md65536

I think all of the problems you came up with involve treating 0/0 as a real number, with a definite value and sharing the properties of real numbers. But wouldn't you be able to do the same thing with say i, deriving contradictions if i is treated as real and using rules that apply to reals? I think this is the only way it could be done. As a mathematical object it would have to be able to retain the property of being indeterminate, and it could not be consistently treated as a real. It could be useless... I can't conceive of a case otherwise. Just to add to what's already been said... By similar reasoning, if you divide 10 into 5 groups, you still end up with 10. Some of the properties of numbers are based on those of physical objects, including conservation of mass, and the operations don't "destroy the input values". If you try to divide 5 into 0 groups, you can't. Yes, you still have that original 5, but it is not the result of the division operation. To make 5/0 = 5 would redefine division and give it very different meaning in different cases. You could always define a new operation.

Do you have examples? I can think of an example only if you don't properly treat it as indeterminate, for example if we say "Since it is unknown we can replace 0/0 with x, where x is unknown", and we've mistakenly implied that if 0/0 is used several times then it should have the same value everywhere it's used. An equation like "0/0 = 0/0" would have to be treated as indeterminate forms, not as unknown reals, and understood to mean that "the indeterminate forms are the same" and not "the forms have the same unknown real value." Either that, or simply avoid defining 'equality' for indeterminate forms. Seems messy and tricky, but I can't think of any absurdity.

x/0 is inconsistent but 0/0 isn't, so it is called "indeterminate" instead of "undefined" as x/0 is. I don't know if this is debatable, or if it's a rule or if it depends on context or what. Because any value of x satisfies 0x=0, x is indeterminate in that equation. You might be able to reason through your questions by considering that asking "what is 0/0?" is like asking "How many times does 0 divide into 0 groups?", and the answer is "any number of times," or "How many groups of size 0 can 0 be divided into?" and the answer is "any number of groups." x/x = 1 doesn't override other rules, it just happens that x divides into x groups 1 times for non-zero x. It's true that 0 divides into 0 groups 1 times, but it also does so 2 times, or 0 times or 5 (I could go on). Conversely, for 1/0, there is no sensible meaning of splitting 1 into 0 groups. There is no number of groups of size 0 that add up to 1.

I meant only to describe the original experiment with some simplification of the concepts, not to actually describe a modified experiment. Edit: I think most of the following, and my previous post, are irrelevant. In the inertial lab frame, any part of the ring is at a constant speed, though not constant velocity. From this frame, you can measure the speed of light and the speed of an object on the ring, along the non-straight-line distance each travels. It doesn't matter that the object is not inertial. ------- I don't think I've quite got it so I'll try to restate it: In explaining the effect, you can consider each point around the ring at the moment light passes through. Here, the point acts the same as an object sharing that point's MCIF. Do this all around the ring and you get a bunch of different objects, each moving in a different direction. But, since you're only dealing with speed, you don't care about direction. The ring has radial symmetry, so each point around the ring is identical with respect to speeds. Ignoring direction, an object that shares an MCIF with any point around the ring is equivalent to one that shares an MCIF with some other point. You could integrate using velocities, and the effects of direction would cancel out, or you could ignore direction and just look at speed, where all the points around the ring are treated the same. That's what I think the "some other object" refers to in the explanation: an object that shares an MCIF with whatever part of the ring you want to consider at the moment, and is inertial at that point. Ignoring direction, the properties of this imagined object are the same all around the ring. Also inconsequential in the explanation is that a single such object would be physically impossible (it wouldn't be inertial and it would have to move around the ring at the speed of light.) Yet another way to put it is, the "some other object" is a measuring device that touches the ring tangentially but is inertial instead of rotating with the ring. You would need them all around the ring, ideally infinitely many of them, but they all measure the same thing, so you can calculate and explain it as if it was one object. I think I'm explaining this in such detail more to see if I get it myself. Edit: Better yet, the explanation might be "Measure the speed of light relative to a momentarily comoving inertial object at one point in the ring. The measurement everywhere else around the ring is the same." Whether it's one object whose single measurement is the used everywhere, or an abstract object that is reused everywhere and produces the same measurement, the imaginary object is simply called "some other object". ... but I think I've gone off track. It doesn't matter that the "some other object" is momentarily inertial??? With respect to a suitable inertial frame of reference, any point on the ring has a constant speed, even without constant velocity (not inertial).

What happens to your idea if you treat the curvature in terms of measurements only (eg. of length and time etc). Since there's no evidence of the existence of spacetime as a thing, I don't think there's any point in speculating that it is, at least not unless the measurements correspond with reality.

I don't know anything about the Sagnac explanation. Variables v and c are speeds, not velocities; there is no object in the rotating ring that has a constant velocity. Could you treat the ring as a set of individual objects, and compare the speed of light to the nearest object, considering only the object's "momentarily comoving inertial frame" (MCIF)? Could the explanation refer to each infinitesimal section of the ring as the "some other object"? Each section of the ring would have its own MCIF, but since they're all the same except for their direction, if you're only dealing with speed and ignore direction, you can deal with all the sections as if they're the same (object).

There are the 2 main postulates of SR: 1. The laws of physics are the same in any inertial frame (no privileged frame of reference). 2. The speed of light is c as measured in any inertial frame. The result is that time, length, and simultaneity are relative, depending on frame of reference instead of being universal. For GR there is the equivalence principle: Inertial mass is equal to gravitational mass. A particular gravitational field is equivalent to a particular accelerating frame. The consequence is that spacetime is curved. (I don't know what else there is but I don't know much especially about GR.) There are other principles too, like the "clock postulate" and some principles of geometry.

I agree with Bignose, who presented a very clear and immediate problem. It's not a matter of opinion, it's a matter of science. I think you either have to show significance or drop the claim. You said you're not interested in fooling yourself but I think you're doing just that. One way is, assuming that your understanding is great enough that a challenge to it is just an "opinion", no more important than your own, and so a refusal to even accept the validity of challenges. Another way is, avoiding facing a major problem that is brought up, brushing it aside and being content to have it "opted out" of discussion. Do you understand the problem Bignose has identified, and its importance? Do you understand how if you can't explain the significance of the values you're using, not even to yourself while being critical, you're tricking yourself?

Not realistic, but maybe something like negative mass or negative squared (imaginary) mass, or time reversal might be a hack. Consider how one might behave as a hypothetical/fictional tachyon. If you could reduce your mass to zero you should travel at the speed of light. If you reduced it further(???) you should travel faster. You can't accelerate through c with mass, but can you smoothly go through 0 mass? (Not realistic, I don't even know what this would mean.) A problem would be, what *are* you if you do this? You can no longer be an observer at c. Would describing this coherently (with a massive object also remaining coherent) be similar to eg. Star Trek transporters? Realism is difficult, of course most sci fi simply glosses over the details without even attempting to explain it, and often the more it's explained the less realistic it is! Edit: upon thinking about that, I'd say that manipulating spacetime (eg. warp drive) like if you could control inflation or "deflate spacetime" or something... http://en.wikipedia.org/wiki/Alcubierre_drive is probably the most realistic, science-based speculative idea for FTL travel?

This should be true if the Earth had no gravity of its own. I believe Kramer supposed this in post #1. If a planet were relatively large and extremely light, so that its own gravity could be neglected, then with the sun as the only gravitational mass to consider, the stuff closer to the sun should have higher velocity and the planet would naturally have a retrograde spin. As it is, the part of Earth closer to the sun is pulled more by the Earth than the sun. I think you could at least approximate the speed of a particle here on its orbit around the sun, with the sun pulling in one direction and the Earth in another treated as a lower net gravitational force. Meanwhile, a particle on the night side of Earth has sun and Earth pulling in the same direction, so a higher gravitational force and therefore a faster orbit velocity around the sun. Thus the natural way for a massive body to turn is in the same direction as it orbits. My understanding is that examples of retrograde orbits are caused by unusual circumstances (an impact knocking a planet off its axis, etc).

It's a basic consequence of special relativity, called relativity of simultaneity. The clocks in B's frame, synchronized in B's frame, are not synchronized in A's frame. The flashing bulbs can be considered to be ticking clocks, synchronized in the cart's frame. Note that in the ground's frame they don't flash at the same time. According to A, all of B's clocks will tick at the same rate (which will be slower than A's "normal rate" clocks), but they'll be set to different times at any given moment (where the moment is a set of events that are simultaneous according to A).

Simultaneity is not shared across different inertial frames. Say you have an event at each clock in B's frame that happens at time 0 according to that clock. In B's frame, with all of its clocks synchronized, all of those events are simultaneous. In another inertial frame, those events would not be simultaneous. The clocks would mark a particular time, at different times according to a clock in A's frame. Anyone (A, B, C, etc) can agree that B's clocks are synchronized in B's frame, but they're not synchronized in A's frame. No preferred frame or point, of course.

The clocks can be synchronized in their own rest frame, but another frame's observer would not see the clocks as synchronized. At any instant in A's frame, each of the clocks in B's frame generally has a different time. There's no paradox with what you wrote, but it doesn't apply to all the clocks.

Thanks. I think I will have to rewrite before I can get my point across. You're using a different definition of apparent simultaneity than the one I cited in the paper.

What do you make of this? http://en.wikipedia.org/wiki/Buffon's_needle There are known relationships between randomly oriented lines, and pi. They have geometrical explanations. Is this similar enough to your idea that you would say that the results of Buffon's experiment is due to the physical nature of matter, and not just mathematical concepts that also work abstractly? Can you rule out a geometrical explanation of your results? Eg. if reality were *not* made up of your model's lines, would you expect to get different results for electron mass or whatever? It sounds to me like your evidence is only your claim that your model works and corresponds with reality. Is there a simpler explanation of why you get your results, other than that they directly model physical reality? (I still think the answer to that last question is "yes", and that by putting constants like 1822.8885 in your code and then doing some random things, you're arriving at some meaningful-looking results but tricking yourself about how they came about.) If yes, then I don't see how anyone else would accept it as actually representative of reality. If you use your model to predict a new, experimentally verifiable result, then people will be more interested.

Yes, that helps, thanks. In his paper, Einstein never explicitly assumes anything about simultaneity, he simply makes a definition and uses it. Your quote proves that it was not just by chance of wording that Einstein did it this "bulletproof" way, but that he knew exactly what he was doing and did it intentionally. It is bulletproof because even if a "better" definition of simultaneity is ever found, it doesn't affect Einstein's definition. Einstein defined simultaneity, but there are other ways that it can be defined (as several people have attempted throughout the past century), none of which have been convincingly demonstrated or broadly accepted to be superior to Einstein's definition. Some kind of definition is still needed. Only the assumption part is superfluous. As an analogy, to measure time you need a frame of reference. You can choose one by defining your observer (as a stipulation, chosen by your free will). You don't have to "assume that a particular observer exists, and the experiment is observed by it". (This I think trips up many philosophers, assuming eg. that the observer is human, then getting too caught up in the details of biological processes of brain+eye etc). It's not settled whether simultaneity can meaningfully be chosen just like frame of reference can, but I think it can.

I too was waiting for a better answer. I don't think the universe was ever gravitationally bound. I think there is an error assuming that it must have been, due to its arbitrarily small size early on. If the expansion rate happens faster than c, the expanding stuffs can't be gravitationally bound to each other. Without inflation, it would be a black hole and remain collapsed. There would be an event horizon which nothing inside could pass. However if you have inflation faster than c, as is modelled, then there is an event horizon where stuff is pulled away from other stuff faster than they could possibly affect each other. As long as the things are separated by a horizon, they essentially can't know the other things exist, and so aren't gravitationally bound. http://en.wikipedia.org/wiki/Particle_horizon I guess in the current theory it sounds like the universe actually would have been gravitationally bound *prior* to inflation, but inflation itself would have undone that. http://en.wikipedia.org/wiki/Horizon_problem#Inflation

I have no helpful advice, but a pessimistic view. I don't think these forums are an appropriate place to find a graduate advisor (neither would you find someone able to fill that role, nor willing, if you haven't heard from anyone yet). I think it would be more appropriate to inquire at specific universities etc. Also, I don't know of anyone eager to make exceptions or treat anyone as a special case. If your degree is sufficient for entry, you would like... go through the typical application process. I don't think anyone would want you to skip a masters unless you already proved yourself somehow. If you want to get to know a prof in order for them to take you under their wing, I think you'd have to study at the school and get to know each other and work with each other (if you ask for special projects or have an idea for one that is up the prof's alley then sometimes that's possible, but still best to get to know them so they know you enough to go for it). http://physics.open.ac.uk/~sserjeant/faq.txt This was posted in another thread and may be specific to astronomy, but the "I'd like to do a Masters or a PhD" part may be generally applicable. In other words: The slow, boring, typical school route is the only one I know of. I don't think there are easy shortcuts. I don't know of anyone who has proved themselves so exceptionally on these forums that someone would go out of their way for them to such a great extent. Perhaps you might get more advice on how to get into the typical school route.

On second thought, there's no point in assuming that Einstein's definition of simultaneity is right, or in challenging that assumption. There are not 3 main assumptions, just the 2 postulates. The definition is still needed, but it works as long as the postulates hold. The question then shifts from whether or not Einstein's simultaneity definition is "right", but whether it is the only one or the best one. Since Einstein never assumes that the definition is right in a physically meaningful way, it doesn't matter if it is or not. All that matters is whether the resulting model and conclusions are right (ie. "correspond with measurements"), and they are. Another example is a definition of speed. There are many different definitions (velocity, proper speed, etc); one isn't "right" while another wrong. The speed of light is c (whether by definition or measurement), and if one argues that there's a better measure of speed that doesn't change the fact. I think I'll have to remove anything assuming or implying that a definition is right or wrong. So far I have zero indication that anyone thinks there's any value in this.

Several things... 1) v = d/t. If you only "slow time" you get smaller durations, which correspond with higher velocities. Don't worry too much about this though cause it doesn't matter in the end (since d can also be smaller), just that the reasoning isn't right. 2) Time of a moving object slows relative to the observer's "normal" clock. An object making a journey from the sun to Earth at high speed doesn't experience slowed time by their own clocks --- but to them, a relatively moving clock such as one on Earth ticks slower. 3) Moving distances are length-contracted. As you approach the speed of light, the distance between the Earth and Sun approaches zero length. From Earth, a fast traveler's clock may tick very slowly. Say it takes 8 minutes on an Earth clock for a ship to travel from Sun to Earth, but a ship clock ticks only about one second during that time. According to an observer on the ship, only one second ticks during its trip from Sun to Earth, but that distance has contracted to about one light-second (think very roughly distance to the moon). Either observer measures the same speed (close to c). The way that light is not a normal object like something with mass, is that it has no frame of reference. If you try to figure out what light would measure, using limits as v approaches c, then you find that relative time slows to a stop, and its distances contract to 0. In other words, everything in the universe in the direction of travel contracts to a plane, and there is no distance to travel so it takes no time to travel, and there is no way to define a passage of time. This is not a valid frame of reference from which sensible observations can be described. From an observer's perspective, no time passes for light. No clock can travel at the speed of light. As a clock approaches c, it slows to approaching stopped. If graphed up to c, there would be no discontinuity in the graph.

Τhen the giant runs you through with his sword and says, "It seems you told the truth", pulls the sword out, and responsibly strangles you with his bare hands. If the giant is known to be honest, why not just say nothing (neither lying nor telling the truth)? The "correct" answer is still a lie if you live. It seems that the implied goal is just to make the giant's statement a lie, and then he'll let you pass. I guess as it was mentioned before, it's totally up to the puzzle maker to decide how a giant or guard will act, and in this case the "correct" answer works if the giant is mainly concerned with reasoning alone, which seems to be the point of the puzzle. But reality doesn't work on reasoning, and it is dangerous to think that something physical like your death can be prevented just by making a semantic statement about it logically impossible.

Yes, must prove S. What do you know about E? What can you say about (FvE), or D, etc? Since this is "homework help" I don't think I can just give a solution, but try this simpler example. 1. P -> Q 2. P :. Q What are we proving? Given premises P -> Q, P, prove the conclusion Q. How, informally? We're given that P is true. Since P implies Q, Q is also true. How, formally? Modus ponens is the rule to use. Do you know what the proof should look like?

Where to start... Do you know what you're trying to prove? ("Check proof now" gives a huge hint) Can you explain in plain English informally how you'd prove it? Does the "example proof" at your link make sense? Do you know the name of the rule that ydoaPs is talking about?

I understand that. There is no confusion about that. I also understand the basis of this distinction between the event and the perception of the event. It is the assumption of standard simultaneity. Basically, Einstein started with a few assumptions: The two postulates of special relativity (1. physical laws are the same in all inertial frames, and 2. the speed of light as measured in any inertial frame is c), and the definition of simultaneity (which in literature is called "standard simultaneity"). The 2nd postulate and the assumption of standard simultaneity are very closely related, so much so that many authors (eg. in "philosophy of science" papers) treat them as one. However, to do that, you need a consistent definition of speed, and therefore of time and distance, and that isn't provided by the postulates. Many authors seem to treat rest distance as the definition of distance, and this works but it is an additional assumption carried over from classical science, and many don't acknowledge that. I believe that Einstein knew better, having concluded that time and distance are variable and intertwined, and realized that the definition of simultaneity needs to be specified independently of the 2nd postulate. Einstein starts with a few assumptions and arrives at a consistent model of motion in flat spacetime. The assumptions aren't proven, but they're reasonable and they're consistent with reality, and they're probably true so I doubt that anyone could ever disprove any one of them. However I'm arguing that the last one, the assumption of standard simultaneity, is superfluous. SR can be arrived at also by assuming a different simultaneity and using a different measure of distance. So yes, in SR there is a difference in time between what is seen and what is happening, but that is not a consequence of SR itself. It is a consequence of the assumptions of SR, the definition of "time" used. It works and it is reasonable so it is accepted, yet it is also known that the convention that determines the simultaneity of distant events (which is needed in order to say that a 10 LY-distant event observed now and another event on Earth 10 years ago were *actually simultaneous* to the Earth-based observer) remains an assumption. I'm not confusing this. I know that SR models a difference between the time of the event and its observation. But I'm trying to argue that this isn't a *necessary* component of SR. Not only does it work with alternative simultaneity, but the details turn out to be quite reasonable. I don't know of anybody in science who has seriously considered alternative simultaneities, I think because the standard works perfectly well and is reasonable. There is no immediate "need" for any improvement. Some have looked critically at standard simultaneity: "Most attempts to negate the conventionality of this synchronisation* are considered refuted, with the notable exception of Malament's argument, that it can be derived from demanding a symmetrical relation of causal connectibility. Whether this settles the issue is disputed." [http://en.wikipedia.org/wiki/Einstein_synchronisation] Several "philosophers of science" have looked at alternative simultaneity and come to various conclusions, but I think they have not done an adequate job with the science of it (being lazy with postulates or definitions, etc). * Note: The linked argument is about Einstein synchronization, and I've been talking about Einstein's definition of simultaneity, and I've been accused of confusing the two (perhaps), but the argument is still valid. If Einstein's definition of simultaneity is conventional, then Einstein synchronization must be conventional. Whether or not the reverse holds doesn't matter in this context.

Earlier in the thread it was suggested that I submit this to a peer reviewed journal. I want to try to do that but I figure the quality of a paper has to be the highest that you can possibly make it before submitting it. I submitted it on these forums because it was at a point where I thought it was good enough for others to read and to ask for opinions. Is it a waste of others' time to submit a paper that you think could still be improved? Do you get "one chance", and if a paper is too low quality will the journal blacklist you forever, or will they tell you to try again after specific improvements? I want to remove any amateur statements, and any claims (opinions, interpretations, etc) that I can't back up purely with evidence and logic. Does anyone have any advice, like which specific ideas to focus on, explain better, or drop? Thanks.