md65536

Romer's measurement assumed universal time. It also works with standard simultaneity. Romer's measurement is based on changing delay of light as an observed object (Jupiter + Io) changes distance to the observer. This delay is not the same with standard simultaneity as it would be with other simultaneities. The one-way delay of light is not itself directly measured but is a consequence of standard simultaneity. Yes it's a one-way measure of the speed of light, but it is generally accepted that you can't measure a one-way speed of light without a notion of simultaneity. All of the arguments that standard simultaneity is not conventional, are based on things like "symmetry", not on experimental evidence.

This is Reichenbach's epsilon notation, I don't think it's been mentioned in the thread. A lot of "conventionality of simultaneity" work is done in the context of philosophy and I don't think it's up to par with scientific standards. Often, a writer will use an alternative definition of simultaneity, and implicitly redefine a bunch of quantities without making note of the redefinitions. So for example, if you have epsilon other than 1/2, the measure of "speed" that is different depending on direction is not exactly the same measurement of "speed" using Einstein's definition of simultaneity. Einstein did this first, and set the standard definitions for things like simultaneity and resulting definition of velocity, momentum, etc. Yet others will provide a different simultaneity definition, with a new measure of rate of motion, but they'll still call it "speed" even though it's not the same as the accepted definition in science. The quantity c is defined using the standard definition of speed; it makes no sense to me that it would change to fit some other new quantities that one might define. It is only some other measure, not the speed of light, that is different in different directions. The literature probably wouldn't agree with me on that, but I think they've generally been not nearly as careful as Einstein with their definitions and with hidden assumptions.

It's not magical. Einstein explains what is needed for measuring time in different places, provides it, and then can use it. That equation is beside the point anyway. It uses two times measured at A, and represents a two-way speed of light. It alone cannot be used to define simultaneity, or to measure the one-way speed of light. Simultaneity is defined just before that, without making reference to the speed of light. I incorrectly paraphrased Einstein as saying that given his definition of simultaneity, the one-way speed of light is measured as c. This is true, but it seems he didn't make that claim and didn't have to. Do you understand that Einstein defined simultaneity on its own, he did not derive it from an invariant speed of light? Do you accept that SR still maintains that definition of simultaneity, ie. that it is not certainly superfluous? This is important because a conversation about conventionality of simultaneity will not go very far if you refute that SR does make use of a convention.

No, that doesn't follow. In SR the respective signals from A and B travelled at the same speed, but were not emitted simultaneously in the train's frame (this is relativity of simultaneity, eg. the signals may have been emitted simultaneously in the track's frame). No, that's not right. You have the clocks synchronized in one frame. They're not synchronized in the other frame. Where they're not synchronized, they're simply not synchronized. That's not "synchronized using a different convention." I don't see an alternative convention that fits the definition of "synchronization", but if it's there I'd call that "different synchronization conventions that are consistent with the predictions of SR" or something like that. I should have said "I don't think it makes sense to look at it in way where one changes the definitions, but expects that the statements making use of them must still hold or else it's 'inconsistent'." But in Einstein's paper, he defines simultaneity and synchronization. If you provide alternative conventions, they don't use those definitions, and some statements that *do* use those definitions (such as the second postulate, I argue) do not apply to the alternative definitions, and that doesn't make them inconsistent. The statements are made with respect to the given definitions. But what is the meaning of t? Have you read the section "Definition of Simultaneity", in the 1905 paper? http://www.fourmilab.ch/etexts/einstein/specrel/www/ Einstein does NOT just assume d=vt has meaning independent of time (including simultaneity), instead he says that "speed" only makes sense with respect to the meaning of "time". That's surely why he avoids using speed in defining simultaneity (otherwise why mention it at all?). Paraphrasing, I think Einstein says, "Given this definition of simultaneity, we can define a one-way measure of the speed of light, which in agreement with experience we accept is always equal to c." How would you go about it the other way, given Einstein's quote above? Is this fair: "Without a definition of simultaneity, there is no means of measuring the one-way speed of light, but let us assume that it is equal to c, which then gives us a definition of simultaneity, which gives meaning to the one-way measure of speed that we've used." How do you avoid problems if you define time according to an assumption about speed, if the meaning of "speed of light" depends on how you define time? By the way, I'm sure this is true. You seem to have a better understanding of simultaneity and conventionality arguments than anyone I remember posting here, definitely better than mine and I've focussed on simultaneity more than anything else in science. But I haven't bothered with Malament etc much, because when I look into stuff like that I find too many people go off track, focussing on things like "symmetries" which add additional assumptions, and too often they lose sight of the core theory, so I've focussed on Einstein's stuff. Where I think you've made statements that contradict SR, I can't get past that to try to understand what you're saying.

I mean he makes no mention at all of any concept of speed in his definition of a common time at the two locations. Propagation time of light isn't the same as speed. No it doesn't follow from that protocol. Simultaneity is by definition, and invariance of speed of light by assumption. Indeed, after defining synchronization, Einstein specifically states (at least according to this translation), (emphasis mine) So I may be nitpicking, but when I went from my initial misunderstanding that Einstein assumes his definition of simultaneity describes reality (he doesn't, he simply makes use of it as a tool without commenting on its reality, which is what allows SR to be compatible with conventionality of simultaneity in the first place), to realizing what he has actually done, and how the way he did it is "bulletproof" (you can't prove a definition is "wrong", even if you could find it somehow doesn't conform to reality)... it gave me a sense that Einstein knew exactly what he was doing and was extremely careful, while so many others since have been too sloppy with their assumptions. Say on the other hand that Einstein didn't do it this way, but instead just assumed that the speed of light is equal to c, and from that concluded that events are simultaneous in accordance with Einstein-simultaneity. Then the definition of simultaneity is assumed to be true, and essentially that simultaneity is not conventional. This would be a mistake, I believe. Einstein truly seemed to grasp that we had not (still haven't) been able to measure whether two distant events are truly simultaneous or not, and it is only within the context of some assumptions that we can say they are. Equating equal timing and equal speed requires another assumption, that too many people make. Einstein's definition is free from problems or ambiguities in all of these intricate details that people could argue over.

I don't think that's true. I think you could make the case, but that might involve circular reasoning. I think at best you could start at either point and get to the other. In Einstein's 1905 paper, he doesn't use the speed of light in his definition of synchronization. http://www.fourmilab.ch/etexts/einstein/specrel/www/ It is only time, and not speed of light that is used here. Next, the travel times of light signals are used to define synchronization. THEN the quantity equal to the speed of light is assumed to be a universal constant. You can do it the other way around, but not without making some similar assumptions. A one-way speed between two points but measured by a single observer needs some way to relate the time at the different locations. If you define speed first such that the speed of light is invariant, and use that to synchronize clocks, I think that you have already implicitly defined simultaneity in your definition of speed.

This sounds like a misunderstanding of some basics that makes it difficult to make sense of the rest of what you're saying. In the famous experiment, all of the individual observers are inertial, and they all measure a one-way speed (using Einstein synchronization or Einstein's definition of simultaneity) of light that is equal to c. No different one way speeds of light are needed. The different observers measure time differently, but they also measure distance differently. There is no inconsistency in SR that you're speaking of. SR does not state whether or not Einstein's definition of simultaneity, and the resulting means of synchronizing clocks and measuring one-way speeds with a single observer, are conventional. SR is simply presented in a way that makes use of Einstein's definitions, so I think the second postulate must be read within the context of those definitions. If simultaneity is not conventional, and if Einstein's definitions are the only ones that truly "work" (eg. if we found evidence that ruled out other conventions), SR remains consistent because there is nothing in it that requires conventionality (I believe you're mistaken about that). If simultaneity truly is conventional, a formulation of SR that makes use of only one convention (as Einstein's) remains consistent. You have some definitions (eg. simultaneity). You have some quantities and measurements (eg. v) that use those definitions. You have some statements based on those measurements (eg. second postulate). I don't think it makes sense to look at it in way where you change the definitions, but expect that the statements making use of them must still hold or else it's "inconsistent".

Some types of compressed files can be compressed further, losslessly... http://www.fastcompany.com/3050180/tech-forecast/these-engineers-just-built-their-own-pied-piper-compression-algorithm yet it is known that there is no possible algorithm that can losslessly compress all possible input data. This puzzle's about that. ---- There is a type of data stream that is a fixed length N bits of binary data. The data is statistically random; every possible variation of 0s and 1s is as likely as any other. There is an optimal lossless compression algorithm that reduces the data size of as many of the possible data variations as is mathematically possible, and produces a variable-length output of M bits. The uncompress algorithm knows the value of N and the size of the compressed data stream. 1. How many of the possible data streams cannot be compressed, ie. where M >= N? 2. For large N, what's the average size savings achieved by the algorithm? 3. Describe or write pseudocode for such an algorithm (compress and uncompress). 4. The CEO of Hooli is offering $1M for your algorithm. Do you take it, or try to develop it with your own startup company?

Is rotation in higher dimensions also ruled out? This is purely speculation... Imagine a one-dimensional universe embedded on the equator of a rotating sphere. Different centrifugal force and preferred direction would be seen on the surface of the sphere, depending on phi coordinate or latitude. The center of rotation is on the r coordinate. In "flatland" style, the 1D beings seeing only the equator would see no preferred direction or center, and inertia/centrifugal force would appear as a homogeneous, isotropic expansion force. Is it possible that a rotation in 5D (or 4D?) could hide a center and preferred direction? Have you watched the Krauss "Universe from Nothing" video linked earlier? It explains how it is possible that a universe, consistent with measurements of our own, can exist with 0 net energy. I think it shows that questions like "what came before that, and what was its cause (ie. anything making or "wanting" the big bang to happen)?" don't need to have answers... or that the answers might just be "nothing."

Then the conclusion would be that there are places with nothing, and that gravity has no measurable effect on nothingness? I suspect everyone could agree on that (if little more than that). Measurements are consistent with a flat universe, but only "on the largest size scales." There is a lot in between "local" and "largest scale". It is not flat on scales of stars and galaxies etc. In areas where expansion dominates, measurements are consistent with both expansion and gravity being present. In areas where gravity dominates, measurements are consistent with both expansion and gravity being present. It's not like only one may occur in a single place. The facts as we observe them are consistent with accepted theoretical physics, if you're claiming otherwise (without the evidence) then you're talking about speculative theory.

(after some websearching) Yes that's what I was describing. The Flamm paraboloid is an embedding diagram, and the z-axis provides an extrinsic representation of the intrinsic curvature. I didn't realize until now that the "funnel" diagrams can actually be very different things. An apparently more-common "funnel" diagram is a plot of gravitational potential (a gravity well diagram), which is approximated by the rubber sheet model. The z-axis of this does not represent curvature. It sounds like it is fairly common to mix up the different diagrams: https://en.wikipedia.org/wiki/Gravity_well#Gravity_wells_and_general_relativity So different "funnel" shapes can arise from plotting different things on the z-axis, none of which correspond to the spatial shape of a black hole in 4d spacetime.

The "funnel" shape does not represent 3 spatial dimensions, it's only a 3d representation of 4d spacetime. The funnel is 2 spatial dimensions, and... ??? Does anyone know what the z-axis (down) represents in these diagrams? It doesn't represent time, right? In the rubber sheet analogy it represents energy or something??? Or is it just a representation of the intrinsic curvature of spacetime, drawn extrinsically with an extra spatial dimension that isn't real? From https://www.physicsforums.com/threads/what-is-the-path-of-light-through-strong-gravity.749087/page-2, by Drakkith: If you take a black hole, and consider 2 spatial dimensions of it, you get a plane. In spacetime this plane has extreme intrinsic curvature. If you embed this intrinsically curved plane in 3 dimensions, it looks like a funnel. So I think the funnel shape is not representative of any geometrical shape, but merely the intrinsic curvature of spacetime illustrated along an extra dimension in the diagram (ie. the intrinsically curved 2d plane embedded in a in a higher (3) dimensional space).

Does Newtonian and GR escape velocity agree at all radii? All the laws? I think the answer is 'no' partly because Newtonian and GR are not describing the same thing here. With Newtonian laws, an object with a velocity of v=c pointed away from the mass at that radius would leave it at a velocity of c, and escape to infinity while its velocity approaches 0. With GR, that escape velocity would only allow it to hover at the event horizon, and the object would never truly escape, never climb anywhere out of the gravity well to where escape is easier. But I don't fully know what that means. It is only at the event horizon that escape is impossible, but does that mean that only at that radius does escape velocity no longer have the same meaning as outside the radius? If we instead considered a point just outside the radius, is the Newtonian and GR escape velocity the same? And in GR does escape velocity allow it to coast out to infinity?

Yes, that's basically in agreement with GR. The bending of light is not a gravitational attraction pulling light off a straight path. The null geodesic "is" a straight path through curved spacetime. Light only bends along with the curvature of spacetime, and no more. For example with a black hole it is not gravity pulling on the light particles that prevent their escape. It is the curvature of spacetime that makes all paths (all "straight lines") within the event horizon curve toward the singularity. (That, and the coordinate speed of light is 0 at the event horizon according to a distant observer.)

"The film Interstellar should be shown in school science lessons, a scientific journal has urged." I finally watched the film based on this comment, and I was really disappointed. I looked up Kip Thorne's book, The Science Of Interstellar, to look for answers. He writes: In the end my main problem with the film is that it doesn't separate what is predicted by science (eg. time dilation) and what is a wild speculation (wormholes, singularities and the insides of black holes, the "quantum data", "Gravity... can cross the dimensions, including time." Ugh, vomit). If the film is shown in science lessons I think it would require a teacher who can explain what's real and what's far-fetched. I don't think it's worth it to introduce relativity this way, if students think all of the speculative stuff is just as valid. But maybe it's better to "know" too much than too little. As for the time dilation all of that seems to follow established laws. I think there are errors, eg:

There was a similar thread here a few years ago. If you completely separate the two tests, so that you remove the hammer from the system when you're measuring the feather's drop, then the feather/moon collision will take negligibly more time than the hammer/moon collision would. However if you leave the hammer or feather on the moon when you drop the other, then the total mass of the system is the same in each drop and the closing time would be the same. This MIGHT (I can't seem to decide) assume that you can still treat the moon+hammer and moon+feather as a uniform balls, and of equal size. The difference in mass is so slight that you couldn't assume that, and details such as the location of the hammer would become significant.

It seems you've accepted the answer, but if you want to convince yourself of it, try considering it in terms of two similar systems, such as two ships moving inertially relative to each other. For each ship, the other's clock ticks slower. If you consider this from the rest frame of either ship, an astronaut on the ship is at rest. If an astronaut was aging faster or slower than normal, while at rest in an inertial frame, there would have to be something special about that inertial frame (which experimental evidence doesn't support). If you accept that all inertial frames are equivalent (the first postulate of special relativity) then no process could tell the difference between one frame vs another, and all processes would occur at the same rate relative to a rest clock in any given inertial frame.

I don't think so, I've just been trying to figure out the implications of only parts of the math, and not even checking to see if the guesses work out, so I've been making mistakes until someone else figures out more math. Anyway I decided to at least test some values using the maths posted. Trying out a few different values, it seems that only choosing the radius of ball A relative to ball B is enough to make the CD system win, regardless of the other values??? It seems that if rA is greater than (or equal to???) half of rB, then the CD system will win no matter what the gap is. If it's less than half, then there will be a crossover (ie. there are small gaps for which the AB system wins, and larger gaps for which CD wins). I don't trust my abilities and don't (yet) want to try solving it algebraically... does anyone find the same results?

It is because the difference in radius (rdiff = rA - rC) is more significant relative to a small gap than to a large one. Let's say you set your variables such that AB and CD touch at the same time. CD has greater mass which is balanced by AB having a shorter distance between the centers of the masses. If you decrease the gap, rdiff becomes proportionally larger relative to the gap, and the distance between the masses becomes more important, and AB touches first. If you increase the gap, rdiff becomes less significant relative to the gap, and the differences between the masses becomes more important and CD touches first.

But a cross-over isn't guaranteed, is it? Let Mdiff = MB - MA The radius of A (and thus also the final distance x) decreases proportional to the cube root of Mdiff, while the total mass of the system decreases linearly wrt. Mdiff. Wouldn't that require that whatever other variables you use (still assuming fixed density of all masses), you can choose the difference in the masses to be small enough that the CD system beats the AB system for any gap size? It seems the converse is not true... if you set the variables so that the AB system wins, it looks like you can make CD win just by increasing the start distance r enough (if AB can win at all, then a crossover can be found by just increasing the gap)??? Or that is... if you choose variables so that AB wins, then simply increase the gap and CD will eventually win. If you choose variables so that CD wins with negligible gap, you need to decrease the mass of A to make AB win, as adjusting the gap won't change the outcome. Perhaps you might be able to choose a low enough density so that CD wins regardless of both gap and mass of A???

A translation of Newton's first law as originally stated is "Law I: Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed." (emphasis mine) So whether "compelled" doesn't imply change doesn't matter, I'm not looking at the meaning of single words in isolation, the law includes the meaning 'change' verbatim, why am I even arguing this it only detracts from my point, perhaps you're right. You would define "exists" so that theory would conform to what you expect to happen, ignoring what is observed to happen? I think this quote applies to all physical laws: Consider it all in this light: Physical laws are not rules that define a set of behaviors that nature is forced to follow. Physical laws are rules that nature is observed to always follow. If you look at a set of laws in isolation, as we're doing here with Newton's first law, if you take the laws and say anything along the lines of "these are the only rules that nature is allowed to use and everything nature does must use these rules as an instruction manual of what to do", then you're doing it wrong! If you take the laws and say "does this observed behavior follow the rules?" then you're doing it right. If observations don't follow the rules, you make new rules. If thought experiments don't follow the rules, you find the flaw, devise physical experiments to test the prediction, etc. If thought experiments follow the rules, as in Norton's dome, and you don't like it... too bad! Go learn more, go devise experiments to prove wrong all the other "human beings who have struggled as hard as they can to understand it". Edit: of course this all needs a huge grain of salt and it's unfair of me to falsely suggest that using a law to make predictions is in any way wrong, only that a prediction shouldn't be treated as evidence against another valid prediction, or something like that. What I don't understand in this thread, with so many people here who understand science more deeply and broadly than I do, is that we all learn to accept this, that the universe does not have to conform to our expectations of how it should behave. We accept it and we learn to make sense of what the science says. But then as soon as something clashes with what we still believe must be, it's like we're back at the beginning! It's like we've only adjusted our common sense to accept some of the science we understand, and still resist thinking scientifically about some things. Apologies if I'm wrong, to those actually being scientific here whom I'm failing to understand.

I disagree with your interpretation of "compelled" (to change by something), but it suits me better for me to be wrong about it. If you're correct, then I retract the argument that the original version implies causality, and I cannot demonstrate any difference in the meaning of the versions (other than re. inertial frames which isn't an issue here), and your interpretation allows even Newton's originally stated 1st law to remain unviolated by Norton's dome. Does "what makes it happen" need to be answered? What makes the mass stay at rest if there is no force? This doesn't have to be answered, it suffices to have a law that describes what is observed (or "what happens", if you wish), which is that it indeed stays at rest if there is no force. I think we all agree, if the mass is not at rest it must be acted on by a force. If the mass is not at r=0, there is a force acting on the mass. So if the mass is not at r=0, there is no need for a reason that the mass should be at rest. Why must there be an additional reason that the mass is moving, if there is already no longer a reason why the mass must remain at rest? AND if you insist that there is such a necessary additional reason, is it demanded by Newton's 1st law? The answer to the "why" question is, I think, "Because there must be a cause for everything". Even if that were true (I doubt it), that's not a part of Newton's first law.

I'm not going to get into an argument over whether a physics law from the early 1700s is better than the version accepted today. It doesn't matter, the link in #1 is using a modern version of the law. "Unless" does not indicate what is the effect (and what is the cause). Consider a cat in a box with a vial of poison that is randomly either broken or not broken at the time it is observed. Consider what is observed: The cat is alive, unless the vial of poison is broken. The vial of poison is broken, unless the cat is alive. "Unless" doesn't indicate causality. The cat being alive does not cause the vial to not break. "The cat is alive, unless compelled by a broken vial of poison to change its state to dead" does indicate causality. Edit: Anticipating misunderstanding of my point, this variation should make it clearer: Consider two cats A and B in a box with a vial of poison that will either randomly be broken or not. Assume the poison is 100% fatal, that if the vial is broken the cats are dead. Assume there is no other cause of death during this experiment. What is observed? Cat A is alive, unless cat B is dead. Cat B is alive, unless cat A is dead. "Unless" doesn't indicate causality. Cat A being dead does not cause B to no longer be alive, etc. "Cat A is alive, unless compelled to change its state from alive to dead by cat B being dead" is NOT something that is observed in this experiment, and is NOT a law at all, while "Cat A is alive, unless cat B is dead," would be a valid law in this experiment if the assumptions were valid.

It is with the full phrasing, "compelled to change by," that it directly states that the force causes the change in state, ie. from "at rest" to not at rest. "In classical physics, a cause should always precede its effect." https://en.wikipedia.org/wiki/Causality_(physics) The version with "compelled" (and accompanying details) requires a causal order of events, requiring that the force that compels the body to change (the cause) precedes the change of state (effect). "Acted upon" describes influence or effect, but it does not state that "the body is no longer at rest" is the effect. That is a common-sense assumption. This is difficult to see the difference because in everyday life, the 1st law follows common sense and Newton's first law is causal. But that's not what it says, and for good reason. Perhaps the only counterexamples where the 1st law does not follow common-sense causality are in quantum mechanics, I don't know. "Acted upon" does not imply a causal relationship between the acting force and the change in state. There is no order of events required. I think this is only clear if you intentionally set aside what common sense says and look only at what the science says.

Something interesting from the second link, is this: This is different from the modern statement of the law. The wording with "compelled" implies causality, and that the force causes the mass to not remain at rest, whereas the modern statement of the law does not. If you could argue that "Newton's first law" may refer to this originally stated law, then I'd agree that Norton's Dome violates this law. However I think "Newton's first law" refers to what remains a law (ie. the modern version). My whole argument would rest on the differences between the original law and the modern, and on accepting that the changes are necessary ones, that the modern statement fixes flaws in the original, and that the original statement is no longer a valid law. In my opinion, all the arguments that hinge on the "cause" of the mass being knocked off balance, would rely on denying the importance of the changes from the original law to the modern. The part that is being violated is no longer a part of the first law. The modern version from https://en.wikipedia.org/wiki/Newton's_laws_of_motion: