Einstein, the farmer and the cows

DaveC426913

Gold Member
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One morning Einstein was walking through beautiful rolling meadows and noticed that 3 cows were munching grass. What surprised him was that the cows had their heads through an electric fence mowing the grass that was on the neighbors field. The electric fence was supposed to prevent the cows from eating the neighbor's grass, but apparently they were not being effected by electricity.

Diagram-1

fence
-----------------------------------
Farmer | |cow1 | |cow2 | |cow3 | | Einstein
A ------------------------------------ B

^
|
[Battery +/-]


Soon Einstein spotted a farmer walk by to the fence carrying a battery and he figured that the battery had probably died and so the farmer had taken the battery for charging and was returning with it. He was about to connect it to the fence. This also explained why the cows were able to eat with their heads through the fence un-affected by electricity.

Soon Einstein takes up position on one end of the fence 'B' opposite the farmer. He watches in anticipation as the Farmer connects the battery at 'A'. The 3 cows jump and scream "MOOOOO". Now Einstein remarks to the farmer "wow...they all jumped at the same time". But the farmer remarks "nope, I saw cow1 jump first, then I saw cow2 jump and then I saw cow3 jump". Who is correct and why? Assume both the farmer and Einstein are equidistant from the center of the fence.
 

Averagesupernova

Science Advisor
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Cows 2 and 3 were not actually touching the fence. Cow number one got zapped and when she jumped she scared cow number two and when she jumped she scared cow number 3.
 

Andrew Mason

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DaveC426913 said:
Soon Einstein takes up position on one end of the fence 'B' opposite the farmer. He watches in anticipation as the Farmer connects the battery at 'A'. The 3 cows jump and scream "MOOOOO". Now Einstein remarks to the farmer "wow...they all jumped at the same time". But the farmer remarks "nope, I saw cow1 jump first, then I saw cow2 jump and then I saw cow3 jump". Who is correct and why? Assume both the farmer and Einstein are equidistant from the center of the fence.
The point here is that the speed of electricity and the speed of light are supposed to be the same so Cow1 reacts first but Einstein has to wait until the light from the reaction reaches him before he can observe it. So he sees them all react at the same time.

The farmer of course, sees it just the opposite way. Cow1 reacts before Cow2 and Cow2 before Cow3.

But since the variation in time of the reactions between the cows would be so much greater than the time differences in when the electrical jolt was received, the farmer could not possibly distinguish between the reactions, so Einstein, of course, is right.

AM
 
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The speed of electron (massive particle) migration is subluminal. The effects of electricity, like the reaction of the cows, are not as a rule perceived to be instantaneous. If you replace the cows with light bulbs, the outcome would be basically the same (symmetric) relative to the observers, as outlined in Einstein's special theory.
 

matthyaouw

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I'm thinking that the path of least resistance for the electricity is through cow one, so it gets zapped and moves, making cow 2 the path of least resistance, it gets zapped, moves, cow 3 zapped.
I'm probably wrong, but meh...
 

mezarashi

Homework Helper
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Using cows and electrocution is a bit of a misleading example if you try to solve it in a pragmatic approach: cow reaction time, etc. We should just generally take the ideal situation as if the cows were say light bulbs as mentioned.

The "paradox" can be explained like this:

1. Farmer plugs in battery.
2. Electric field propagates at the speed of light through wire to cow A.
3. Cow A gets shocked and the photons of it being shocked travel towards Einstein at the speed of light.

(Note how the photon from cow A now is travelling in the same direction and at the same speed as the electric field propagating the wire.)

4. Electric field reaches cow B with the photons from cow A also currently at cow B.
5. Cow B gets shocked and makes it own photons which now travel along towards Einstein as well.

6. Repeat for cow C, and we see how Einstein is seeing all three cows jump at once.

On the other side with the farmer, of course, the result as he saw it is intuitive.
 

Averagesupernova

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The farmer and Einstein are both right. That is, assuming the speed of the light and the speed of electrons in the wire are the same. Also assuming the reaction times of the cows are all the same.
 
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Einstein was wrong and he should have known it. True, the light from the 3 jumping cows reached Einstein at the same time., but he knew that the light from jumping cow 1 had travelled a farther distance and therefor must have been emitted at an earlier time than that of jumping cow 2. Perhaps he wasn't as bright as people say.

I am not very steady on my feet when it comes to relativity, but I was under the impression that in order to 'see' different things, two observers had to be in motion with respect to each other. Is this not correct?
 

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