U know this paradox:

I drive my car into your garage at close to the speed of light. From my frame, your garage has shrunk and my car won't fit in. From your frame my car has shrunk and there will be lots of room. Whe my car hits the back wall of the garage it will be BOTH completely inside the garage AND sticking out the front!

I have real problems in coming to terms with this. Can anyone tell me a more complete (and comfortable) way of looking at this!!!

Check out the thread here on sciforums about the bug rivet paradox. It is somewhat recent so you should be able to find it quickly. It is basically the same paradox in a different guise.

http://www.sciforums.com/showthread.php?s=&threadid=30362

I’d make it analogous to the pole-barn paradox (http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/polebarn.html#c1) by having garage doors on the front and back that I simultaneously close to completely contain your shrunken car within my garage, then immediately open to let you pass through unimpeded. That way there’s no stopping, no uncontraction, yet we’re left to explain how you fit in the closed garage from your perspective given that the garage was shrunk to a smaller length than your car. I’ll go with that.

From my frame, when you almost reach the back of my garage and you are completely contained within the garage, I simultaneously close both doors, then immediately re-open them. The doors close and re-open so quick that you have moved negligibly in the meantime. Suppose I close the garage doors at MY 5 PM. From my frame, MY 5 PM occurs everywhere in the garage at the same moment (all garage clocks reach MY 5 PM simultaneously).

From your frame, the back door closes first and the front door closes later, because events that are simultaneous for me in my frame are observed in your frame to happen starting at the back of the garage and then moving to the front of the garage. From your frame, garage clocks reach MY 5 PM over time, not simultaneously. By the moment that MY 5 PM reaches the front of the garage, at which moment the front door closes, the back door has already opened, because it is now MY 5.001 PM there, say. By the moment in your frame that the front door closes, you already extrude out the back door. You are never completely contained within the shrunken garage from your perspective.

If you have a problem coming to terms with relativity of simultaneity in general, as in understanding why MY 5 PM moves from back to front, ask & I can explain further.

Originally posted by zanket
From your frame, the back door closes first and the front door closes later, because events that are simultaneous for me in my frame are observed in your frame to happen starting at the back of the garage and then moving to the front of the garage.

I guess my problem stems from the fact that not only do u OBSERVE the doors closing at different times from my frame of reference (as u say) but they ACTUALLY DO close at different times. Whereas in your frame of reference they close simultaneously. There is no absolute reality it seems (at least when it comes to time of events!)

I know I am going top stir the ridicule pot with this question but here goes.

What if we let go of relativity for a moment.

And we actually manage to propell oursleves to the speed given for light. ( Not light speed but the speed suggested as absolute)

The only reason we think this is impossible is that for relativity to be accepted requires it to be true.

ouch!!! says just about every one.....

If we think a little about actually travelling to "c" with out worrying about relativity theory for a moment. Say the theory for the moment has never been written. What stops us from traveling at this and higher speeds? Is it the theory that stops us or is it a reality that stops us? This I think is my question.

Well without relativity, travelling faster than the speed of light results in (for one), time travel and all of its paradoxes so I think Einstein was glad when his theory did not permit anything to travel faster than light!

Originally posted by John Connellan
There is no absolute reality it seems (at least when it comes to time of events!) The time becomes another coordinate in Minkowski space-time; that was the point. Then, you have to go to the deeper geometrical picture to get the absolutes (absolutes have a name in the theory; they are called tensors). There are still objects in the theory that do have a kind of absolute quality, it's just that time the way an observer interprets it is no longer an absolute in the theory (not since the 1910's).

As far as this being a faithful description of reality, who knows? There does seem to be something about the theory that gives it merit, though.

Originally posted by Quantum Quack
What stops us from traveling at this and higher speeds? Is it the theory that stops us or is it a reality that stops us? This I think is my question. The theory doesn't stop anything except the validity of certain assertions in its own context. In the context of relativity, massive bodies do not move at c with respect to any other massive bodies. If you want to increase your speed with respect to something else, then you must accelerate with respect to that something else. How do you accelerate? I don't know what the fundamental mechanism is for acceleration, but from all the theory I've seen, a system must conserve momentum, and so you must give something the opposite momentum that you want to achieve. Well, there is, IMO, some limit on the amount of momentum that you can give another object with respect to yourself, and it is based on the fundamental interactions. You could, of course, continue to throw stuff out the back of your spaceship as you attempt to achieve higher and higher velocity, and each time, you gain some momentum with respect to the frame in which the stuff and you were at rest. It does seem at first glance that there shouln't really be a limit here. I don't know how to resolve this without invoking some of the ideas from modern relativity.

Originally posted by John Connellan
Well without relativity, travelling faster than the speed of light results in (for one), time travel ...That is a curious statement. Can you explain in more detail?

Originally posted by errandir
That is a curious statement. Can you explain in more detail?

Have u heard of the grandfather paradox before? In special relativity a particle moving FTL in one frame of reference will be travelling back in time in another. This is obviously a huge paradox and almost certainly negates the existance of any meaningful travel into the past EVER.

Originally posted by errandir
As far as this being a faithful description of reality, who knows? There does seem to be something about the theory that gives it merit, though.

Well all Im saying is that, each frame of reference can disagree on something as trivial as "is the car in the garage or not" and that therefore they have seperate 'realities'! But this kind of thing happens in quantum mechanics all the time so Im not poking fun at Relativity (dont get me wrong!).

Originally posted by John Connellan
Have u heard of the grandfather paradox before?Yes, I know this one.




Originally posted by John Connellan
In special relativity a particle moving FTL in one frame of reference will be travelling back in time in another.Really? Can you elaborate on this/show the calculation that gives this result?

BTW, I thought you said that this would happen without relativity.




Originally posted by John Connellan
This is obviously a huge paradox and almost certainly negates the existance of any meaningful travel into the past EVER. Well, not if you want to invoke the many worlds interpretation. You could go back and interupt a sequence of events that would eventually lead to your own existence. But, since you know first hand that you exist, then you know that there had to have been some probability of your existence, which means that, no matter what happens, in some "world" you exist. Your own timeline went through that "world," even though after the interuption, the reality in which you now find yourself probably won't contain that timeline.

Originally posted by John Connellan
Well all Im saying is that, each frame of reference can disagree on something as trivial as "is the car in the garage or not" and that therefore they have seperate 'realities'! But this kind of thing happens in quantum mechanics all the time ...Can you give an example of this in QM? I can't think of one off the top of my head. The fact that it "happens all the time" in special relativity shouldn't depend on QM for affirmation. Why does the happenstance of QM make you more comfortable in accepting something than that of relativity. IMO, QM is the far more bizarre theory, and thus more deserving of skepticism.

BTW, why do you say that they have "separate realities?" They both exist in the same spacetime, just not at the exact same points in space-time. This shouldn't be surprising, should it?

Originally posted by errandir
Can you give an example of this in QM? I can't think of one off the top of my head. The fact that it "happens all the time" in special relativity shouldn't depend on QM for affirmation.

Yes, the many worlds theory is one. Scrodingers cat paradox is another. It doesn't Happen all the time in relativity. This is the first time I have come across what appears to be a paradox implying alternate realities in relativity. Its much more common in QM. Im not relying on QM for affirmation of anything

Why does the happenstance of QM make you more comfortable in accepting something than that of relativity. IMO, QM is the far more bizarre theory, and thus more deserving of skepticism.

Im not more comfortable with some QM theories but it shows that modern physicists have to throw away our notions of reality in favour of experimental evidence.

BTW, why do you say that they have "separate realities?" They both exist in the same spacetime, just not at the exact same points in space-time. This shouldn't be surprising, should it?

They are seperate realities for each observer because they both witness different events happening. The car is in the garage in one and not in the other. It is the same car!

Originally posted by John Connellan
Yes, the many worlds theory is one. Scrodingers cat paradox is another. It doesn't Happen all the time in relativity. This is the first time I have come across what appears to be a paradox implying alternate realities in relativity. Its much more common in QM. Im not relying on QM for affirmation of anythingI think you and I are talking about two different things.




Originally posted by John Connellan
They are seperate realities for each observer because they both witness different events happening. The car is in the garage in one and not in the other. It is the same car! Oh, I think I might see from where the confusion arises. Relativity says that they are THE SAME events. It is the particular coordinatization that is different for the two observers. In relativity, "the car being in the garage" is not an event, it is a projection of a collection of events (in this case, the number of pertinent events can be simplified to two, but not one) onto one coordinate system. There ARE two events that are observed by both observers. The closing/opening of the garage doors. These events must be represented by 4-vectors (1^st rank tensors), not by points in time and space. It is only upon projecting these tensors onto two distinct coordinate systems that there seems to be a contradiction.

It's not like one observers sees the closing/opening of the doors while the other one doesn't. They both see both events, just not with the same representations in their corresponding coordinate systems.

OK but tell me this. Was the car completely inside the garage or not?

Yes, from my perspective. No, from your perspective.

From my perspective you were completely inside the garage when I simultaneously closed and immediately re-opened the doors. From your perspective the back door closed and re-opened just before you reached it and while the back end of your car stuck out the front door. Then the front of your car passed through the back door. Later, just after the back end of your car entered the garage the front door closed and re-opened.

Originally posted by zanket
Yes, from my perspective. No, from your perspective.

Well if the car is inside the garage, that is one situation. I'll usae the word situation rather than event this time. The car not being in the garage is another situation. Each of these situations are real and one observer will not observe the other situation so there ARE 2 realities and two situations.

Originally posted by John Connellan
OK but tell me this. Was the car completely inside the garage or not? The word "was" is the past tense of "to be." Past tense has the prejudice of orgainizing 4-space into 3-D space and 1-D time. A better way to ask would be:

"Is there some 4-D volume in which the car can be totally enclosed which has, as boundaries in the x direction, the two garage doors?"

The answer to this question is yes. The confusion is coming, I think, from the fact that, the 4-D volume can be a 4-cube in one coordinate system while a 4-D parallelepiped in another. It is somewhat like a square can have a square-shaped shadow if it is cast perpendicular, or a diamond-shaped shadow if it is cast at askew. When you make a particular coordinatization, this is kind of like projecting the actual physical object onto your coordinate system.

hey John could it actually be more like three realities.

You are observing the contradiction betweeen two realities from the position of a third observer. So you have the two already described and the third being the observation of the paradox.

I havent thought too much about this but say there was a flash of lightning at the point in time where, to the observer in the garage, the car was completely inside and to the driver the car was not completely inside. In the latter case the car gets destroyed killing the driver. In the former case the driver survives - 2 realities eh?

Basically assume that, unless the car is fully inside it gets destroyed by lightning.

You’d either die from both perspectives or live from both perspectives. If lightning kills you outside the garage before reaching the garage from your perspective, then from my perspective you’d be dead before you entered the garage. If the entire car is destroyed in a single moment from your perspective, from my perspective the destruction takes time; the car is destroyed from back to front over time.

If the entire car is destroyed in a single moment from my perspective (an explosion within the garage, say), from your perspective the destruction takes time; the car is destroyed from front to back over time as the car progresses through the garage. When the destruction reaches the driver’s seat, you die.

There is no point in time where, to the observer in the garage, the car was completely inside and, to the driver, the car was not completely inside.

Originally posted by zanket
You’d either die from both perspectives or live from both perspectives. If lightning kills you outside the garage before reaching the garage from your perspective, then from my perspective you’d be dead before you entered the garage.

I just don't get it. How can I be dead when Im completely inside the garage from ur perspective???

See my last sentence above. If the lightning strikes you, then from my perspective you weren’t completely in the garage when the lightning struck you, given that "unless the car is fully inside it gets destroyed by lightning."

Let me elaborate on “There is no point in time where, to the observer in the garage, the car was completely inside and, to the driver, the car was not completely inside.”

From my perspective there is a time, let’s call it MY 5 PM, at which you are fully inside the garage and I simultaneously close both doors. MY 5 PM occurs at both the front and back garage doors simultaneously from my perspective.

From your perspective there is no time when you are fully inside the garage. You notice the back door close at MY 5 PM, at which time it is not yet MY 5 PM at the front door; it might be MY 4.99 PM there, say. Since I won’t notice the back end of the car within the garage until MY 5 PM, it follows that the back end of the car hasn’t entered the garage yet. Later, when it’s MY 5 PM at the front door, the back end of the car will be in the garage, but at that moment (from your perspective!) it will be MY 5.01 PM at the back door, say. Since I’ll notice the front end of the car has left the garage at MY 5.01 PM, it follows that the front end of the car has left the garage.

You & I agree on events, just not whether those events were simultaneous. An event is something happening at a specific location and time (either the time on my clock or the time on your clock). The whole car or the whole garage is not a specific location. In this case an event might be “the front end of the car is near the back door at MY 5 PM.” Both of us will agree that this event happened as described.

Originally posted by zanket
“There is no point in time where, to the observer in the garage, the car was completely inside and, to the driver, the car was not completely inside.”


This sentence implies that if the car was completely inside to you, the car was completely inside to me, the driver too (or else the car didn't exist!)

I suggest focusing on these two events:

“the front end of the car is within the garage at almost the back garage door at MY 5 PM, at which time I close and immediately re-open the back garage door.”

“the back end of the car is within the garage at almost the front garage door at MY 5 PM, at which time I close and immediately re-open the front garage door.”

Relativity of simultaneity means that if I see these events happening simultaneously, you (moving relative to me) do not. I see all the garage clocks reach MY 5 PM simultaneously. You see the clock at the back door reach MY 5 PM first. I see the car wholly inside the garage (the events occur simultaneously) at MY 5 PM. You agree that the events occurred as described, but from your perspective they didn't happen simultaneously, so you were never wholly inside the garage from your perspective.

zanket,

John's point I think is well made. He has stipulated that if the car is inside it is not struck by lightening. If it is not inside it is.

(lets assume the garage is metal and takes the lightening strike in lieu of the car if it is inside. Lets also assume the lightening strike is precisely at your 5PM while you see the car indoors and have both doors temporarily closed.)

Now from your perspective the lightening must hit the garage and the car isn't struck. The driver is safe.

However, if you argue that from the drivers perspective he is not ever totally in the garage then he is struck and he is not OK.

Rembember the lightening strike is precisely at your 5PM while you have the car inside and both doors closed.

hmmm so what does this paradox tell us about relativity?

Originally posted by MacM
However, if you argue that from the drivers perspective he is not ever totally in the garage then he is struck and he is not OK.

This is where your story goes astray. From the driver’s perspective, the lightning takes time to strike. The strike hits the rear of the garage first, when it’s MY 5 PM there. The front of the car is almost at the back garage door then, and so the front end of the car is safe. As MY 5 PM moves from the rear to the front of the garage, the lightning strike follows. As MY 5 PM and the strike moves from the rear to the front of the garage, the car moves through the garage. When the strike reaches the front of the garage the back end of the car is within the garage, and so the back end of the car is safe. The whole car is safe along with its driver.

Quantum Quack
hmmm so what does this paradox tell us about relativity?

The paradox is resolvable within relativity, hence it’s not a real paradox and relativity remains logically consistent.

Originally posted by John Connellan
I havent thought too much about this but ...That's what we're here for, right?




Originally posted by John Connellan
... say there was a flash of lightning at the point in time where, to the observer in the garage, the car was completely inside and to the driver the car was not completely inside. In the latter case the car gets destroyed killing the driver. In the former case the driver survives - 2 realities eh?You need to be more specific about why/how every single point in space outside the garage suffers destruction all the time while every single point inside the garage is exempt. I find that to be a wild physical situation, prior to any paradox in any physical theory.




Originally posted by John Connellan
Basically assume that, unless the car is fully inside it gets destroyed by lightning. Then it will always get destroyed. The car is moving. Only for a very brief period in time will it be totally inside the garage. If you assume it started in the garage, then it will be destroyed in short order at the moment it leaves. If you assume it starts outside the garage, then it will be destroyed invariably, as you have defined it to be so.

Originally posted by John Connellan
I just don't get it. How can I be dead when Im completely inside the garage from ur perspective??? I don't see the confusion. If you're dead as you roll into the garage, then it would be more surprising for you to spring to life at that moment.

Originally posted by John Connellan
This sentence implies that if the car was completely inside to you, the car was completely inside to me, the driver too (or else the car didn't exist!) I agree.

Originally posted by MacM
John's point I think is well made. He has stipulated that if the car is inside it is not struck by lightening. If it is not inside it is.I don't see how this point is well made. This is about all I got out of it. To me, all this seems to be saying is:
"Let's assume there is a logical inconsistency in relativity. Then, how can the paradox be resolved?"




Originally posted by MacM
Now from your perspective the lightening must hit the garage and the car isn't struck. The driver is safe.

However, if you argue that from the drivers perspective he is not ever totally in the garage then he is struck and he is not OK.

Rembember the lightening strike is precisely at your 5PM while you have the car inside and both doors closed. If lightning strikes everywhere in space at exactly the same time (a far fetched idea, but I'll bite) in the garage frame, then, if there is a lightning strike at the moment the car is observed to be entirely inside the garage, the car will not be destroyed. What happens in the car's frame is that, not every point in space gets "lightningized." As the car enters the garage, the "lightningification" approaches the other end, meeting the car head-on. By the time the "lightningification" reaches the entry point, the garage is covering the ass-end of the car, and the car passes through unscathed.

errandir,

I have heard lightening never strikes twice but I have never heard of the same lightening bolt striking two different places at two different times.

There is one lightening strike. Its strike point is and should be at the same location. That location is such that it either strikes the garage door because it is closed and the car is inside or it strikes the car because it is not inside and the door is open.

Since the observers time of 5:00PM is that of the one in the garage, relate the lightening strike in those terms to where the car is in the drivers time please.

Try again.

The lightning strikes at different times on the driver’s clock.

zanket,

I can accept that but the occasion of lightening striking is universally a single event. You haven't stated if the car is struck or not. If so why since the observer in the garage say the car was inside and doors closed.

Originally posted by MacM
I have heard lightening never strikes twice but I have never heard of the same lightening bolt striking two different places at two different times.I was just trying to entertain the notion that, no matter what, if you are outside, you're dead, and if you're inside, you're alive. The only way I could make sense of that is to assume an omnipresent electrification.




Originally posted by MacM
There is one lightening strike. Its strike point is and should be at the same location. That location is such that it either strikes the garage door because it is closed and the car is inside or it strikes the car because it is not inside and the door is open.Well, it sounds like you just answered the question. The name for such an object is "event." This is handled quite easily in SR; it is a very basic object in the theory.




Originally posted by MacM
Since the observers time of 5:00PM is that of the one in the garage, relate the lightening strike in those terms to where the car is in the drivers time please.

Try again. I don't know why we have to confuse the issue with 5:00 PM here and there. It just seems like unnecessary complication to me. I think it was zanket who brought that up, so I'll forward all such questions to zanket.

errandir,

Thanks for the effort. It has been claimed here that it is all logical and that simultaneity shift answers the question. i'm still waiting to see it the car is struck by lightening or not for in either case it would seem that one observers view is in error.

MacM,

You seem to agree to treat the strike as an event. In that case, the analysis is greatly simplified. An event requires four specifications in SR, three for spatial position, and one for temporal position. The point of SR is that these are not mutually exclusive categories; the coordinate system "rotates" (not really, but if you can accept rotation about an imaginary angle, then that's basically what's happening) according to how fast it is going.

OK, so the strike is an event, but <i>the car being inside the garage is not an event</i> according to the same usage that I am applying to the strike. The whole point of the relativity of simultaneity is that two events can happen at the same time in one coordinate system and not in another, literally, not just as an illusion. So, the front end of the car reaching the end of the garage is an event, and the rear end of the car entering the garage is a <i>separate</i> event. The strike is an event, so it has a particular point in space at a particular time, and these don't have to agree from one frame to another (as they don't in this case).

If you don't like space-time diagrams, then I find that unfortunate, because they clarify immensely. If you find them hard to follow, then I will try to draw one up extremely explicitly.

errandir,


You can do the diagram is you wish but I don't require it. I agree with most of what you say. I do take exception to the following:

but the car being inside the garage is not an event


Every orbit of an electron is an event and collectively these events occur in temporal points of time. To me the claim that the car being inside the garage to the garage observer is not an event is nothing more than a dodge of the problem.

That is indeed an event to that observer just as is the lightening strike, the opening and closing of the doors and the movement of the hands of his clock are events.

Lets see if I can tighten the terms of the test a bit.

Stipulation:

1 - If the car is inside the metal garage with both doors closed a lightening strike will not hit the car.

2 - At exactly 5:00PM garage observer time. The garage observer sees the car inside the garage with both doors closed and there is a lightening stike which hits the garage door but not the car. The driver is fine.

Now from the perspective of the car driver, who as you say never sees himself completely in the garage with both doors closed at anytime, it would follow that the car is struck by the lightening bolt and the driver is killed.

You now have two different realities which are not reconcilable.

Where is that wrong?

Originally posted by MacM
Every orbit of an electron is an event ...I don't know how to make sense of this. The orbit of an electron is a QM eigenstate, which is a completely different concept from a SR event. I don't see what the two have to do with each other, nor why you want to complicate the issue by considering electrons.




Originally posted by MacM
... these events occur in temporal points of time.If this is referring to the electron orbit thing, then I still don't know how to make sense of it. If this is referring to an event as defined by SR, then it is an incomplete definition. At any rate, this definition is not useful to the discussion, as it will convolude it with semantics. In SR, an event is defined as a mathematical point in 4-D space-time. This definition preceeds physics, and it is more abstract (more fundamental) than the set of four numbers that define it. Defining an event that occurs in a temporal point in time is not incorrect, but this is not the same definition that I use when I talk of SR.




Originally posted by MacM
To me the claim that the car being inside the garage to the garage observer is not an event is nothing more than a dodge of the problem.That's a little harsh. Science needs definitions. I'm sorry if you don't like the SR definition for event. I myself am torn between calling it an "event" and calling it a "point." I think the reason it is called an event is to alert the audience that the metric is not that of Euclidean space. This termonology allows one to clearly say things like, a point in space is a worldline in spacetime.

For whatever reason, the term "event" is well defined in the context of SR to be a point in 4-D space-time prior to coordinatization. Any nontrivial object, like a car, has some finite volume in 3-space, so it is some hyper-tube in space-time, containing an infinitude of events (mathematically). Fortunately, analysis of most of these paradoxes allow a dramatic reduction in dimensionality and significant number of events. In this case, the number of dimensions reduces to 2, as does the number of significant events (or, maybe more events, depending on what you want to allow).

A huge source of confusion caused by this definition is that, an event is not sufficiently specified by a time; it must also have spatial specification.




Originally posted by MacM
That is indeed an event to that observer just as is the lightening strike, the opening and closing of the doors and the movement of the hands of his clock are events.All of these things are events in the non-SR sense. If you use the SR definition for "event," then the car being in a particular place at a particular time is a collection of events, not just one, whereas these other things are single SR events (if I understand your list correctly).




Originally posted by MacM
1 - If the car is inside the metal garage with both doors closed a lightening strike will not hit the car.That seems reasonable. I won't dispute this. But my confusion comes from this being a proposed lemma for the arguement, or this being a logical conclusion from the nature of lightning.




Originally posted by MacM
2 - At exactly 5:00PM garage observer time. The garage observer sees the car inside the garage with both doors closed and there is a lightening stike which hits the garage door but not the car. The driver is fine.Here we go with the 5:00 PM stuff again.:rolleyes:

OK, are we going to declare this situation as a lemma? Might I suggest that we refer to the collection of things that happen at the same time as a "situation" and that we refer to things that happen at a particular time and point in space as an "event?" So, in this termonology, the car being totally inside the garage is a "situation," while the lightening striking the closed garage door is an "event."




Originally posted by MacM
Now from the perspective of the car driver, who as you say never sees himself completely in the garage with both doors closed at anytime, it would follow that the car is struck by the lightening bolt and the driver is killed.This would follow if the inverse of 1- were true, but, just taking 1- as the working logical statement, the only other thing we can conclude is the contrapositive, namely:

given:
statement: if inside, then not hit

valid:
contrapositive: if hit, then not inside

not necessarily valid:
inverse: if not inside, then hit
converse: if not hit, then inside

This last statement of yours assumes the validity of the inverse. As I have said before, the only way I can make sense of that is to assume that everywhere outside the garage is always electrified.

errander,


quote:
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Originally posted by MacM
Every orbit of an electron is an event ...
--------------------------------------------------------------------------------

I don't know how to make sense of this. The orbit of an electron is a QM eigenstate, which is a completely different concept from a SR event. I don't see what the two have to do with each other, nor why you want to complicate the issue by considering electrons.

ANS: My point is that any motion or change in energy, etc in the universe is an event in time. It is not an attempt to confuse the issue. The stipulation of conditions of the thought experiment consists of trillions of such smaller events but within the context of the stipulation those sub-conditions all collectively create the matter that makes up the objects and conditions stipulated as the conditions per the garage observer at a given point in time, within the volume of spatial dimensions and within temporal time and constitute conditions of "An Event" at an instantaneous present.


quote:
--------------------------------------------------------------------------------
Originally posted by MacM
... these events occur in temporal points of time.
--------------------------------------------------------------------------------

If this is referring to the electron orbit thing, then I still don't know how to make sense of it. If this is referring to an event as defined by SR, then it is an incomplete definition. At any rate, this definition is not useful to the discussion, as it will convolude it with semantics. In SR, an event is defined as a mathematical point in 4-D space-time. This definition preceeds physics, and it is more abstract (more fundamental) than the set of four numbers that define it. Defining an event that occurs in a temporal point in time is not incorrect, but this is not the same definition that I use when I talk of SR.


ANS: Definitions are fine and necessary but I don't see how you can claim that the conditions stipulated for the observer in the garge do not constitute a set of conditions (events) all part of an instant in time for the observer in the garage.


quote:
--------------------------------------------------------------------------------
Originally posted by MacM
To me the claim that the car being inside the garage to the garage observer is not an event is nothing more than a dodge of the problem.
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That's a little harsh. Science needs definitions. I'm sorry if you don't like the SR definition for event. I myself am torn between calling it an "event" and calling it a "point." I think the reason it is called an event is to alert the audience that the metric is not that of Euclidean space. This termonology allows one to clearly say things like, a point in space is a worldline in spacetime.

For whatever reason, the term "event" is well defined in the context of SR to be a point in 4-D space-time prior to coordinatization. Any nontrivial object, like a car, has some finite volume in 3-space, so it is some hyper-tube in space-time, containing an infinitude of events (mathematically). Fortunately, analysis of most of these paradoxes allow a dramatic reduction in dimensionality and significant number of events. In this case, the number of dimensions reduces to 2, as does the number of significant events (or, maybe more events, depending on what you want to allow).

ANS: It would seem any attempt to eliminate stipulations of conditions (events) at a specified point in time as being "An event in a dynamic present" is nothing short of methodology on not addressing the paradoxes created head on.

In this case the stipulations are itemizing those events which all are conditions at a given instant in time for that observer. If you must break it down into finer points of time at the corners of the garage and assume a physical orientation of the observer within the garage, so be it. but there simply must be a correlation of such conditions for the observer at such specified time.


A huge source of confusion caused by this definition is that, an event is not sufficiently specified by a time; it must also have spatial specification.

ANS:This has all been specified. Inside the garage according to the garage observer with doors closed, the lightening strikes at that time. What is missing?


quote:
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Originally posted by MacM
That is indeed an event to that observer just as is the lightening strike, the opening and closing of the doors and the movement of the hands of his clock are events.
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All of these things are events in the non-SR sense. If you use the SR definition for "event," then the car being in a particular place at a particular time is a collection of events, not just one, whereas these other things are single SR events (if I understand your list correctly).

ANS: I think we are in agreement in that all the minor conditions, such as location of individual electrons at that given moment has nothing to do with the problem. It is the collection of such conditions that establishes the macroscopic view of "An Event" which has spatial oridinates at a specified point in time to a specific observer.

quote:
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Originally posted by MacM
1 - If the car is inside the metal garage with both doors closed a lightening strike will not hit the car.
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That seems reasonable. I won't dispute this. But my confusion comes from this being a proposed lemma for the arguement, or this being a logical conclusion from the nature of lightning.

ANS: I would think that it is understood that lightening is wholly unpredictable and its striking any particular point can not be assumed in reality but for the purposes of a thought experiment testing the concept of Relativity and not the nature of lightening, I would think it is a reasonable stipulation that it will hit the garage door if the car is not present and the door is closed.

quote:
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Originally posted by MacM
2 - At exactly 5:00PM garage observer time. The garage observer sees the car inside the garage with both doors closed and there is a lightening stike which hits the garage door but not the car. The driver is fine.
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Here we go with the 5:00 PM stuff again.

OK, are we going to declare this situation as a lemma? Might I suggest that we refer to the collection of things that happen at the same time as a "situation" and that we refer to things that happen at a particular time and point in space as an "event?" So, in this termonology, the car being totally inside the garage is a "situation," while the lightening striking the closed garage door is an "event."

ANS: I actually fail to see why the lightening strike is not a common part of the event. That is the clock strikes 5:00PM, the car is totally in the garage and the doors are momentarily slamed closed and as part of that moment there is a lightening strike. So you have (4) events stipulated in your situation.

However, if for some good reason you feel it must be seperated, then as long as we stipulate that it strikes at the moment (5:00PM) to the garage observer sees the car inside and the doors are closed, I don't see that I would object.

(Maybe if this allows you to slip out of this corner I'll object then. :D)

quote:
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Originally posted by MacM
Now from the perspective of the car driver, who as you say never sees himself completely in the garage with both doors closed at anytime, it would follow that the car is struck by the lightening bolt and the driver is killed.
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This would follow if the inverse of 1- were true, but, just taking 1- as the working logical statement, the only other thing we can conclude is the contrapositive, namely:

given:
statement: if inside, then not hit

valid:
contrapositive: if hit, then not inside

not necessarily valid:
inverse: if not inside, then hit
converse: if not hit, then inside

This last statement of yours assumes the validity of the inverse. As I have said before, the only way I can make sense of that is to assume that everywhere outside the garage is always electrified.

ANS: I fail to see the problem. The statements would seem to agree; including your assumption that the outside of the garage area is electrified, meaning if the car is not inside the garage and the doors closed then the car is struck.

MacM,
No offense, but I followed almost none of what you said in your last post. Please let me know whether you are trying to learn something or not; I would appreciate knowing whether I am waisting time or am slowly but surely guiding you to an understanding of the relativity of simultaneity.

I'm not going to detail/itemize my response.

In the language of SR, specification of an event requires specification of a point in space <i>and</i> specification of a point in time. If I'm not mistaken, you don't seem to have any problem with this.

Since I didn't find a straight-forward resolution to my confusion about what is being assumed, then here is what I will work with as given:

The car does not get struck.
The lightning strikes the garage door that closed just behind the car.

From these statements, I don't see any paradox. It doesn't matter from what frame I view the car, garage, or lightning. I will always see the lightning strike a closed garage door that closes right after the ass-end of the car is inside the garage. It doesn't matter that the front-end of the car is sticking ten-thousand miles out the other side. The lightning strikes the closed garage door, end of story. Where is the paradox? Do you think that SR says lightning will strike the other door in a different reference frame or something? Well, SR doesn't say that.

errandir,

No offense, but I followed almost none of what you said in your last post. Please let me know whether you are trying to learn something or not; I would appreciate knowing whether I am waisting time or am slowly but surely guiding you to an understanding of the relativity of simultaneity.

I'm not going to detail/itemize my response.

In the language of SR, specification of an event requires specification of a point in space and specification of a point in time. If I'm not mistaken, you don't seem to have any problem with this.

No offense taken. Communication I think is key here. My efforts are not to prove Relativity wrong but to insist on a clear description of just how simultaneity resolves the issue of the driver of the car being killed or living.



Since I didn't find a straight-forward resolution to my confusion about what is being assumed, then here is what I will work with as given:

The car does not get struck.
The lightning strikes the garage door that closed just behind the car.

From these statements, I don't see any paradox. It doesn't matter from what frame I view the car, garage, or lightning. I will always see the lightning strike a closed garage door that closes right after the ass-end of the car is inside the garage. It doesn't matter that the front-end of the car is sticking ten-thousand miles out the other side. The lightning strikes the closed garage door, end of story. Where is the paradox? Do you think that SR says lightning will strike the other door in a different reference frame or something? Well, SR doesn't say that.

No. And it appears you have almost answered the question. I am pursueing this more for clairity of the soultion since I believe I understand the issue.

Let me see if I can state it properly rather than attempt to force your to say what I want. then please correct me if my understanding is invalid.

Solution: From the perspective of the observer in the garage at 5:00PM the car is inside and both doors are closed. However, it is surfluous information that the front door is also actually closed as per this observers view since the lightening strike is at the rear door. So the car is not struck.

However, from the view of the driver while he nevers sees himself totally in the garage, nor both doors closed at the same time (the simultaneity seperation) the lightening strikes just as he has entered the garage and the rear door closed and he is not struck even though the front of the car extends well outside the garage and that door is still open in his view.

Does that generally express your solution?

If so, my next step is to propose (as Einstein did a somewhat different stipulation using two lightening flashes).

Test #2:

There are two lightening strikes simultaneous to the observer in the garage and they are at the doors at both ends of the metal garage while the car is inside and both doors are closed.

The same rules apply. If the car is not inside the metal garage with that door closed it is struck. Since the stipulation is from the view of the garage observer, the car is not struck.

To the driver of the car you have agreed above that the rear of the car has entered the garage and the door is closed. Now the door is closed and that coincides with the door being closed by the observer in the garage.

But the driver sees the front of his car sticking out the open door and is struck.

What now?

Rather than tortue you, the answer I believe is that the driver doesn't see the lightening strikes as simultaneous. He sees the lightening strike the front doot while it was closed but before he entered the front of his car through the door when it opened, which would be after the 1st lightening strike. The 2nd strike occurs later when he has jpassed through the rear door and it closed. So he is not struck.

In either scenario the view of the lightening strike(s) produce the same result.

MacM,
What's the catch? If I understood you correctly, then you accept the resolution that the relativity of simultaneity has to offer. Is there some deeper unresolved issue for which you are awaiting resolution? Your last paragraph doesn't seem to leave any loose ends.

errandir,

:D Just try to remember that "Understanding" and "Believing" are two distinctly different issues.

Originally posted by errandir
1) The car does not get struck.
2) The lightning strikes the garage door that closed just behind the car.

3) From these statements, I don't see any paradox. It doesn't matter from what frame I view the car, garage, or lightning. I will always see the lightning strike a closed garage door that closes right after the ass-end of the car is inside the garage. It doesn't matter that the front-end of the car is sticking ten-thousand miles out the other side. The lightning strikes the closed garage door, end of story. Where is the paradox? Do you think that SR says lightning will strike the other door in a different reference frame or something? Well, SR doesn't say that.

OK maybe I should butt in here since I started this thread!

1) First of all that is not what we assumed. We are trying to find out IF the car gets struck.

3) From those statements there is no paradox, but what I meant by lightning is a complete 'situational' electrification (as u say) of everywhere around the front AND back door of the garage. Now how do u explain the car not being electrecuted? What is missing from this argument Errandir?

Originally posted by John Connellan
1) First of all that is not what we assumed. We are trying to find out IF the car gets struck.OK, sorry. I was just trying to entertain MacM for a while since he was the squeaky wheel. But, I will comment to you on this.

If we assume a lightning strike that hits a particular place at a particular time, then it is no good going on without specifying this place and time and really nailing it down (such as striking the garage door when it is closed). Otherwise we'll (I'll) get all confused about what we're really saying is supposed to be happening. The only way the car gets struck is if lightning strikes it. I hope you don't disagree with this. So, it is a quite trivial analysis:

If lightning strikes the car, the car gets struck.
If lightning does not strike the car, the car does not get struck.

Any further/deeper discussion would either be of the physical nature of lightning or some other specification not yet mentioned.




Originally posted by John Connellan
... what I meant by lightning is a complete 'situational' electrification (as u say) of everywhere around the front AND back door of the garage. Now how do u explain the car not being electrecuted? What is missing from this argument Errandir? I never said that the car would not be electrocuted for this consideration. As a matter of fact, if you look back at my earlier posts, I hold that there is no possible way the car will not get struck for this consideration.

I am assuming you mean that everywhere outside the garage is electrified ("is electrified" I mean to be a state of being where "electrified" is being used as a participle, not passive voice; damn english language).

errandir,

OK, sorry. I was just trying to entertain MacM for a while since he was the squeaky wheel. But, I will comment to you on this.

:D Actually, watching you guys squirm trying to sort out all the loose ends and put them together under the theory is quite entertaining.



John C: The point is if you employ Relativity correctly it says that the car is either hit as per both observers or it will not be hit according to either observer. It nevr gets hit by one and not the other.

Originally posted by MacM
Actually, watching you guys squirm trying to sort out all the loose ends and put them together under the theory is quite entertaining.You almost had me fooled into thinking you were actually trying to learn something instead of just being a jackass.

errandir,

Hey don't be one yourself. I think I posed questions very much like those in the minds of others here and forcing you to explain serves the educational purpose of the MSB, or so it has been said.

Originally posted by errandir
I never said that the car would not be electrocuted for this consideration. As a matter of fact, if you look back at my earlier posts, I hold that there is no possible way the car will not get struck for this consideration.

There is though, when the car is in the garage, the lightning strikes. The electrification dissipates at incredible speed so when the car comes back out, it is fine.

MacM: The point is if you employ Relativity correctly it says that the car is either hit as per both observers or it will not be hit according to either observer. It nevr gets hit by one and not the other.

yeah but what in relativity (when u apply it corrrectly) says that the car fully inside or fully outside the garage when lightining strikes, will still both be struck or not struck?

p.s. maybe someone could provide a good link coz Im finding what u guys 'obviously know well', difficult to learn here!

Hi All,
1st I would like to say....excellent discussion, I for 1 have learnt a lot.

Now, I think (or hope) that I maybe able to shed some light on this based on what I have read. To simplify it I'm goint to change a few things...

1) replace car/driver with a cockroach.
2) replace garage with a rubber (insulated) mat big enough so that the cocky can fit onto it when both are at rest.
3) replace lightning with a metal table that is wired to (insert very large number for fun) volts.

Lets say that the rubber mat is on top of the table and the cocky is able to travel at the speed of light. Lets also say that something is at rest on the mat and able to observe the cocky approaching at the speed of light. According to this observer the cocky will be entirely on the mat at stationary observer time (t_so) = 5. At precisley t_so = 5 the table is live.

From what I have read here
1)the stationary observer will see the cocky on the mat (safe) and the table 'electrify' instantly at t_so = 5
2) the cocky will see the table elctrify not instantly but starting from the end of the table (end closest to cocky's head) and move (with time) towards the end of the table at the rear of the cocky, BUT the cocky will never see the table electrified at the same point as he is standing except for when he is on the mat, ie no part of he's body will ever be touching an electrified part of the table because while the back half is touching the table the elctricity hasn't traveled that far along the table and when the front half of he's body is touching the table the electricty has already passed through that point and that point on the table is no longer electrified.

now this appears to be 2 different realities...but I don't think that that is an issue because the only thing that could ever see these 2 realities is a 3rd observer that can see from both the stationary observers (above) reference frame AND the cocky's reference frame simultaneously....which is not possible (as far as I can tell anyway) I might be wrong. so.....the paradox can only exist inside a thought experiment where we have the luxury of simultaneously observing something from 2 different frames of reference.

anyway that is my interpretation please correct anything I have said if it confuses the issue even more.

What about if there was a duck, you know like in the experiment?

Should I just give up and stick with quantum physics? Relativity is way too hard!!!

Originally posted by Rambler
Now, I think (or hope) that I maybe able to shed some light on this based on what I have read. To simplify it I'm goint to change a few things...

Have the cockroach move at < c, say 0.9c, since c is thought impossible for material objects. Other than that your story looks good.

Originally posted by John Connellan
p.s. maybe someone could provide a good link coz Im finding what u guys 'obviously know well', difficult to learn here!

Here (http://casa.colorado.edu/~ajsh/sr/simultaneous.html) is a decent link that I found with Google.

Zanket yes off course <c.

I am more interested in your (or anyone elses) feedback regarding my thoughts on why this is not a paradox? ie that this will only appear to be a paradox to an observer that can see the event in both reference frames simultaneously.

thanks.

"I am more interested in your (or anyone elses) feedback regarding my thoughts on why this is not a paradox? ie that this will only appear to be a paradox to an observer that can see the event in both reference frames simultaneously."

That is exactly the problem why paradoxes arise, and why MacM doesn't buy any of this SR talk.

You cannot witness an event from two reference frames simultaneously, that is exactly where the problems appear. Each event has its own spacetime coordinates in one reference frame, and other coordinates in another. Both observers will always agree that a car got electrified, or a car -- the relativity of simultanity does not imply the relativity of reality ;). The point is that spacetime coordinates for "lightning strikes car" of "current fries cockroach" are different for different observers.

If you were to witness such an experiment with 20 observers (*), and put them all together in the end, they would all disagree with eachother. One guy would say that the car got electrified 10 seconds after the experiment started, another guy would say 20 seconds. The only way to get an agreement between all results is to realize that the measurements of one observer are related to the others by Lorentz transformations.

Is there an intuitive way to see this ? No, you just have to go through the math. Nothing more, nothing less.

(*) all moving with a different velocity with respect to the experimental setup

Bye!

Crisp
(hoping that this stops all these appearant paradoxes talk -- they all contain the same mistake)

Crisp,

Crisp
(hoping that this stops all these appearant paradoxes talk -- they all contain the same mistake)


ANS: Being a "mistake" is a RELATIVE view. :D pun intended.

There are no mistakes anywhere, I am not assuming u 'have' to see the event simultaneously from two frames of reference!

Ok how about looking at it from this perspective.

If a car is fully inside the garage at any time then it gets blown up.

What happens?

John,
You will probably need to give a bit more detail.
What blows it up?

Originally posted by Rambler
What blows it up?

OK lets say at each end of the garage there are terminals with a high potential difference across them. At each end of the car there are highly conductive rods (rather like a lightning conductors) which are connected by a wire. Along this wire (in the center of the car) is an explosive device which only detonates when current flows though it.
Only when the rods touch the garage terminals does the car blow up. In one frame the car never touches the terminals and never blows up. In another it blows up. Which is reality and which is not or do we invoke the many worlds theory here again?!!!

Originally posted by John Connellan
OK lets say at each end of the garage there are terminals with a high potential difference across them. At each end of the car there are highly conductive rods (rather like a lightning conductors) which are connected by a wire. Along this wire (in the center of the car) is an explosive device which only detonates when current flows though it.
Only when the rods touch the garage terminals does the car blow up. In one frame the car never touches the terminals and never blows up. In another it blows up. Which is reality and which is not or do we invoke the many worlds theory here again?!!!

In both frames either the car blows up or it doesn't.

Remember, electricity is bound by the same laws of physics and can't travel instantaeously either. Thus it takes time for current to develop.

For instance, When one end of the car touches the positive terminal, it causes a disturbance in the electrons at that end of the car, and this disturbance will travel through the car towards the other end at some velocity below c. The same happens at the negative end. When these disturbances meet at the center, we can say that a current is flowing at the center. (And the bomb blows up. ) From the frame of the car, this happens because the two terminals are touched at the same time and it takes an equal time for each pulse to reach the device.

From the frame of the garage the two terminals do not touch at the same time, but in sequence. But neither will the disturbances be seen to travel at the same speed with respect to the car (addition of velocities theorum). The result is the from the frame of the garage, the disturbances still meet at the center of the car at the same time, and the car blows up.

If you want to add the requirement that the current must exist across the whole length fo the car in order for the device to detonate, then the ends of the car must slide over the terminals for some given time, long enough for the current to develp.

From the frame of the car the length of the terminal would then say, have to be x. But these terminals are moving with respect to the car, and undergo length contraction, thus they must be somewhat longer than x in the garage frame.

What this means is that from the garage frame, that while the two ends of the car will first contact the terminals at different times, before the first one breaks contact, the second one will make contact, and there will be a time while both are in contact. Again, you will still see conditions that will lead to the detonation of the explosive device from both frames.