If we have a comet that has been travelling at relativistic velocity relative to Jupiter for 10,000 years, and that comet has a vector that according to Jupiters Frame would cause it to collide with Jupiter at 12.00.05pm 10/7/99 Would both the comet and Jupitor agree that: 1] According to the Comet and Jupitor a collision occurs at the time predicted. [their NOWs being simultaneous] 2] Misses Jupiter in the comets Reference frame but strikes it in Jupiters RF. [ their NOWs being non-simultaneous] 3] Misses Jupiter in both reference frames, [ their nows being non-simultaneous] The moment of t=0 being non-suimultaneous when comparing both observers. Proposition: As Jupiter is a moving target with an orbital velocity of x kmph any non-simultaneity would bring about a situation where by there would be no collision even though the two objects would be sharing the same space time co-ordinate. Both arriving at that space time co-ordinate with different or non-simutaneous nows, meaning that one is in the future Now of the other at the wrong co-ordinate for that future NOW. The idea and challenge is to prove mathematically that a collision would occur even though the NOWS [t=0] of both objects are according to SRT non-simultaneous. This could be seen as similar to the "pole in the barn" gendanken except in this scenario the barn is moving. Can objects that have non-simultaneous NOWs collide? How do we calculate the degree of non-simultaneousness between the the "NOWS" of two object at relative velocity? [ The NOW being the zero duration point in time between the past and future or reflective potential of a photon ]
12.00.05pm 10/7/99 according to who? Which frame is this time given in? If the comet collides in one frame, it collides in every frame. If it doesn't collide in one frame, it doesn't collide in any frame. All observers agree about which events do or do not occur, always. That is impossible. Two objects which share the same space and time coordinate in any frame of reference are at the same place at the same time, so they must collide. I have no idea what you mean by simultaneous or non-simultaneous NOWs. That concept is not part of physics.
I am pretty sure I stated "according to Jupiters Frame". If they don't collide at predicted time Jupitor would be in a different position in it's orbit and the comet would miss hitting Jupiter. then prove this mathematically, .....should be easy I would think if what you say is correct. But of course a collision at a give position would be impossible yes if the collision was not simultaneously experienced by both objects. So you are saying that non-simultaneity is a fudge.....eh? Then what on earth is non-simultaneity referring to if not something that is non-simultaneous. What does simultaneous mean then? I thought it meant happening at the same time...... How can it be claimed that time is relative yet not state clearly what it is that is relative regarding time? How can we calculate the degree of non-simultaneousness? How far into the future or past of the other frame does an object at relative velocity exist?
JamesR, I'll put it this way, For two objects to collide they must experience time simultaneously at the point of contact. At what point in the non-simultaneous flight of objects do they suddenly become simultaneous? Say one object is 10 hours into the future of the other object, how can it be claimed that the collision is simultaneous and for that matter how can the collision occur any way. So I suggest even as an exercise that the collision be proved mathematically as simultaneous. But first we would have to be able to determine exactly the degree of non-simulteousness. As far as I can tell non-simultaneousness can only refer to the fact that one object is not sharing the same moment between past and future therefore one object must be either in the past or the future of the other object. If our comet is a couple of days into the future of Jupiter then it would dissect Jupiters orbital path at a location that would take Jupiter a couple of days to get to, thus miss hitting Jupiter.
Ahh!! I managed to dig up an old posting made by a poster along time ago. It was his attempt at solving this time riddle mathematically. Unfortunately he failed to stay at the forum long enough to complete the task. I have copied and pasted it below. "There are several ideas about problem that we can try to solve. But the most appropriate for our Team, I guess, is the one that arrives from QQ’s willing to know what are NOW, PAST and FUTURE and what connection they have with each other in respect of the different inertial observers. If we want to develop this issue, we have to define what is NOW, PAST and FUTURE. I already did it for NOW in the appropriate thread and my proposal was “NOW is a set of all events that are happening simultaneously at given moment t for the given observer”. So, each NOW is functional of t and given reference frame K. It means we should write it as NOW{t; K}. Let another observer, K’, having the origin of its coordinates in the same point as K, has the directions of coordinate axes as K. Let K’ is moving in respect of K with velocity v along axis X. Let K’ clock are synchronized with clock of K in moment t = 0 of coincidence of origins of coordinates of those two RF. Then K’ will have his NOW{0, K’} different from NOW{0, K}! Why it is so? To see it, we need to do one small step – to notice that fact like the following one- “this particle at moment t is in point r” already is an event by itself. (“Coincidence of a given physical particle with given point of my coordinate system” – this indeed is a physical event for observer!) If we apply that to all material content of the entire World, we will see that NOW for any observer is the entire World at given moment of time! The problem is only the one: “entire World” in those two NOW-s, NOW{0, K} and NOW{0, K’}, are the different! And they are different not only by the distribution of material content, but also by what this content is! Indeed, as we know no pair of events, A and B, that happen in different points of one inertial RF simultaneously can be simultaneous in any other inertial RF. Therefore, there is the only one event that indeed is simultaneous at t = 0 in both RF – the coincidence of origins of their coordinates! The entire World of K’, i. e. Now of K', except the origin of the coordinates, at moment t = 0 consist of events that are from the PAST and the FUTURE of the entire World of K. These entire can easily be seen on the Minkowskii (x, y ct) coordinates graph, if he/she will recall that the moving RF has x and ct axes slopped on angle arcthan(v/c) in respect to axes x and ct of the rested RF. But if there are touched PAST and FUTURE, it means that the distribution of the material content will be different because of the natural motions of things in Nature. More over, some material content from PAST of any RF will not reach the NOW of that RF and/or some material content from NOW of any RF will not reach FUTURE of that RF; also some new content will appear (born) between PAST and NOW, and between NOW and FUTURE. Therefore, NOW{0, K’} differs from NOW{0, K} not only by distribution of material content, but also by what this content is. And that fundamental fact deeply concerns practically all parts of Physics. Let me show it on the example of the old Quantum Mechanics. Let assume we live in 1930. Let imagine that there comes some guy like QQ and asks: “We know the Hiesenberg’s principle of uncertainty Δp Δx ≥ h…………………………………………….(+) Why not H ≥ Δp Δx ≥ h And what is H in that case?” QQ will be very reasonable, because he knows that SRT prohibits the motions faster then speed of light in vacuum and, for example, things can come in FUTURE from NOW only inside the light cone. It means that no matter what Δx is, Δp can not be more than ΔPo = m[v]c/(1- v²/c²) Because Δx itself can not be more than ΔXo = cΔt We came to the conclusion that it should be true that EΔt/(1- v²/c²) ≥ Δp Δx ≥ h. what at v much less than c gives EΔt ≥ Δp Δx ≥ h………………………………………(++) Wouh! We got restriction on the possible growth of uncertainties in classic QM! Did you see anything like that in any textbooks? I did not… Why (++) is very important? Because no matter what, any wave function should lead to (+). Therefore, we can conclude that no matter how we will develop relativisation of QM (i. e. construction of our QFT, Quantum Field Theory; recall: we are in 1930!) the wave functions of this theory should lead in limit v much less than c to (++). Does our contemporary QFT satisfy to this requirement? The answer is NO! So, my first proposal is to develop “NOW, PAST and FUTURE” problem. Unfortunately, due to being rather mathematically illiterate I am not sure what he is actually demonstrating here but suffice to say the issue of non-simultaneity is not that simple to prove mathematically. Possibly some one with mathematical knowledge would care to interpret and complete his work? edit: The reason I have not posted his handle [ name] is that I am unable to contact him and ask him if he minded me using his work now. The post was over a year ago and his position on this subject may have changed considerably. Suffice to say that he was one of SRT's greatest supporters.
Had a bit of a think and: How can we measure the difference in time between [t,K] and [t,K'] on the assumption that t=0 in both frames?
I'll try to give a go at explaining this. First, everyone will agree as to the fact that the collision takes place. What they wil not agree to is at what time this collision takes place according to certain clocks. For example, in your post you have the comet striking Jupiter at a given time in the Jupiter frame, But you give the time as an Earth-based value (an Earth date and a time I'll assume is GMT. We'll assume for now that this is where Juiter's refernce clock is located (on Earth), and we'll ignore the relative velociies between Earth and Jupiter for simplicity. Now, When the collision occurs, in the Jupiter frame, the Earth clock reads the given time. But what about in the comet frame? Let's assume that the comet is traveling along the line that passes between Jupiter and the Earth, and is coming inbound. In that case, when the collision occurs in the comet frame the earth clock will not read the given time but some time later. The comet and Jupiter will not agree as to what time it is on Earth when the collision happens. IOW, the Earth clock reading the stated time and the collision are simultaneous in the Jupiter frame, but are not in the comet frame. This is waht is meant by non-simultaniety. Events that are simultaneous in one frame are not always simultaneous in another. It depends on the relative velocity and the distance as measured along the line of relative velocity. The equation for this is vx/c². IOW, if two events are deemed simultaneous in frame K, then in frame K' they will be separated by a time of vx/c² where v is the relative velocity btween the frames and x is the distance between the events as measured along the line of relative motion. I think this question is based on a confusion between how you personally are treating time vs how it is treated in SR.
This post assumes that SRT is correctly stated and applied by Janus58. The explanation above opens the SRT to a scrutiny such that exposure of the falsity of SRT is unconditionally and undeniably confessed. Taking a simple and popular example where an observer, O’, on a platform moving with velocity v is collocated with the midpoint of two emitted pulses of light located in the embankment. Likewise, there are two clocks collocated with the embankment emitters at the instant the pulses are emitted. It is technologically trivial to embed the time of arrival of the pulses in the moving platform. There are two events here burdened with questions of simultaneity. First, Einstein uses the fact that the observer O’ on the platform first detects the pulse from the emitter located in the direction of motion. Later the pulse from the rear of the platform catches up to O’. O’, considering his platform at rest and the embankment whizzing by concludes that the first detected pulse emitted into the platform frame before detection of the second pulse. This muses Einstein indicates that what was simultaneous in the embankment is not simultaneous in the moving platform. However, as the clocks on the platform were collocated with the emitters on the embankment at the instant the lights emitted; both of these clocks measure the simultaneous emission of the pulse on the platform. Let us assume that the light signals entering the platform are immediately embedded with the time of arrival of the emitted lights. Similarly, observers on the platform located behind O’ observe the simultaneous arrival of the pulses at the emitter midpoint in the embankment. O’, asserts that his observations conclusively establish the loss of simultaneity of the lights emitted onto the platform, yet O’ is moving with respect to the emitters and therefore the lights travel unequal distances before detection by O’. However, SRT tells us dogmatically that the O’ observations are the authoritative and definitive arbiters of physical law described in SRT where the SRT laws run equally throughout the moving platform. When O’ is urged to review the time signatures of the two pulses he detected and notices that the two times of arrival in the platform were identical, the fact that O’ detected the pulses sequentially, is insufficient to justify ignoring the glaring reality of the time signatures that prove the lights were measured simultaneously in the moving platform. What is simultaneous in the embankment is simultaneous in the moving platform. O’ may argue that the measured times in the moving platform have no bearing of the reality that he, O’, detected the sequential arrival of the two pulses proves, with an unswerving use of the postulate of the equivalence of inertial frames, that as to O’ the simultaneous arrival of the two lights was a physical impossibility. What O’ is missing is that his motion imposes an experimental condition that results in O’ measuring the lights after the lights had traveled different distances. The platform observers located behind O’ had no problem observing the lights arriving at the embankment midpoint simultaneously. O’ has been empowered by the corruption of SRT rationalization that his, O’s location on the platform, is such that his observations must be preferred over all the other observations and conclusions of other platform observers. What is embedded in theoretical reinforced concrete is the rejection of the concept of “preferred frames of reference” that is the basis of the equivalence of inertial frames postulate. Reason and logic and the laws of physics demand that not only must the same laws of physics be employed in all inertial platform but that on each inertial platform the laws of physics must be strictly invariant at every point on each platform. As a corollary, there is no observation point on any inertial platform that is preferred over any other point. Geistkiesel
Janus58, Firstly thanks for taking the time to respond. Can I ask you a simple question: If a collision occurs, both the Comets frame and Jupiters frame MUST share a co-incidence of events? By this I mean that both frames t=0 at the "momment" of collision must be simultaneous? Can we agree that if the t=0 is not simultaneous for both frames a collision will NOT occur? If this is the case are you not simply stating that whilst the passage of time may be different their NOWs or t=0 are simultaneous. From what I see it is SRT that is confusing two aspects of time. 1] the relative rate of time passage [ given dilation due to gravitational effects and velocity] and 2] the simultaneousness of the t=0 or NOWs of those frames.
