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Author Topic: Schrodinger's Dog - a relativity paradox  (Read 13402 times)

Offline Solvay_1927

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Schrodinger's Dog - a relativity paradox
« on: 25/08/2006 22:42:33 »
Can anyone here help me resolve the following paradox in relativity theory?


Me and Mr.Einstein are standing, say, 20 metres apart, with a light detector exactly mid way between us.  We both switch on a torch at the same time, so that the light from both our torches reaches the detector at the same time.  (So the events “my beam hits the detector” and “Einstein’s beam hits the detector” are SIMULTANEOUS EVENTS in our reference frame.)

Mr.Schrodinger (Erwin to his friends) is walking briskly past us (but a few metres away).  Because he’s moving (relative to Albert & me), he does NOT see our two beams hitting the detector at the same time.  According to the theory of relativity, in Mr.Scrodinger’s reference frame the above two events are NOT SIMULTANEOUS.

But this leads to a rather worrying paradox.

Suppose that the light detector is actually a bomb – but this bomb is ONLY detonated if the beams from the two torches hit it at exactly the same time.  And if detonated, the explosion is just enough to kill anything within, say, one metre of it.

Suppose also that Erwin happens to be walking his dog (Fido).  Fido runs ahead of Erwin and goes up to sniff the bomb.  And it’s at that point that we switch on our torches.

Albert and me see the bomb explode, and say “oops” as we watch poor Fido disappear in a puff of smoke.

But as far as Erwin is concerned, the bomb has NOT exploded.  He continues walking and whistles Fido to catch up with him.  And Fido comes bouncing along to continue his walk.


Where am I going wrong?


 

another_someone

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Re: Schrodinger's Dog - a relativity paradox
« Reply #1 on: 25/08/2006 23:13:39 »
What is Fido's reference frame?

If Fido is sniffing the bomb, then he must be in the same reference frame as the bomb, which is a different reference frame from Erwin.  If Fido rushes past the bomb at Erwin's heal, then he may not himself ever feel the force of the bomb.



George
 

Offline thebrain13

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Re: Schrodinger's Dog - a relativity paradox
« Reply #2 on: 26/08/2006 00:41:38 »
Schrodinger will see both beams hitting the detector at the same time, if the events are simultaneous. The two beams will hit the detector at exactly the same time in ANYBODYS frame of reference. The only way a simultaneous event will not be seen as simultaneous by someone else relative motion, is if the two events are seperated by distance. When both beams of light hit the detector they arent seperated through distance anymore, so they will always hit at the same time no matter what.

However a moving observer could disagree on who lit the torch first you or einstein, due to the fact that you two are 20 meteres apart.

You should read about relativity of simultaneity, again it resolves all relativity paradoxes.
 

Offline lightarrow

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Re: Schrodinger's Dog - a relativity paradox
« Reply #3 on: 26/08/2006 10:01:40 »
quote:
Originally posted by Solvay_1927


...But as far as Erwin is concerned, the bomb has NOT exploded.  He continues walking and whistles Fido to catch up with him.  And Fido comes bouncing along to continue his walk.


Where am I going wrong?

You are wrong in the previous statement, because the bomb HAS exploded even for Erwin:
in his reference frame, he sees a device designed to explode NOT when the two beams of light arrive simultaneously, but when they arrive with a specific time dilation, exactly the time dilation between the two beams of light arriving there!
 

Offline thebrain13

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Re: Schrodinger's Dog - a relativity paradox
« Reply #4 on: 26/08/2006 16:17:27 »
lightarrow, there is no time dilation between when the two lightbeams from the torches arrives at the middle, from any frame of reference. The bomb will appear to explode as seen by anyone at any speed. youve mis interpreted relativity of simultaneity.
 

Offline lightarrow

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Re: Schrodinger's Dog - a relativity paradox
« Reply #5 on: 26/08/2006 18:00:29 »
quote:
Originally posted by thebrain13

lightarrow, there is no time dilation between when the two lightbeams from the torches arrives at the middle, from any frame of reference. The bomb will appear to explode as seen by anyone at any speed. youve mis interpreted relativity of simultaneity.
My english is not always good, unfortunately. With "dilation" I intended "delay".
« Last Edit: 26/08/2006 18:03:01 by lightarrow »
 

Offline Solvay_1927

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Re: Schrodinger's Dog - a relativity paradox
« Reply #6 on: 26/08/2006 22:34:57 »
quote:
Originally posted by thebrain13
Schrodinger will see both beams hitting the detector at the same time, if the events are simultaneous. The two beams will hit the detector at exactly the same time in ANYBODYS frame of reference. The only way a simultaneous event will not be seen as simultaneous by someone else relative motion, is if the two events are seperated by distance. When both beams of light hit the detector they arent seperated through distance anymore, so they will always hit at the same time no matter what.


Very good point, Brain, you know your stuff.  However, you’re assuming that the detector/bomb has no thickness.  If the bomb is, say, 1m wide, and is detonated by the light beam simultaneously hitting the front and (1m away) the back of the bomb, then Erwin will NOT see the beams hitting the front and back of the bomb simultaneously.

But I think that Lightarrow's resolved the paradox anyway:
quote:
Originally posted by lightarrow
... the bomb HAS exploded even for Erwin:
in his reference frame, he sees a device designed to explode NOT when the two beams of light arrive simultaneously, but when they arrive with a specific time {delay}


I accept this argument, although it's still kind of weird (and leaves me with an uncomfortable feeling - not to mention a pain in my head):  Erwin has a bomb that detonates according to one cause (simultaneous light-beam-hits) when he's standing still, but which detonates due to a different cause when he's running away from it.
« Last Edit: 26/08/2006 22:36:03 by Solvay_1927 »
 

Offline bostjan

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Re: Schrodinger's Dog - a relativity paradox
« Reply #7 on: 29/08/2006 07:16:51 »
the bomb explodes (or not) based on the bomb's frame of reference, anyway, as lightarrow pointed out.

thebrain13 is correct, as well.  if two events are simultaneous at a specific point in space, they will be seen as simultaneous in every reference frame.

 

Offline lightarrow

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Re: Schrodinger's Dog - a relativity paradox
« Reply #8 on: 29/08/2006 11:06:03 »
quote:
Originally posted by bostjan

the bomb explodes (or not) based on the bomb's frame of reference, anyway, as lightarrow pointed out.

thebrain13 is correct, as well.  if two events are simultaneous at a specific point in space, they will be seen as simultaneous in every reference frame.
Now I agree with you and thebrain13. Erwin sees one torch (the light's beam of wich travels in the same sense of the bomb) switched on before the other, so that the two beams arrives to the core of the bomb's device at the same time, even if Erwin sees the back end of the device to be hit before the front end of it; infact, the electric signal from the back end have to cover a longer path than the front end signal, to reach the core.
Hey, my knowledge of special relativity has improved because of you. Thank you!
 

Offline Solvay_1927

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Re: Schrodinger's Dog - a relativity paradox
« Reply #9 on: 30/08/2006 23:10:21 »
Many thanks, everyone, you've put my mind at rest - this paradox turns out not to be a real paradox after all.

The thing that strikes me most about this final explanation is that the thickness of the bomb is actually irrelevant:

Even if the bomb has thickness (so Erwin sees NON-simultaneity - i.e. the back end of the bomb is hit before the front end of it), information still has to be passed between the front & back of the bomb before it detonates (i.e. you still have to allow time for the transmission of information WITHIN the bomb - the information that the front has been hit and the back has been hit).

So you still end up needing to get information to a single specific point (within the bomb - not necessarily the centre, the detonator could be at some other location within the bomb) - and at that specific location (wherever it is), Erwin WILL see the information arriving simultaneously.
 

Offline Solvay_1927

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Re: Schrodinger's Dog - a relativity paradox
« Reply #10 on: 30/08/2006 23:10:21 »
Many thanks, everyone, you've put my mind at rest - this paradox turns out not to be a real paradox after all.

The thing that strikes me most about this final explanation is that the thickness of the bomb is actually irrelevant:

Even if the bomb has thickness (so Erwin sees NON-simultaneity - i.e. the back end of the bomb is hit before the front end of it), information still has to be passed between the front & back of the bomb before it detonates (i.e. you still have to allow time for the transmission of information WITHIN the bomb - the information that the front has been hit and the back has been hit).

So you still end up needing to get information to a single specific point (within the bomb - not necessarily the centre, the detonator could be at some other location within the bomb) - and at that specific location (wherever it is), Erwin WILL see the information arriving simultaneously.
 

Offline jdepillis

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Re: Schrodinger's Dog - a relativity paradox
« Reply #11 on: 13/09/2006 17:23:09 »
quote:
Originally posted by Solvay_1927

Can anyone here help me resolve the following paradox in relativity theory?


Me and Mr.Einstein are standing, say, 20 metres apart, with a light detector exactly mid way between us.  We both switch on a torch at the same time, so that the light from both our torches reaches the detector at the same time.  (So the events “my beam hits the detector” and “Einstein’s beam hits the detector” are SIMULTANEOUS EVENTS in our reference frame.)

Mr.Schrodinger (Erwin to his friends) is walking briskly past us (but a few metres away).  Because he’s moving (relative to Albert & me), he does NOT see our two beams hitting the detector at the same time.  According to the theory of relativity, in Mr.Scrodinger’s reference frame the above two events are NOT SIMULTANEOUS.

But this leads to a rather worrying paradox.

Suppose that the light detector is actually a bomb – but this bomb is ONLY detonated if the beams from the two torches hit it at exactly the same time.  And if detonated, the explosion is just enough to kill anything within, say, one metre of it.

Suppose also that Erwin happens to be walking his dog (Fido).  Fido runs ahead of Erwin and goes up to sniff the bomb.  And it’s at that point that we switch on our torches.

Albert and me see the bomb explode, and say “oops” as we watch poor Fido disappear in a puff of smoke.

But as far as Erwin is concerned, the bomb has NOT exploded.  He continues walking and whistles Fido to catch up with him.  And Fido comes bouncing along to continue his walk.


Where am I going wrong?




J de Pillis
 

Offline jdepillis

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Re: Schrodinger's Dog - a relativity paradox
« Reply #12 on: 13/09/2006 17:27:01 »
Did you ever get this (one-year old) problem resolved?
John de Pillis
Univ of California
jdp@math.ucr.edu
............................................................

quote:
Originally posted by Solvay_1927

Can anyone here help me resolve the following paradox in relativity theory?


Me and Mr.Einstein are standing, say, 20 metres apart, with a light detector exactly mid way between us.  We both switch on a torch at the same time, so that the light from both our torches reaches the detector at the same time.  (So the events “my beam hits the detector” and “Einstein’s beam hits the detector” are SIMULTANEOUS EVENTS in our reference frame.)

Mr.Schrodinger (Erwin to his friends) is walking briskly past us (but a few metres away).  Because he’s moving (relative to Albert & me), he does NOT see our two beams hitting the detector at the same time.  According to the theory of relativity, in Mr.Scrodinger’s reference frame the above two events are NOT SIMULTANEOUS.

But this leads to a rather worrying paradox.

Suppose that the light detector is actually a bomb – but this bomb is ONLY detonated if the beams from the two torches hit it at exactly the same time.  And if detonated, the explosion is just enough to kill anything within, say, one metre of it.

Suppose also that Erwin happens to be walking his dog (Fido).  Fido runs ahead of Erwin and goes up to sniff the bomb.  And it’s at that point that we switch on our torches.

Albert and me see the bomb explode, and say “oops” as we watch poor Fido disappear in a puff of smoke.

But as far as Erwin is concerned, the bomb has NOT exploded.  He continues walking and whistles Fido to catch up with him.  And Fido comes bouncing along to continue his walk.


Where am I going wrong?




J de Pillis
 

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Re: Schrodinger's Dog - a relativity paradox
« Reply #12 on: 13/09/2006 17:27:01 »

 

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