md65536

0.625/gamma gamma = 1.25 I don't want to be drawn into any hostile arguments, but I'll go along with it if it helps me figure stuff out.

Then you're stretching the meanings of the words beyond the point of meaninglessness. Just because inefficiency is a *desirable* quality of that machine, doesn't mean that "inefficient" now means "efficient". We'd have to agree on what "machine" and "efficiency" means, but I think the expected meaning is "something that performs a (mechanical) action" and 100% efficiency means the energy used is conserved fully in the intended (mechanical) action, and none is converted to other forms. (Mechanical) might also be replaced by electrical, etc.

In post #3 xyzt identifies that post #1 is speaking of coordinate speeds. It seems like it's defined and understood early on in the thread, and only later (post #25?) is there issue taken with it, and since then stifled, even though it's used meaningfully throughout the thread. Edit: It would have been clearer to call it "coordinate speed" throughout the thread. Aren't Iggy and JVNY still discussing the core of the topic that was brought up in post #1, that of differently accelerating rockets that maintain a proper distance, while xyzt is complaining that it is too complicated and pushing for a discussion of a physically unrealistic uniformly accelerated rocket or nothing at all? All of xyzt's objections seem to only be directed against discussing the topic as it was introduced. Are you sure that others are derailing the thread, or is it possible that xyzt changed the subject but appears on topic due to insistence?

The modern, mainstream view is quite clear on this issue, end of story. When there are multiple "perfectly valid" interpretations, one alone is never the "end of story", and I don't think it's a good reason to try to kill a discussion that others are having. Others are calculating things using a perfectly valid interpretation. Do you have a problem with the results, or their interpretation?

Yes, when measured locally. If you're measuring from a different gravity potential---different coordinates---you get different results. You can still calculate, as JVNY and Iggy have been doing. For example, from a distant observer's perspective, light near a black hole's event horizon is not moving very fast in your coordinates. You can say that it is slowed in the lower gravitational potential. However, in local coordinates it is still moving at c.

It makes sense to me. I'm not an expert and am also interested in how others would comment on it.

We're in total agreement. In addition, and the point of this thread, is that the proper time measured over the path traveled by a single clock, is the same as the sum of the proper times measured by multiple clocks each traveling a section of the same path (where every subsection of the path is traveled by exactly one clock). If the path can be split into inertial sections, as in post #1, then the proper time along the path can be measured by clocks that don't accelerate.

I haven't followed the whole thread and it's over my head, but are you saying that you've set up the accelerations so that the 3 ships all have an equivalent accelerating frame, which they can treat as a single frame of reference? There is no time dilation between any two ships, they're able to keep their clocks synchronized according to an observer on each ship?

The front and rear of your single rocket can be modelled by two separate rockets configured properly. It is equivalent to a single rocket. If your one-rocket example is simpler than is possible with 2 rockets, then you're doing something wrong. It doesn't matter if the force accelerating the front of a rocket is transmitted through the structure of the ship, or comes from a separate nozzle at the front. Edit: I looked back and realize the 2-rocket description is describing something entirely different. I see now, the problem is with using 2 different accelerations, not with treating a rocket as separate parts.

How is this simpler? Are you trying to calculate relativistic effects at the front vs back of the ship, while assuming that the ship accelerates as one uniform thing (simultaneously all over the ship for everyone)? If so this is not physically realistic. Otherwise, even if you model the ship as simply as you suggest --- perfectly rigid but still obeying relativity, accelerating from a single point --- you can still model its various parts using separate rockets. If you treat the various parts of the rocket as the same, the rocket has negligible length, then you can't continue calculating relativistic effects along its length.

Don't worry too much about it, because 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 100 = 10^2 It's easy to see why... if you just shift everything past the 10 over, ie reordered to... (1+9) + (2+8) + ... I haven't followed all the math in the thread, but there are 2 things here, the squares of numbers with all 1s, and the sequences that add up to squares. If you imagine multiplying eg. 11111 "the long way", you get 11111 x11111 = 11111 11111 11111 11111 +11111 =123454321 And that might give you a clue about why it works, but if you have more than 9 rows you're going to get digits carrying and it unsettlingly stops working so easily. Now as to why the digits add up to squares, what you're doing is... Suppose you call the sequences Sn, where S1 = 1 = 1^2 S2 = 1 + 2 + 1 = 2^2 S3 = 1 + 2 + 3 + 2 + 1 = 3^2 Then Sn+1 = Sn + n + n+1 ---- You're adding 2 numbers into the middle of the previous sequence. I'm sure there's a better way, but one way to see that this is always a square is to think of it geometrically. Imagine a square grid of n by n blocks. Then add a row of n blocks, and add a column of n+1 blocks, and you end up with a square again, with sides 1 larger than the previous square. So, while the squares of 1111111111111111... doesn't keep working, the "ascending and then descending" sequences keep adding up to squares.

This is a fairly straightforward example of SR and the Lorentz transformations with inertial motion. I think that using "age from birth" is useful for understanding a concrete example of the meaning of time in a real world situation. It also works the same if you use any clock and any initial clock settings (a baby ages one year per year from birth, but so does a 90-year-old, and an atomic clock measures 1s per sec and a container of yogurt grows 1 year worth of mold per year, etc). I think choosing the most absolute concrete example is useful, but then also considering the most abstract too can help prevent attaching too much meaning to absolute clock times.

I agree but on the other hand, common use and misuse can define a phrase, so that literally literally means figuratively, "couldn't care less" and "could care less" mean the same thing, etc. So if people have carelessly used "one in N" and "one out of N" often enough, then the "wrong meaning" can become an accepted meaning (which I find unfortunate), and even careful writers end up being able to choose according to style.

Dark matter doesn't interact electromagnetically with itself. If there is a corresponding "dark electromagnetic force" it doesn't seem to be evident with dark matter. What would dark photons help explain?

The connotation that I think of is... One of a set of equals is one in a million, emphasizing inclusion in the set. One separated from that set is one out of a million, emphasizing exclusion. If you want to say "Anyone can win the lottery", one in a million equally likely winners will win. If you want to say "Most lottery players are losers", only one out of a million will be separated from all the losers. Two out of ten people are weirdo outliers, while another two in ten people are exceedingly average people. I don't think there's an explicit difference in meaning, just a subtle difference in emphasis that others might not even interpret the same way as I do.

There are a ton (estimated) of threads that mention why relativistic mass should not be used as a definition of mass. The latest one I've seen is a link posted by swansont to this: Your argument is problematic because for example if an observer accelerates itself relative to something else, then it is "adding mass" to that something else. How does it do that without transferring energy to it? It's just a different type of energy... kinetic energy, which is relative, but not mass energy. So it is gaining "relativistic mass" which isn't the same as "mass".

Dark matter isn't distributed evenly through space. For example, gravitational lensing can show where matter is vs where visible matter is: http://en.wikipedia.org/wiki/Bullet_Cluster#Significance_to_dark_matter Two galaxies collide; normal matter interacts and slows more than non-interacting dark matter which passes right through. Isn't dark energy evenly distributed through space ("vacuum energy")? It has a repulsive effect, and can't meaningfully be called "stuff" or matter.

But it could be. Absorption of a photon is an event. Then it's not a single light signal observed twice, but two signals sent to each observer. Anyway events coincident with the observations could easily be defined, or unambiguously implied by the thought experiment. I don't see how this is an issue. How does defining the events that yknot is implying change anything? The issue is that delay of light has to be considered, not that the number of events is wrong.

Addendum: Say you're far from Earth and vibrate back and forth at a high fraction of c. According to standard simultaneity, moments on Earth that are simultaneous with moments where you are can vary back and forth through time on Earth. But even this does not require a block universe; the block universe is just one of the simpler interpretations. Perhaps you're having the Earth merely cycle back and forth through the same set of events, with each event having only one existence --- a block universe. Perhaps these events don't actually happen unless you can later measure them --- some sort of delayed causality or an alternative physical simultaneity perhaps. Then whatever may happen on Earth but is "undone" via changes to relative simultaneity, didn't really happen. Perhaps each time you vibrate the Earth goes through different sets of events from a superposition of all possible events --- some sort of multi-world interpretation. And it can get worse... perhaps you're "spawning new realities" by vibrating or doing any action. I think the more complicated interpretations are ridiculous, but the block universe isn't required, it is just an interpretation that doesn't assume any extra complications.

Let me just play devil's advocate and admit: Yes, if you ignore relativistic effects and the postulates of SR, you're no longer speaking of SR, and you can describe it however you want. Perhaps you might speculate that light behaves differently for the different observers? Everyone is giving you answers according to SR. There's no point in asking others what the answer might be other than what SR says. If you think there's an answer, you'll have to provide that, but then you'll have a long road ahead showing that your answer is consistent with observations, the way that SR is.

That's simply "relativity of simultaneity". Personally I don't think that that on its own requires a block universe, however it does seem that relativity of simultaneity together with an assumption of standard simultaneity (aka Einstein simultaneity) seems to. Just as an example of what I'm trying to say: Say you're far from Earth and suddenly change velocity relative to it, and there is a change in relative simultaneity with respect to Earth. You might have a situation where you consider it December 2013 on Earth, and the next moment you consider it November 2013 on Earth. You haven't (necessarily) reversed time or anything... all the events can be considered the same on Earth, just differently lining up with your current time... a block universe. However, the Earth is so far away and nothing of whether it is Nov or Dec there can be observed by you yet. There is no physically measurable effect of the change in simultaneity from Dec on Earth to Nov on Earth. Furthermore, you receive light from the various events on Earth in order, so you will never observe any backward change in time. The only thing you have to be certain of the change in simultaneity is the knowledge that incoming photons travel at c, allowing you to define standard simultaneity, and only according to that definition and SR, can it be Dec on Earth one moment and Nov the next, according to you. Without the assumption of standard simultaneity, you can still have relativity of simultaneity, but might not need the block universe.

I would guess that just by being the first and naming it how you want would set a precedent which would tend to be used, if it's appropriately named. I don't think there are any laws to govern rights to name discoveries or anything. If you think someone might try to steal credit, you can easily create proof of who wrote it and when. Decades ago people would mail a physical sealed copy to themselves, but now anywhere that is indexable by Google should be proof enough. Posting to a blog or a writing repository or a prepub repository (arXiv, or vixra if you don't have credentials) should make it easy to prove that you wrote about the idea when you did. Hundreds of years ago scientists kept their work secret, so there was a fight over eg. who invented calculus. Newton kept his work secret for decades, I think.

Not an expert but I'll try... When we describe how light behaves it's not meant as a description of what it is "really doing", only the best description of how its behavior can consistently be measured. If we say it behaves as a wave or as a particle depending on how it's measured, it's because it consistently does either, and we don't have any better description of what it is doing that explains both at once. As a wave it behaves not as though traveling on a line but as a wave front (spherically shaped), which is how you can get descriptions like "the wave seems to go through both slits in a double-slit experiment." Measurements consistent with it being a particle are consistent with it traveling in a straight line (or null geodesic as you mentioned, to be precise) and at an invariant speed c along that line. So the reason we wouldn't say that its actual path is zig-zagged and faster than c, is that... 1) there's no theoretical prediction that it should, but there is a prediction from electromagnetic theory that it should travel at c 2) there's no measurement of light as a particle that is inconsistent with it traveling along the straight line path. There's no evidence that it does otherwise. If you hypothesized that it traveled off of a straight line, and then were able to come up with a test that would have different results if it did vs didn't, then it might be tested and the answer decided. But unless there's such a test, there's simply no reason to describe light's behavior as a particle except that it travels along null geodesics, and adding anything to that would no longer be describing how its behavior is measured, but guessing about what it's "really doing", which is useless unless it's simpler or better than the current description, or has measurable evidence.

What about the simplest possible machines, like a single molecule performing some action or something? It's not so much a law at the quantum level, is it? Rather it's more of a statistical thing, where the probability of performing a large number of actions without loss is statistically impossible, and the effort required to make a large system more efficient makes it more complex and even less likely to be 100% efficient. Either way, > 100% efficiency would not be possible, but does Newton's law hold in quantum mechanics?