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: 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?
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. 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. 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. 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). 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. Here we go with the 5:00 PM stuff again.Please Register or Log in to view the hidden image! 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." 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: -------------------------------------------------------------------------------- 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. -------------------------------------------------------------------------------- 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: -------------------------------------------------------------------------------- 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). 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: -------------------------------------------------------------------------------- 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. 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: -------------------------------------------------------------------------------- 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. 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. Please Register or Log in to view the hidden image!) quote: -------------------------------------------------------------------------------- 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. 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, Please Register or Log in to view the hidden image! Just try to remember that "Understanding" and "Believing" are two distinctly different issues.
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?
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. 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, Please Register or Log in to view the hidden image! 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.
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.
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. 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.
Have the cockroach move at < c, say 0.9c, since c is thought impossible for material objects. Other than that your story looks good. Here 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 Please Register or Log in to view the hidden image!. 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)
