a flash so it leaves an imprint of the ruler in the film. If I was to then stop and go back along the film to the point where I made the flash I would expect to measure the length of the imprint as 12 inches not 3 inches. Or in other words as the ruler was always in my frame I wouldn't expect to see it length contracted.

This is analogues to the thought experiment I originally mentioned and hence why I am confused.

8. Jun 13, 2015

### Orodruin

Staff Emeritus
No. What I said is that as long as it is the same event in space-time it does not matter. This event is where the light originates and it is impossible to talk about a frame as you seem to want to do.

If you shine the light such that it hits from the side you will also need to take into account that the plate is moving.

9. Jun 13, 2015

### rede96

Yes of course, but for the thought experiment I was trying to ignore any angles and assume the light always flashes parallel to the ruler.

Ah right. Well lets talk about it from my frame, if that makes more sense.

Scenario 1, I am in a room, I have a 2 meter long flash bulb that is positioned horizontally to the floor and at a distance of say 1 meter from the wall. The wall is covered with photographic film. I have set up and experiment where an arbitrarily thin object of 2 meters in length will pass by me horizontally from left to right at a speed of 0.968c. As the object passes by it triggers the flash, which takes a 'picture' of the object by leaving an dark impression on the film. When I measure the imprint left by the object I would get a length of 1/2 meter due to length contraction.

Scenario 2, I am in the same room, but this time I have made a modification to the object so attached to it is the a 2 meter long flash bulb that is fixed parallel to the 2 meter long object (both are horizontal to the floor). As it is attached, it will travel along with the object. The new set up now travels again from left to right at a speed of 0.968c and I have set up the experiment so the flash bulb triggers in exactly the same co-ordinates (as measured by me in the room) as the first flash triggered in scenario 1. So as the flashes in both events are being triggered at the same point, you would expect to see the same result on the film. I.e. measure the length of the imprint at 1/2 meter.

But I don't fully understand how this can be the case in scenario 2 as I would expect the imprint to measure 2 meters in length as the flash triggered in the same frame as the object. Or in other words it is what I would see if I was travelling along with the flash bulb and object in scenario 2.

10. Jun 13, 2015

### harrylin

I think that your description is too vague: "The flash is activated at some point as the ruler passes over the film in such a way that it leaves a shadow on the film as per the original experiment."
As first formulated, "I time the flash to fire such its light will reach the film when the center of the ruler is above the center of the film." That refers to timing in the reference frame in which the photographic plate is in rest. The prediction relates to that timing.

11. Jun 13, 2015

### rede96

Ah ok, thanks for that. I can see how that matters in the first scenario above, but would it matter in the second scenario as the light source is moving with the object?

But in any case yes, the flashes are triggered when the object is at the same co-ordinates in the room as measured by me.

12. Jun 13, 2015

### harrylin

Assuming that you have a light source that emits light in all directions, it doesn't matter much that it is moving. What matters is that the light reaches both ends simultaneously according to you. If the light reaches both ends simultaneously according to the rest reference frame of the object, the conclusion should be inverse.

The first thing to analyse is the example of PAllen with the "moving frame" taken as rest frame.
PS. In a nutshell: from the perspective of the other frame, the light rays arrive under an angle and the measurement is deemed to be faulty as they hit the plate near the ends at different times.

Last edited: Jun 13, 2015
13. Jun 14, 2015

### rede96

Ok, great. thanks. Just so I understand what you've said does that mean that in the scenario where the light is emitted in the rest frame, the imprint will be 1/2 meter long as the light hits both ends at the same time as seen from the rest frame. And in the second scenario where the light was in emitted in the moving frame, the imprint will be 2 meters long. But in the second scenario, as the light hits both ends at the same from the moving frame and not the rest frame, the rest frame will see it as faulty result. I assume because the rest frame will say the imprint was lengthened due to the light not hitting the ends at the same time.

Is that right?

14. Jun 14, 2015

### Mentz114

Yes. If the measurement interactions are not simultaneous in the frame of the thing being measured the result is not the rest length.

15. Jun 15, 2015

### rede96

Thanks for the help. Just one last question. I take it if the light source and 2m object were in the rest frame and the wall (with film on) was moving past at 0.968c, then the wall & film would appear length contracted. So in this case the imprint left from the flash of light passing over the 2m object would appear 2m long on the wall in the rest frame, but when the wall stopped and the imprint measured it would be 8m long. (As the wall was contracted x4)

16. Jun 15, 2015

### Mentz114

The imprint would be the same whichever coordinates you used to calculate it. If you get a different answer it is a mistake. All that matters is the time gap between the beams that shadow each end ( measured in the objects frame).

17. Jun 15, 2015

### rede96

Is that right? Or maybe I didn't explain it too well. In my thought experiment the imprint is always measured in the rest frame after the experiment so it isn't coordinate dependant.

From what I understood, and assuming that the light always hits the ends of the object simultaneously in the object's frame, if the light flash and film are in the rest frame with the object moving, then the imprint will measure 1/2 meter. ( As per PAllen's original post) If only the film is in the rest frame and the light flash and object are moving then the imprint will measure 2 meters. And thirdly, if the light and the object are in the rest frame and the film moving, then after the film stops and is measured in the rest frame then the imprint would measure 8 meters.

Last edited: Jun 15, 2015
18. Jun 15, 2015

### Mentz114

Heh ?
I'm sorry I don't know what you are saying. I have nothing to add or change in my last post.

19. Jun 15, 2015

### rede96

Ok, sorry. In your last post you said:
In the thought experiment the imprint is the physical image left on the photographic film. It isn't something that is calculated. After each exposure of the film to light, the object will leave an image on the film. It is this that is being measured.

20. Jun 15, 2015

### Mentz114

OK, if 1/2 is the rest length then I agree.

Could be right.
ditto.

So, the result of the measurement depends on the time gap between the interaction with the ends of the rods.