## Physics Puzzle

The question below was set in a VCE (high school exam) physics exam in Victoria Australia.  After the exam the question was discussed by a number of physics experts who failed to reach a concensus on what the correct answer was!

What do you think?

It's all relative

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### 11 Responses to Physics Puzzle

1. I would still be tempted to plump for answer A) because of the velocity that it is coming towards the viewer.

I am thinking of police car sirens in the street coming towards and going away…

Is that too simplistic?

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2. Rick Williams says:

Well, at first look, it seems only partial specified.
One difficulty in relativity is understanding that sycronicity is relative – “the instant that Fred and Nancy are opposite each other” according to who?
I’m not certain whether this makes a difference in this case.
But I suppose that we may assume that it is from Fred’s point of view, given that it says that this is the reference for when he sees Alan’s and Bob’s lights.

Also, this means that Alan and Bob lit their matches before Fred judged himself to be closest to Nancy.

Then in Fred’s frame, Bob must’ve be closer than Alan to Nancy, when lighting his match, as the train has moved in the time taken for light to travel from A and B to F.

Now this is where I get lost… does this mean that in Nancy’s frame of reference, Bob is still closer to her than Alan, and hence she would see his light first?

My guess is yes, Bob’s light reaches Nancy first, because he was closer to Nancy when lighting it.

So B.

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3. dougaj4 says:

I’ll return to this topic later, but for now I’ll just comment that on the forum where I saw it good arguments have been put forward in favour of A, B and D, and a rather weak argument (by me) in favour of C.

I’m now pretty convinced that the answer is definitely not C.

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4. jonpeltier says:

I was going to say it’s a combination of C and D, then Rick pointed out that although Fred sees both lights at the same time, the matches were lit at some small time before this, and at this earlier time, the front of the train (Bob) was closer to the observer than the rear of the train (Alan).

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5. Ben Farmer says:

I may have gotten carried away explaining this. Anyway my kind of long explanation is here for those who still care:

http://chilledfruit.blogspot.com#5810182727073890807
My apologies for any typos, poor grammar and/or lack of clarity.

I can see where the confusion comes from, one can argue for answers A or D with different assumptions. A is probably slightly more correct but D is probably what they were thinking. C and B are no good as far as I can reason, though perhaps for B something can be assumed which I haven’t thought of.

Bit of a dodgy question to throw at high-school kids.

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6. dougaj4 says:

Thanks for the contributions everyone. Those with an hour or three to spare might like to have a quick browse through:

http://www2b.abc.net.au/science/k2/stn/newposts/3937/topic3937797.shtm

The question is certainly not as straightforward as it might seem at first.

This is what the examination board people had to say about it:

“When Fred and Nancy were opposite each other, Fred saw the light from the two matches simultaneously. Therefore the matches were lit some time before that; that is, when Nancy was closer to Bob and further from Alan. Since the speed of light was constant, the light from Bob will reach Nancy before that from Alan (option B).

This question was intended to test the ideas of simultaneity at a basic level appropriate to VCE and the Physics VCE Study Design. However, as there was a lack of consensus about this question and as it did not discriminate well it was rescored as shown, effectively removing it from the examination.”

All well and good, except that the right answer is D if the transverse separation between Nancy and Fred is negligible (or is ignored) or A if there is a significant transverse separation.

It seems that the examiners thought about this question at a very superficial level, or to be charitable, expected the students to think about it at a superficial level. Interestingly the responses show that the students favoured answers A and D, indicating a deeper level of understanding than the examiners:

A 45
B 10
C 10
D 33

The report says there was no concensus in the results, so all responses were marked correct. It looks to me like there was a concensus, but they didn’t want to admit they got it wrong!

A neat summary of the reasons for the final conclusion is given at the end of the thread linked above:

“From: KJW (Maths) 17/12/2008 10:49:59 PM

Subject: re: Relativity Question from VCE exam post id: 3942112

After a more careful consideration of the problem when the transverse separation is not zero, I have come to the following conclusion:

The answer is “A” in all cases when the transverse separation is not zero (but “D” when the transverse separation is zero), but the analysis depends on the meaning of: “the instant that Fred and Nancy are directly opposite each other”. My earlier analysis of the problem took this to mean the point on Fred’s spacetime trajectory which is closest to Nancy’s spacetime trajectory. This point does *not* depend on the FoR.

When this meaning is used, Nancy will see Fred see the light from the matches at the same time as Nancy sees Fred directly opposite her. There will be a delay between when this happens at Fred’s location and when Nancy sees it, but the delay will be the same for both events. Thus, my reasoning based on the transverse separation increasing the distance to the closer struck match to a greater extent (and noting that “D” is correct for zero transverse separation), leading to “A”, is correct.

On the other hand, if we consider the time Fred sees the struck matches as when he sees Nancy directly opposite him, then the delay of the light from Nancy to Fred will place Nancy closer to Alan when Fred sees the struck matches than in the case of zero transverse separation, again leading to “A” (Fred will see Nancy still ahead of him when he is at the spacetime point of closet approach to Nancy).

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7. dougaj4 says:

“A is probably slightly more correct but D is probably what they were thinking. C and B are no good as far as I can reason, though perhaps for B something can be assumed which I haven’t thought of. ”

That was pretty much the conclusion on the other forum as well.

“Bit of a dodgy question to throw at high-school kids.”

Definitely. A great question to prompt thinking about the subject, but a lousy exam question.

I’d have been right pissed off if I’d answered A or D and found that B and C were marked right as well.

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8. dooley5 says:

The lights are lit on the train by Fred and Bob sometime before being observed simultaneously by Alan. Alan and Nancy are face to face at this instant, since the wavefronts coincide at this time at A and N they both see them simultaneously, call this
t = t’ =0, also since the lights are generated on the train and N is an external observer make the train the stationary system and N the moving frame. When the lights are initiated B is closer to N but their is a term for t’ contains a V/(C*C) term that takes into account the direction of travel (compared to incident light) this compensates for this initial difference.

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9. dougaj4 says:

dooley5 – I agree that making the train fixed and Nancy moving simplifies the problem (or at least makes it easier to picture), but I don’t agree with your conclusion.

Note that it is Alan and Bob who light the matches, and Fred is in the middle. Let’s insert a stationary observer (relative to the train) directly opposite Fred, say Charles.

When Fred sees Alan and Bob strike the matches he also sees that Nancy is just passing Charles.

Because Charles is further from Alan and Bob than Fred is, he will see the matches struck later than Fred, so when Charles sees the two matches struck, Nancy will be some disatance past him, and will be closer to Alan than to Bob.

Therefore Nancy will see Alan strike the match first.

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10. jeff weir says:

Can you still smoke on trains in Victoria?

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11. dougaj4 says:

Jeff – good question.

Apart from which, lighting a match at that speed would surely be a fire hazard.

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