Then we have a few issues. First, West/East/North/South are direction in 2D and we're dealing with 4D. Second, distances in relativity can't be defined without incorporating reference frames as distance/length itself changes from observer to observer depending upon velocity (i.e., speed and direction), acceleration, and angular momentum. The above sets up a scenario in which there is absolute space that Galilean relativity suggests doesn't exist and which is completely foreign to special & general relativity. Distances are necessarily defined by four coordinates because, as no (absolute) uniform motion exists by which we could actually determine that the distances here:
So we have: Alice > 1 light hr > Charlie > 1 light hr > Bob > 1 light hr > David.
are meaningful. They are made meaningful once we introduce inertial reference frames or more generally how they are space-like separated relative to one another. The only way in which they can be space-like separated is relative to one another and over a time-like interval.
In this case, Bob's button sends the two pulses at the exact same time.
Except to do so entails either rejecting both special and general relativity entirely or defining "exact same time" in terms of reference frames. There is no possible way in which to measure, determine, or otherwise ensure that Bob could possibly send two pulses at the exact same time other than that this exactness is completely unique to Bob, while Charlie and David can both easily assert that the pulses weren't sent at the same time AND both disagree which was sent first. The only way to ensure that such disagreements are settled is introducing Minkowski metrics and Lorenz transforms such that we can related different reference frames.
Again, the only possible way to determine the "time" at which the signals were sent or received is in terms of all observers' inertial reference frames in 4D.
From whose perspective? The famous twin paradox, described as simply as is possible, clearly indicates that one's experience of time depends (among other things) upon one's velocity and acceleration. You have assumed absolute positions which requires an absolute uniform motion that doesn't exist and an absolute space in which it would have to exist despite no such space.
It, in no way, limits Alice's decisions or actions.
Because it assumes a description in which events unfold in time relative to an absolute space (or equivalently absolute uniform motion) just to define distances between the individuals. The reason we require a 4D universe in which time isn't distinct from space is because there is no way to say that anything ever happens other than from infinitely many reference frames.
Now, if Alice keeps looking east, it is inevitable that she will see David's light one hour after seeing Charlie's.
It is absolutely guaranteed that she won't unless we can track her "motion" in 4D. There are infinitely many ways for her to not see David's light one hour after Charlie's, but only one way she could.
But, as far as I can tell, the conclusion about limitations on free-will regarding the scenario have more to do with the inevitability of physics, and cause-and-effect, than it does with free-will.
If you can't define time such that there is anything other than a subjective ordering of causes and effects and, more importantly, there isn't any way to determine whether or not effects actually were caused or did happen other than via a cosmos in which all causes and effects are no longer described as sequential moments in time but coordinates in a "frozen" 4D spacetime, then all causes are simply one of infinitely many 3D subspaces of a 4D space in which the fourth coordinate changes uniquely for each. Simply put: any would-be decisions you make tomorrow are already made.
I'm not sure if someone answered you already but the theory of relativity answers this easily. It's also the correct answer here...
The rate of time slowed down for the faster moving reference which was Alice's train car.
Light hits both of them at the same time relative to there reference because the Speed of Light is constant. Or light will always travel a specific speed. The only thing that was different was the passing of time for the person inside and outside the train car. So when the train fully stopped, Alice's watch would have been slower than Charlie's watch.
We don't notice this in every day life, but it does happen. It's just that we are travelling no where near the speed of light so we are dealing with very very small increments of time. But it has been tested on airplanes that traveled long distances carrying very accurate atomic clocks which can measure small precisions.
Given the theory of relativity, I don't think it will be a foundation to asserting further notions of free will. Free will can occur in different time references.
"Rate" is defined by time. It is utterly impossible for the rate of time to slow down when rate is defined either as a ratio of units over units of time, or as the instantaneous change in speed for an infinitesimal temporal unit.
Light hits both of them at the same time relative to there reference because the Speed of Light is constant.
Given you haven't represented any theory of relativity accurately (although this could be because you simplified something you do have a much deeper understanding of), it isn't a surprise that you don't find it very relatable to "free will".
There are two relativity theories. TGR is more than simply an extension of special relativity.
I used it for the questions, as have physicists since before I was born.
...doesn't make much sense in relativistic physics where time isn't distinct from space. More importantly:
"Rate" is defined by time. It is utterly impossible for the rate of time to slow down when rate is defined either as a ratio of units over units of time, or as the instantaneous change in speed for an infinitesimal temporal unit.
It doesn't hit them at the same time, and relativity eschews such a notion as nonsensical. There is no simultaneity.
Given you haven't represented any theory of relativity accurately (although this could be because you simplified something you do have a much deeper understanding of), it isn't a surprise that you don't find it very relatable to "free will".
It doesn't. It suggests that free will is a priori impossible as what happens in the "future" has already happened from another observer's perspective.
I tried to limit my verbosity. As to complexity, there are entire volumes dedicated solely to this, so you'll have to forgive me if my simplicity glosses over many nuances.
Because there is no "now". There is only "now" according to me, you or some other observer.
It doesn't. It suggests that free will is a priori impossible as what happens in the "future" has already happened from another observer's perspective.
I tried to limit my verbosity. As to complexity, there are entire volumes dedicated solely to this, so you'll have to forgive me if my simplicity glosses over many nuances.
The original question was asked differently concerning light reaching essentially from the same place to the both observers with the same distance at time 0.
Alice and the trian is in motion, Bob being outside the train is not in motion.
At time 0, both distances to the back fo the train are still the same. At time after 0, alice's distance to the back of the train will always be the same. Bob's distance to the back of the train will be less because the train is in motion and Bob's initial position was in the middle of the train. It will be less until the train passes Bob completely. The light will reach the back of the train faster for Bob because the train is in motion for bob and not in motion for alice. This is newtonian math...
[Edited] I misread the recent question. Forget everything I just wrote.
Let me put it another way and I believe I tried to explain this initially with the theory of relativity.
Alice's watch will be the same value as Bob's watch when when the light hits both of them. However, because Alice was in motion her passage of time was slower than Bob's. So when Alice syncs up with Bob, her watch would indicate less time has passed than Bob's.
After this point and concerning free will, I might be conjecturing but I don't think it matters who observed the incident first. Data still travels at the speed of light so without data I don't see how an effect can occur from a cause. You still need the data to reach from one point to another point. This is with the current model.
However, with the concepts of holograms and quantum entanglement, this does suggest that there is no free will... Also, multiple universes suggest that free will is an illusion because every conceivable thing happened.
I'm the first to admit that I am wont to overly complicate things. Here, however, I believe that the issue is itself more than a little complicated. To give some idea of what I am talking about purely from a descriptive standpoint, I offer some quotations taken from a paper by P. S. Wesson in the volume Petkov, V. (Ed.) (2010). Minkowski Spacetime: A Hundred Years Later (Vol. 165 of Fundamental Theories of Physics). Springer. I have hidden them so that they don't detract from the flow of my response, but I would suggest reading them as they are from the physicists who founded relativity and spacetime and other notables.
Einstein (as reported by Hoffman): "For us believing physicists the distinction between past, present and future is only an illusion, even if a stubborn one."
Eddington: "General scientific considerations, favour the view that our feeling of the going on of time is a sensory impression; that is to say, it is as closely connected with stimuli from the physical world as the sensation of light is. Just as certain physical disturbances entering the brain cells via the optic nerves occasion the sensation of light, so a change of entropy...occasions the sensation of time succession, the moment of greater entropy being felt to be the later."
Hoyle: "All moments of time exist together. There is no such thing as waiting for the future." "It could be that when we make subjective judgments were using connections that are non-local...there is a division, the world divides into two, into two completely disparate stacks of pigeon holes."
Ballard: "Think of the world as a simultaneous structure. Everything thats ever happened, all the events that will ever happen, are taking place together." "Its possible to imagine that everything is happening at once, all the events past and future which constitute the universe are taking place together. Perhaps our sense of time is a primitive mental structure that we inherited from our less intelligent forbears."
Why doesn't Alice see the light wave from the rear lightning strike until "after" Bob sees it?
Because she is moving forward towards the front lightwave and away from the rear. Neither Alice nor Bob actually "see" the "time" at which either lightning bolt strikes the train. Our eyes translate lightwaves into visual information when they reach our eyeballs.
More technically, when they activate receptors located at the rear of our eyeballs that create "spike trains" or series of action potentials/neural firings that "travel" via our visual pathways to our occipital lobe and spread via local & nonlocal neural networks to various regions of the frontal cortex.
As fast as light is, it still requires a certain amount of "time" to traverse some distance. At a certain "moment", Bob & Alice are parallel to one another, both view one another as equidistant from the ends of the train car (i.e., Alice is in the middle of the train car and Bob is outside the train car but both ends are just as far apart; see the figures posted earlier). At that moment we can describe lightning striking both ends of the train from the Godlike/bird's eye perspective. However, neither Alice nor Bob can "see" either lightning bolt strike until the lightwaves reach their eyes.
For Bob, at rest with respect to the train, the light waves both traverse the same spatial distance to reach his eyes, and as light travels at a constant speed, they both reach his eyes at the same time. This is true also of when he sees the lightwaves meet.
Alice, however, is travelling towards one lightwave and away from another. Like Bob, she can't register any information about lightning hitting anywhere until the lightwaves reach her eyeballs. However, because she is travelling toward one and away from another, she "sees" one happen first.
As is, this doesn't seem particularly problematic. It is only problematic once we realize that we have assumed a 4D, godlike perspective in order to say that the lightning strikes both ends of the car at the same time. Then we have to realize that there is no way to say that these events occur at any time except from a particular, subjective perspective. Bob perceives events unfolding in one way (he slices up spacetime, or it is sliced up by, according to his worldline & worldtube). It is important to realize that he is stationary only relative to the train, and that there are other ways in to be stationary relative to it or for it to be stationary relative to some other reference frame.
The key, the real essence of the issue, is the absence (or relativity of) simultaneity. When things happen is necessarily subjective (as is how they are perceived, including how long they are). Everything in the cosmos is always at motion and stationary relative to something else (many somethings, really). There is, however, for assuming one observer is at motion except as relative to another and even this is can be a completely arbitrary choice. Likewise, as events "occur" in time only insofar as they can be shown to happen at the times they do, and as this depends upon where one is in spacetime.
Nor is it simply just a matter of different observations of events from observer to observer. The amount of time that passes for a particular observer depends upon their speed and acceleration relative to another observer. Thus not only are events defined as "now" subjectively, but the time in which they can occur lengthens and contracts based upon motion (hence the necessity of spacetime geometry to describe events in astrophysics, cosmology, and similar branches of the sciences which have to deal with the macroscopic scale).
To give some notion as to the complexity involved, I'll use another's description:
"In the case of length contraction relativity of simultaneity clearly demonstrates that while measuring the same meter stick two observers in relative motion measure two different three-dimensional objects. This becomes completely evident when it is taken into account that the meter stick (as an extended three-dimensional body) is defined as all its parts which exist simultaneously at a given moment of time. As the two observers have different sets of simultaneous events it follows that two different three-dimensional meter sticks (two different sets of simultaneously existing parts of the meter stick) exist for them. Therefore the two observers do measure two different three-dimensional meter sticks. However, this is possible only if the worldtube of the meter stick is a real four-dimensional object, which makes it possible for the two observers to regard two different three-dimensional cross-sections of it as their three-dimensional meter sticks; what is the same meter stick is the meter sticks worldtube. Hence the physical meaning of length contraction turns out to be profound as Minkowski argued length contraction (and therefore relativity of simultaneity as well) is a manifestation of the four-dimensionality of the world. And indeed, if the world were three-dimensional, this effect would be impossiblethe meter sticks worldtube would not be real and therefore both observers would measure the same three-dimensional meter stick (the same set of simultaneously existing parts of the meter stick), which would mean that the observers would have a common class of simultaneous events in contradiction with relativity.
Although length contraction alone is sufficient to settle the issue of the dimensionality of the world consider the following more general argument as well. The world cannot be three-dimensional since such a world is defined in terms of (i) the pre-relativistic division of events into past, present and future, and (ii) the pre-relativistic concept of absolute simultaneityas everything that exists simultaneously at a given moment. So a three-dimensional world is defined as the class of simultaneous events at a given moment. To see that the world cannot be three-dimensional according to relativity, assume for a moment the pre-relativistic view of realitythat reality is indeed a three-dimensional world. Then it inescapably follows from relativity of simultaneity that two observers in relative motion have two different three-dimensional worlds since the observers have different classes of simultaneous events. But this is possible only if these worlds are different three-dimensional cross-sections of a real four-dimensional world. As in the case of length contraction it is again evident that relativity of simultaneity is a manifestation of the four-dimensionality of the world. That is why no relativity of simultaneity would be possible in a three-dimensional worldif the world were three-dimensional, the class of simultaneous events constituting such a world would be common to all observers in relative motion, which would mean that simultaneity is absolute."
Petkov, V. On the Reality of Minkowski Space Found. Phys (2007) 37: 14991502.
It doesn't. It matters whether or not one can say there was a time at which the incident occurred and why. If it is entirely subjective, and the past, present, and future, are slices of spacetime that are entirely subjective, then they are illusory. What you have done is what you are doing and what you will do depending upon a particular reference frame.
Data still travels at the speed of light so without data I don't see how an effect can occur from a cause.
Let's say that Alice blinked when the lightwave from the front of the train reached her eyes and then again when the lightwave from the rear reached her eyes. For her, the cause of the first blink is that lightning struck the front of the train first, and then another bolt struck the rear later: two causes, two effects, unfolding linearly in time, one set after another.
For Bob, the causes that Alice perceived didn't happen. Neither did their effects. She blinked because she was in motion towards the lightwaves from two lightning strikes (two causes/events) that reached her at different times because of her motion. Thus she blinked at one moment because of her motion forward towards a lightwave and again later because of her motion away from a lightwave, but both were initiated at the exact same time. The cause for the effects wasn't that one lightning bolt struck first, but Alice's motion.
You still need the data to reach from one point to another point.
This is a tricky issue. Correlations between space-like separated quantum systems clearly indicate that "something" travels not only faster-than-light, but instantaneously. However, special relativity precludes this, and is rescued by understanding that while the effects are instantaneous, no "information" can be transmitted from Alice to Bob instantaneously and for reasons that have nothing to do with SR or really even TGR.
However, with the concepts of holograms and quantum entanglement, this does suggest that there is no free will
How do holographic multiverses relate to free will? As for quantum entanglement, they are used as a method by which free will may operate (including by one of the most famous physicist to demonstrate entanglement, Gisin).
Also, multiple universes suggest that free will is an illusion because every conceivable thing happened.
Multiverse theories/many-world cosmologies are equivalent: Bousso, R., & Susskind, L. (2012). Multiverse interpretation of quantum mechanics. Physical Review D, 85(4). The motivation for many-worlds (and, in general, all relative state interpretations of QM) is the measurement problem, which are resolved (by advocates) by such models via the interpretation of the probabilistic nature of the wavefunction as being ontological in that every possibility given any and every observation is instantiated in "some world". This doesn't preclude that observers are unable to make choices. In fact, there is an entire monograph from the edited series Series on Knots & Everything by Amoroso & Rauscher (The Holographic Anthropic Multiverse- Formalizing the Complex Geometry of Reality) in which it is argued that that modern physics suggests a theistic cosmology, not just free will.
The last I heard, scientists were still scratching their heads about speed of light effects.
For example they found that it travels at exactly the same speed no matter in which direction their instruments send a pulse of light, regardless of the 67,000 mph speed of the earth's orbit through space.
So we're up against quantum mysteries again
The last I heard, scientists were still scratching their heads about speed of light effects.
For example they found that it travels at exactly the same speed no matter in which direction their instruments send a pulse of light, regardless of the 67,000 mph speed of the earth's orbit through space.
So we're up against quantum mysteries again
That the speed of light is constant pre-dated quantum physics and quantum physics isn't necessary for it. In fact, the most serious challenges to the special & general relativity (both of which, but the former especially, derived from the implications of light propagating at a constant speed regardless of any media) is quantum physics.
But it's still a mystery isn't it, quantum or not?..
i mean, when scientists fired a pulse of light forwards in the direction of the earth's orbit around the sun, they expected to find that it'd get a 67,000mph boost from the speed of the earth, but they were amazed to find it got no boost at all.
Same when they fired the pulse in the opposite direction, they thought it'd be slowed by being fired backwards from a moving platform (earth), but again the speed was unaffected.
In other words, the speed of light remains constant regardless of the speed of the platform, and scientists can't explain it (the last i heard).
I suppose. Mystery, at least to me, suggests that the answer to a question isn't known despite our seeking for an answer. Here, though, we have answers that we are seeking to understand and especially understand in terms of one another. But yes, it is a mystery.
i mean, when scientists fired a pulse of light forwards in the direction of the earth's orbit around the sun, they expected to find that it'd get a 67,000mph boost from the speed of the earth, but they were amazed to find it got no boost at all.
Both were in motion. There is no absolute uniform motion and therefore no absolute rest; just at rest relative to some other observer/reference frame.
It doesn't. It matters whether or not one can say there was a time at which the incident occurred and why. If it is entirely subjective, and the past, present, and future, are slices of spacetime that are entirely subjective, then they are illusory. What you have done is what you are doing and what you will do depending upon a particular reference frame.
Let's say that Alice blinked when the lightwave from the front of the train reached her eyes and then again when the lightwave from the rear reached her eyes. For her, the cause of the first blink is that lightning struck the front of the train first, and then another bolt struck the rear later: two causes, two effects, unfolding linearly in time, one set after another.
For Bob, the causes that Alice perceived didn't happen. Neither did their effects. She blinked because she was in motion towards the lightwaves from two lightning strikes (two causes/events) that reached her at different times because of her motion. Thus she blinked at one moment because of her motion forward towards a lightwave and again later because of her motion away from a lightwave, but both were initiated at the exact same time. The cause for the effects wasn't that one lightning bolt struck first, but Alice's motion.
This is a tricky issue. Correlations between space-like separated quantum systems clearly indicate that "something" travels not only faster-than-light, but instantaneously. However, special relativity precludes this, and is rescued by understanding that while the effects are instantaneous, no "information" can be transmitted from Alice to Bob instantaneously and for reasons that have nothing to do with SR or really even TGR.
How do holographic multiverses relate to free will? As for quantum entanglement, they are used as a method by which free will may operate (including by one of the most famous physicist to demonstrate entanglement, Gisin).
Multiverse theories/many-world cosmologies are equivalent: Bousso, R., & Susskind, L. (2012). Multiverse interpretation of quantum mechanics. Physical Review D, 85(4). The motivation for many-worlds (and, in general, all relative state interpretations of QM) is the measurement problem, which are resolved (by advocates) by such models via the interpretation of the probabilistic nature of the wavefunction as being ontological in that every possibility given any and every observation is instantiated in "some world". This doesn't preclude that observers are unable to make choices. In fact, there is an entire monograph from the edited series Series on Knots & Everything by Amoroso & Rauscher (The Holographic Anthropic Multiverse- Formalizing the Complex Geometry of Reality) in which it is argued that that modern physics suggests a theistic cosmology, not just free will.
There is an absolute speed limit being the speed of light because no amount of energy can interact faster than the speed of light. This again is with the current model.
Although, one should assume all objects are in motion and relative to each, for practical purposes concerning this problem, we assume objects outside the train are not in motion and objects inside the train are in motion. Also, if you supplied a velocity of the train then one can calculate the time and distance dilations that occurs inside the train compared to outside the train. The time dilation forms the difference between Alice's watch and Bob's watch when the two syncs up again. There are some other factors involved here but the basic foundation of special relativity and space-time is used to solve this.
General relativity considers mass. However, assuming that 1) the train, alice, and bob are at the same elevation, and 2) the mass of the train, alice, and bob are negligable to the problem, then we ideally use special relativity to solve the problem.
I have to agree with Kilgore that you are making this a bit more complicated than it needs to be.
Concerning free will, which I did mention a bit of conjecturing myself, I still don't see how the theory of relativity which your problem is based on further adds or subtracts to the notion of free will.
Here is a simple problem from the introduction of a monograph on this topic which is intended to serve as a simple illustration of the issues I spoke of. You can tell me if you find it conceptually simpler, and if so I will revise my example:
"An inertial reference frame S' moves with respect to another inertial reference frame S in the positive x direction of S'. The clocks in S' and S are synchronized at the instant t = t' = 0 when the coordinate origins O and O' of the two frames coincide. At this moment a light wave is emitted from the point O ≡ O'. After time t it is observed in S that the light wave is spherical with a radius r = ct and is described by the equation r2 = x2 + y2 + z2, which means that the center of the light sphere as determined in S is at O. Find the shape of the light wavefront in S' at time t'. Is it also a sphere whose center is at O'? If so, does this lead to a paradox? If not, does this lead to a contradiction with the principle of relativity?"
"...an observer in S' should determine that the wavefront of the propagating light signal is also a sphere whose center is at O'...But our everyday experience tells us that there must be something wrong here- the center of the same light wave cannot be at two different places (at O and O' which may be thousands of kilometers apart). The standard explanation of this apparent paradox is the following: the wavefront of the propagating light sphere constitutes a set of simultaneous events and since according to relativity simultaneity is relative, the ovservers in S and S' have ddifferent sets of simultaneous events and consequently different light spheres...This explanation is conceptually incomplete since it merely shifts the paradox from the specific case of light propagation to the relativity of simultaneity itself. What remains unexplained is why the two observers in S and S', who are in relative motion, have different sets of simultaneous events and therefore different light spheres...given the fact that the two spheres originated from a single light sphere."
Petkov, V. (2009). Relativity and the Nature of Spacetime (2nd Ed.) Springer.
I still don't see how the theory of relativity which your problem is based on further adds or subtracts to the notion of free will.
Take any choice, decision, or action you voluntary make "tomorrow" from your current point of view (in spacetime as well as mentally/conceptually). If, from another observer's perspective, you've already made any such choice, decision, or action, then there is no possible way in which you could do otherwise. You have no free will to decide or act in any way other than one that is more than determined, as there is no real time for such a decision or action to occur in and even the subjective experience of time entails observers for which your would-be "freely" willed actions are already in the past.
There is an absolute speed limit being the speed of light because no amount of energy can interact faster than the speed of light.
"The existence of a finite, invariant speed of light in vacuum suggested early on that it would be impossible to send signals faster than light, and Einsteins attribution of this limit to the structure of space-time itself suggested that in fact all physical fields would be subject to this limitation. Yet arguments to this effect are nowhere to be found in Einsteins original work...Nonetheless, it is commonly asserted that special relativity rules out the possibility of sending signals faster than light, of superluminal signaling. However, it is well-known that there are physical phenomena perfectly compatible with special relativity in which something travels faster than light."
Weinstein, S. (2006). Superluminal signaling and relativity. Synthese, 148(2), 381-399.
TGR admits the possibility of retrocausality whereby interactions between physical systems could not only occur faster than the speed of light, but also faster than instantaneous signaling via esp. CTCs. The standard model simply worsens things:
"It is well known that general relativity permits the existence of closed timelike curves (CTCs). There is now a significant body of results in the quantum information literature on quantum interactions with CTCs, offering a possible window on what we might expect in a future theory of quantum gravity."
Bub, J. & Stairs, A. (2014). Quantum interactions with closed timelike curves and superluminal signaling. Phys. Rev. A 89, 022311.
This is all without a very different kind of possible superluminal interactions demonstrated empirically since Aspect et. al.'s 1982 realization of a violation of Bell's inequality. Such experiments have repeatedly confirmed that e.g., paired photons "interact" instantaneously despite being space-like separated (last I checked the greatest space-like separation was ~16 kilometers). A brief summary of this general type of realization of nonlocal interactions is provided below:
"In an optical EPR experiment, two photons are produced in an entangled state and sent to two analyzing stations A and B. The quantum entanglement manifests itself by the interference fringes that are observed in the coincidence counts of the detectors in A and B. These interferences are predicted by QM; still, many physicists are not at ease with correlations that arise between two space-like separated events. The correlation are sometimes considered as due to a superluminal influence that the first particle to reach its detector sends to the second one. In this work, we call speed of quantum information vQI the superluminal speed at which this influence should propagate from one station to the other one."
Scarani, V., Tittel, W., Zbinden, H., & Gisin, N. (2000). The speed of quantum information and the preferred frame: analysis of experimental data. Physics Letters A, 276(1), 1-7.
See also Salart, D., Baas, A., Branciard, C., Gisin, N., & Zbinden, H. (2008). Testing the speed of spooky action at a distance. Nature, 454(7206), 861-864.
A central problem in various cases which would appear to violate faster-than-light constraints is what exactly it means to send a "signal", which is to essentially to say we have problems explaining why long apparent violations of this constraint is what this constraint really means:
"The characterization of superluminal signaling is less straightforward. There are a variety of approaches to the analysis of signaling in the literature."
Weinstein, S. (ibid).
Which current model? The current standard model hasn't united the two most successful theories in physics (relativity and QM). Moreover, recent empirical results have presented challenges not only to the standard model but once again to the notion that signals can't travel faster than light. In particular, both theoretical an empirical findings have shown that neutrinos potentially violate Lorenz invariance and superluminal constraints. See e.g.:
Stecker, F. W. & Scully, S. T. (2014). Propagation of superluminal PeV IceCube neutrinos: A high energy spectral cutoff or new constraints on Lorentz invariance violation. Phys. Rev. D 90, 043012.
Díaz, J. S., Kostelecký, V. A., & Mewes, M. (2014). Testing relativity with high-energy astrophysical neutrinos. Physical Review D, 89(4), 043005.
Izumi, K., Gu, J. A., & Ong, Y. C. (2014). Acausality and nonunique evolution in generalized teleparallel gravity. Physical Review D, 89(8), 084025.
Although, one should assume all objects are in motion and relative to each
Sort of my central point, or at least a central reason for the challenge to the possibility of free will.
Also, if you supplied a velocity of the train then one can calculate the time and distance dilations that occurs inside the train compared to outside the train.
This tells us how two observers disagree. As infinitely many other observers are possible who would disagree with both, we are again left without simultaneity and as a result no basis for asserting that "now" exists such that the past, present, and future can be distinguished. Rather, an observer's now is "objectively" not only relative to all other observers but changes in that another observer's sense of "now" can change from the past relative to another observer to the future relative to that same observer thanks to acceleration and (in the spacetime of general relativity) changes in angular momentum.
There are some other factors involved here but the basic foundation of special relativity and space-time is used to solve this.
It is true that insofar as by "mass" you mean gravitation general relativity explains the observed "attraction" between objects with mass by spacetime curvature.
then we ideally use special relativity to solve the problem.
I re-read the entire thread. Some of the questions lead to my misinterpretation of the original problem statement. Also, some of the posts were edited so I'm sure not if any of the previous posts lead to my confusion. Overall, I think your exercise has been great, although, did you need to supply A', B', A and B? I think maybe you could simplify it with either only A' and B' or A and B. I learned quite more from this thread concerning relativity.
This is all without a very different kind of possible superluminal interactions demonstrated empirically since Aspect et. al.'s 1982 realization of a violation of Bell's inequality. Such experiments have repeatedly confirmed that (...)
Scarani, V., Tittel, W., Zbinden, H., & Gisin, N. (2000).
Similarly, from other reference frames our 3D slice of spacetime that we conceive of as the present is for another reference frame the past or future. What we will do weve already done depending upon the frame of reference.
