md65536

Any transfer of information across distance requires time (with a lower limited determined by c). The acceptance or use of any received information could probably be described by definition as a "change". For example, without time, light cannot propagate... nothing in the universe can be observed or interacted with. "What is the existence of something besides whatever information can be received from it (ie. what effect it has on others)?" is a question I don't think I could answer, which for me means that I wouldn't know what a "paused video game" universe would be (if anything at all!). Also, the lack of a tenable concept of a "universal instant" further complicates the idea of a universal paused state. What observer's instant would it be that everything is paused in? Would the state necessarily be different for different observer locations? This is not classical physics however. I think if you remove "change", a lot of other things become undefined. Also, I think it's possible to remove time without removing "change" simply by allowing causal relations without distance (like if you removed time and distance at the same time). I don't think my answer can be considered "accepted science", sorry.

However, information has a speed limit: c, which couples time and distance. If you want to have an arbitrarily long causally related sequence of events occur in an arbitrarily short period of time, it will have to occur in a correspondingly small enough space. There's only "an infinite amount of time" (or more precisely "an infinite rate of events" -- the reciprocal of time) in an infinitesimal space. c makes a rate of time finite for any non-zero distance.

I believe that the ultimate understanding of something in physics comes from an understanding of the math. For example, you might say "The power density of a sound wave decreases as it expands" and that might give you a grade-school understanding of it, with very limited usefulness. Or you could say "The power density of a sound wave is proportional to 1/r^2" and that gives you a precise and useful mathematical understanding of it, but you might not know why it is so. Or you could say "The power of a sound wave propagating as a spherical shell remains the same as the sphere expands, and is spread evenly across the surface area of the sphere," but you might not know that surface area is proportional to r^2. The last two statements say the same thing, and they are both mathematical (area is a geometrical concept which is mathematical). Using just numbers and equations might work well but leave you unenlightened; using just words may give you knowledge without being able to apply it. Having the math and understanding why it works is in my opinion the essence of true understanding. That said, it must be noted that physics can progress just fine without knowing why the equations correspond to reality. Observations still give you useful data, and those data can be used to evaluate the equations and suggest new ones. I do believe that knowing "why" (and having logical explanations to go along with the math) does provide extra insights that suggest new ideas which lead to new experiments, observations, and theories. Logical explanations are a bonus; the math is required.

Either the observation fits the model or it doesn't. I thought different interpretations of the same thing share the same predicted observations. Where the observations differ, the models differ (not just the interpretations). Can you give an example of what you mean?

It was parody, not a logical argument. If my post is treated seriously, the implication that my argument is equivalent to owl's is certainly a straw man. To brush it off as just a straw man is a good way to avoid thinking critically about one's own arguments. Perhaps it could be considered an extreme example of similar reasoning that owl is using, but that in itself does not prove that owl's flawed reasoning is flawed. It adds no weight to the argument but provides an opportunity for thinking about it in a different way.

That looks like an excellent resource, thanks. After a quick glance at the section it looks like his explanation works with simpler requirements (his works with slow-moving objects but mine requires high-speed oscillation of all masses). I'll have to spend some time trying to figure out the lecture notes.

In various topics on this forum, I get the idea that it is still a mystery how or "why" spacetime curvature causes gravitational acceleration. Am I mistaken? Did Einstein and others who understand GR also understand that gravity immediately follows from spacetime curvature? It seems intuitive to me that it does (thus "why"), however the details are not at all intuitive, and I wouldn't even begin to know where to begin with the math. My basic "understanding" of how spatial curvature causes gravitation is as follows: 1. Movement through curved space means that the distances between remote points changes as you move through space. I think this is because distances in curved space are defined in terms of local flat spatial curvature. For example, if you go to google maps, you get a flat representation of the curved Earth; if you scroll the page north or south, the map scale ruler will change in size, meaning that the relationship between pixels and meters changes. In real life, the scale ruler would stay the same size while the "map" (ie. your measurements of the universe) changed and scaled or warped. 2. Uniform oscillatory motion of particles in a curved mapping of the curvature of space will tend to be non-uniform in a flatter mapping of the same space. 3. Repeatedly moving according to one mapping of spatial curvature (eg flat), and then changing the mapping to fit the different curvature of the new location in curved space, will tend to accelerate you towards greater spatial curvature or whatever. As an analogy of this, consider a typical world map (Mercator projection). Uniform distances on these maps do not map to uniform distances on the Earth. A very small area around the poles is expanded to take up the entire width of the map. Imagine someone doing a random walk on the flat map, and then following that path on a globe. They could do this by picking a random direction to move, and moving by a fixed (or random) distance on the map. Clearly they would tend toward the poles more than toward any other specific point on the globe, because the poles take up so much more room on the map. An observer on the globe who is unaware of the map but saw the walker tending towards a pole might think that some force is drawing them there, but there is no force... just a uniform movement in one mapping that corresponds to non-uniform movement in another. Obviously this isn't exactly how gravity works because it's still a random walk, and the person will still wander away from the pole, and gravity is not evidently random. This map example ignores point 3, which would involve something like the walker creating a new and different map at each step, or perhaps changing step size with each step; so acceleration isn't demonstrated. The details of what such new maps (or step size) would look like is a complication that eludes me. They would certainly not be Mercator projections. Does this make sense? Is this a good analogy for how gravity works? Are there already similar analogies (and better)?

I'm in the reality where North America is up, and Australia is down. I've heard there's another reality where Australia is "up" to some people in the southern hemisphere. If that were so, then North America would have to be down, to them. Since my "up" can't be "up" and "down" at the same time, and I haven't seen any evidence of up and down morphing (for example, if I woke up to find I'd magically floated to the ceiling during the night), this is obviously false. You can't have it both ways. Up is either up or down, not both. Some observer being somewhere else doesn't change which direction I fall. So I must conclude that Australia doesn't exist. I think this is compatible with your baseless objections to the modern concept of time. As long as we're rolling back science a few hundred years, why can't we roll back maps of the Earth too?

Well no one seems to want to answer but I'm interested in whether my reasoning is right, so...

No, the equations are based on mathematical and logical consequences of observations of the speed of light. Physicists determine the equations based on what is observed, not the other way around. Nothing will ever appear to be moving at greater than c, relative to any observer. If you can imagine objects moving relative to you at near c, then you'll also have to imagine length contraction and time dilation. If you do this (guided by the equations to figure out precisely what will happen), you'll see that time will dilate and space will contract and make it impossible for anything to actually move or appear to move faster than c relative to you. If you follow derivations of the Lorentz transformations you'll probably come to understand why--or at least that--this must be so.

Out of curiosity, is it possible to define some type of abstract curved space where two things can separate faster than 2c? It would require that while each thing travels away from you at < c, the distance between the 2 increases at a greater rate than the sum of the change in distance relative to you. If possible, would it require that the 2 things are not traveling on the same geodesic which intersects you? Or would it simply require inhomogeneous spacetime curvature? OR is it true that the distance between any 2 points A and C is <= the distance from A to B + distance from B to C, for all possible points B? Is this true for any metric space? Or for any conceivable spacetime curvature? Probably "separation velocity" but after a quick glance at the website I didn't see anything specific. I think you may be giving a specific example of a situation that is handled by more general SR math that can be used to figure out that example as well as many more examples. To see what I mean, try flipping the problem over, and instead of imagining an inertial observer in between 2 relatively separating objects, imagine it instead from the perspective of one of the separating objects. For example, if one object C is moving away from another A at 0.9 c, and then you imagine a third object B in the middle that's moving away at half the speed -- from A's perspective nothing is moving relative to anything else at > c -- and then calculate the velocities relative to the middle object B you should find that A and C are each moving away from each other with a separation velocity greater than c...

I don't think we're talking about the same thing here. Coordinate time and proper time of events are the same thing in SR only according to clocks that are at the same location of the events (or relatively at rest and synchronized to the observer's clocks) [second paragraph of http://en.wikipedia....Coordinate_time]. When we speak of time dilation, we're speaking of one clock ticking at a different rate relative to another clock. http://en.wikipedia..../Lorentz_factor The former refers to coordinate time (is this incorrect?), the latter to proper time. If I'm using the term coordinate time incorrectly, then what term should be used instead to describe the time according to a remote moving clock that ticks slower relative to "wristwatch time"? Edit: I think I see my mistake...s... - Coordinate time and proper time don't inherently refer to different clocks. In SR, the coordinate time and proper time of a given clock and observer are the same. - Each clock will have its own proper time. - The time of a remote moving clock is just the "time of that clock according to the observer"... it doesn't have a special name.

Isn't the proper time of one observer a coordinate time of another observer? I don't understand how curved spacetime prohibits correspondence to a real clock. Any observations of a distant clock (or signals from one) would arrive via a geodesic, which would define a distance to the clock, and thus a specific time delay of the observation, regardless of curvature. So it seems that the observer could calculate the time registered by the real clock -- and wouldn't this correspond to the coordinate time? EXCEPT... the time delay would be measured in proper time. With SR you could just divide by gamma to find the delay in terms of coordinate time? Is there no similar thing in GR?

The observer on Earth would use my clock (which travels to Mars) to measure coordinate time, correct? If they use their own clock, is that wristwatch time? It couldn't count as proper time. Or would it be coordinate time also? I was calling this "local time" but that seems a misleading phrase for measuring the time of remote events (using a local wristwatch). We could say that to an Earthbound observer, the time between my leaving and the observation on Earth of my arrival on Mars, can be measured in proper time.

Is proper time equivalent to "local time in the frame of reference of an observer, for events that happen at the location of the observer"? And local time (is there a better term?) is a bit more general, because it can also be used to describe the timing of remote events? And is coordinate time then basically time according to any clock that is remote from the observer? Is it correct to use these phrases when speaking of relativistic scenarios? Eg. a traveling observer's ideal clock measures proper time and always ticks at a constant rate. For other observers the same clock measures coordinate time, which ticks at a variable rate in general. Are there other related or better terms for describing time according to various observers and clocks?

True, I was sloppy with semantics. To be precise I should have said that logical validity doesn't imply logical soundness. If correct evidence contradicts a logically valid argument, the premises are incorrect. The logic is still valid but it's useless. The examples in this thread suggest building logical arguments out of flimsy premises, as if the logic will solidify them. (Or more likely, the examples in this thread are also confusing 'logical' with 'intuitive'.) It is not just "formal verbal logic" or "common logic" that is important to science, but logical soundness, as you've pointed out. I don't know of any examples in science of where logical soundness is shunned, so I must disagree with the OP.

Can you explain which meaning of 'absolute' you're using, and if that doesn't make it obvious, describe how SoL is not absolute? We don't have to suppose it, but we did. It's not about what we want to believe but what the evidence suggests. So far the evidence doesn't contradict it; it is within the range of what is possible. It's still an open question so of course the evidence isn't conclusive, however the evidence does rule out some other possible early universe scenarios that many people might find much more logical (young earth hypothesis, for an extreme example). If the evidence contradicts the logical, the logical is incorrect.

If it doubled for 12*3600 seconds there would be 2^43200 algae, which is quite a bit more than the number of atoms in the universe. I'd say that though the lake was full at 12pm, it was probably also full a lot earlier than that. I'd say it was half full within the first minute (~10^18 "alge").

Step 1. Kidnap every person the victim knows, keep them in the well in my basement, and torture them daily. Uh... I don't think your rules are very well specified, because I think this plan fits but that it isn't quite what you were looking for. I think my plan would do that.

Just to be on the safe side, make it a 30 ft. pole.

I recently saw an astronomy picture that had the moon in it and a nebula which looked as big as the moon. I can't remember where I saw it... does anyone know if there are nebulas that actually look as big as the moon from Earth? And how far away would such a nebula be? Here's my puzzle: Suppose you had a nebula that looks as big as the moon. Suppose that this imaginary nebula happens to be as dense as the moon. Which would have a stronger gravitational pull on us? You can assume the nebula is spherical and whatever distance away you want. Say, 100 light years.

At most 49 / 99 are troublemakers.

Go through both doors in superposition. Collapse the wavefunction of whichever reality is nicer.

I think Feynman makes a good argument here: This is from the first of a series of lectures that can be found here: http://www.vega.org.uk/video/subseries/8 If you take his quote out of context you might twist it to support your case. But what he's saying is that the math isn't sacrosanct. It is just a set of techniques used to arrive at the "final count of beans" of a theory without counting every bean individually. It's not the math that's important but the predictions made by that math, and they're accepted when they best predict the outcome of whatever they model. The story of the Mayans that he uses is that they were interested in predicting when Venus would show up in the morning vs. the evening, and they figured this out by observing it and counting days, and creating the math for that. This allows them to make accurate predictions. From this, they (we assume) had no idea why Venus followed those predictions, and as Feynman points out, trying to figure it out based only on the observations (the counts of days) is not likely to get you anywhere. The explanation "it's because Venus and the Earth each orbit the sun with different periods" is nice to know and it's certainly important to us, but it gets you nowhere towards predicting when Venus will show up in the morning or the evening, without complicated math involved (more complicated than the Mayan method). So beyond what Feynman says, my point is also: - A new theory doesn't replace an old one just based on explanations, but based on new observations, and on predicting/modeling new phenomena or the same phenomena more accurately. - New theories do not replace math with logic, but with different math (typically the math doesn't get simpler, I should think). I do agree that in the future, the explanations for why the math works will become simpler and more satisfying in many cases. As Feynman says several times in that lecture, nobody knows why it works. But that is not how it is judged. Feynman also points out that it's incredibly successful at predicting a large range of phenomena with high precision, and that is why the math is so valued.

If the math doesn't change, the predictions don't change, and the theory doesn't change. Different explanations for the same predictions are different interpretations of the same theory. I agree, these ideas lead to new or modified interpretations of the existing theory. It happens all the time and it will keep happening, and progress will be made. If one interpretation (ie. explanation) shows itself to be logically "right" vs another interpretation, it will probably only do so by improving or expanding the theory (and its math), or by suggesting a new way to test the different interpretations. Otherwise, even if an explanation is "completely logical", yet it makes the exact same predictions as another explanation, mathematically, with no test, then there is no way to show that the other explanation is wrong.