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Not really. I intentionally chose 2 processes that are not regular: one is accelerating, the other is slowing down. But I would say that every regular process can be used as a clock. If you take my process as clocks, then every process is a clock. (which maybe theoretically right, but not very practical). I just took the argument Markus made, that every change in a process can, so to speak, plotted against the change of another. You can leave time out, if you do not need it. I do not understand what you are asking. Can you elaborate?

But the essence of Markus' argument is that you can leave time out. You can express the change of one process in term of the change of another process, without referring to time. And it is my viewpoint that this is exactly what one is doing when one uses time: describe the change of one process with an other, standard process: the ticking of a clock.

I would say that your guess is wrong. Say, you want to make a picture of the stone after 20 meters of falling. Now you can look at your can of water, and at the moment it has 1.5 liter water left in it, you make the picture. Think about what a prediction is, e.g the totality of the sun eclipse starts at 11:03h. It means that when a certain event occurs (your clock shows 11:03h), then another event happens, in this case the sun is totally covered by the moon. So a prediction is nothing else than saying two events will happen together. Obviously that makes most sense when one of the events is of a series of standard events we all know, i.e. the turning of the days on a calendar, and the running of a clock.

Think about two processes: let's take a stone falling, and water running out of a can with a small hole in the bottom. Both are functions of time: the stone falls faster and faster (as usual in such examples we neglect air friction...); but the water output becomes less and less during time (because the water pressure becomes less and less, because water is running out of the can). Now if your experiment is very precise, you will get the same relation again and again: when the stone has fallen 10 meters, there will be still 2 liter water in the can, and this for every point (20 meter fallen 1.5 liter water, 30 meters fallen 1.2 liter water etc etc.) This means you have a function between the two processes: if you have 1.5 liter water, you know that the stone has fallen 20 meters, or the other way round, if the stone has fallen 30 meters, you know there is still 1.2 liter water in the can. So to every value of one process, belongs exactly one value of the other process, and the other way round. Mathematically this means that one value can be expressed as a function of the other, in this case in both directions. With that, you can leave out the time as 'independent factor'. You can express the change in one process in terms of the other, and yes, therefore one function is the inverse of the other. You do not need time as intermediate factor if you are only interested in the relationship between the distance the stone has fallen, and the amount of water left in the can. And, as Markus points out, you can also express the 'measure of change' of one process in terms of the 'measure of change' of the other. That is what his mathematical formula is saying.

Exactly. But would the same not apply to space? One can define the length of a rod in terms of the length of another one. One does not need the abstract notion of 'distance', and therefore not the just as abstract notion of space. And can you really define 2 points in empty space? Don't you need at least a coordinate system with an origin? I know that this is easy stuff in mathematics (e.g. just pick one based on independent vectors), but what would be the physical meaning of that? To paraphrase your argument against my idea: I can define 2 events on a timeline without reference to any change. But when the 'timeline' is empty this is pretty difficult, just as with space. Well, I think you here are confronted with the probability character of QM. A clock based on the decay of one single unstable particle would not be a very precise clock, is it? But of course you could do it with many particles of the same sort, say 6x1023 muons, and e.g. you define the 2.16 microseconds as the time that half of the muons have decayed. But still I do not see how I could define this 'lifetime' without reference to other changes, e.g. compare with 6x1023 uranium-238 nuclei. You just must wait a little longer before half of them has decayed... Or you use some regular events like a clock, might be easier. Forgot this one: Weren't we talking physics here?

Time and space are not fundamental at all. They are abstractions. Time is the most general abstraction of change, and space is the most general abstraction of distance. It makes no sense to speak of time or space when nothing changes and there are no objects at all. It is one of the reasons that Einstein, in explaining his special theory of relativity (from which the idea of spacetime was born), falls back to operative definitions of time and space: e.g. the ticks of a clock (=(regular) change), or the length of a rod (= distance between one end of the rod to the other).

This is not from you, beecee, but from the article. In another thread this was discussed: The word 'dragging' suggests that space is a substance that can touch matter (and/or energy) and exerts a force that pushes everything around. No miracle that some people come here with wrong ideas. I think that even popular science writers should be very careful with their words.

I assume that the creation of electron-positron pairs then also cost ~7.64% of the energy of the sun (or the Beta+ decay of protons). So the net effect is zero.

You do not seem to be prepared to learn. In another thread I reacted and told you that Dirac was able to predict the spin of the electron and anti-matter, by making quantum mechanics consistent with special relativity. No conflict here. Your examples are all related to special relativity. The problem you seem to have heard of, is the combination of general relativity with QM. Normally there is no problem: in QM one can neglect gravity because it is much too weak; in cases where we need GR to explain phenomena (strong gravity or very precise measurements, for weak gravity Newton suffices), there are such huge concentrations of mass that we can neglect quantum effects. (We do not need QM to describe the movement of the moon.) But there a 2 notorious exceptions: the singularity of black holes, and the very beginnings of the big bang. There the sizes involved are so small, that QM must be taken into account, and there the combination fails. So we are very aware of the domains where we can apply QM and GR. In their respective domains there is no problem. SR and QM are proven to the bone: if you think you find an error, you can be sure you made an error in your thinking. GR is proven not so much, because the situations in which its results deviate from classical Newtonian gravity are not so abundant. But it passed all tests until now (gravitational redshift and time dilatation, gravitational waves, ...) so we are pretty sure GR is correct in its domain.

Yes, I think there are. This is my favourite on the topic of GR. No rubber sheet (the maker of the video actually criticises the sheet analogy), but a demonstration with (his own built?) spacetime stretcher. Just 4m:12s. Until now I haven't seen a better video on gravity according to the GR for lay people. DLTherrien, try it out!

Huh? Why would you need that? To have the 'distance-loophole' closed you must assure that you measure the spins of the electrons in a way that what your first measurement is, cannot reach the other measurement with light speed. That is easier with photons, of course, but that can be done with electrons too. Huh? They go without resistance because they behave as bosons. But bosons must not be massless. And how could one remove rest mass from an electron' Or from any particle that has rest mass? This sounds all pretty nonsensical to me. The article you refer to, just shows another way of creating entangled electrons.

If I am allowed to reflect a little on such postings, as the OP, or better, on the reactions to it. We see three kinds of reactions here: the 'beecee-reaction', the 'Janus-reaction', and the 'Markus-reaction'. (All are equally valid). Beecee's reaction is global, saying more or less that SR is empirically tested to the bone, so anybody thinking he found an error in relativity will have a very hard time: it is difficult to argue against endless observational tests, and the fact that SR is technically used, e.g. in particle accelerators. These would not work the way they do if we would not take SR in account. Janus' reaction is technical, to the point, showing where discountbrains makes errors in his argumentation. For me, with a limited understanding of SR, it is always a joy to read his exposés about errors made by 'Einstein-was-wrong!' (im)posters. Often his reactions improve my understanding another little bit. Markus' reaction I find, as a philosopher, the most interesting: it shows that SR belongs to the absolute fundamentals of our understanding of the world, of the laws of nature. This is even so much so that the Lorenz transformations can function as a filter for new laws of nature. If new found laws are not invariant under Lorenz transformations, they cannot be fundamental laws of nature. At most they are approximations. Historically, this has been a strong guide to find more fundamental laws of nature. The most astonishing example I find is Dirac: by discovering that the laws of QM, as they were known in his days, were not invariant under Lorenz transformations, and changing them by making them so, he was able to predict the spin of the electron and the existence of the anti-electron. Spin was already postulated on other grounds, but got its fundament with Dirac. The anti-electron was found about a year after Dirac's prediction. I am sure physicists here can come with more examples. I think e.g. that we could turn around Markus' argument: imagine we would only have known about the electric field and its impacts, but had not discovered the magnetic field. By making the electrical field Lorenz-invariant, the magnetic field would roll out. So, discountbrains, by saying 'Einstein had a fallacy' you are opposing the whole body of established physics. I think it are the outrageous sounding effects of time dilatation and length contraction that are so counter-intuitive, and are often presented as examples par-excellence of special relativity, that lay people think this is mainly what special relativity is about (just forgetting that E=mc2 also follows from special relativity), and that there must be an error. (And think that Einstein came to this theory and since then there was nothing anymore to it.) One could even defend that special relativity is not a physical theory, but a meta-physical theory (no, not metaphysical): every theory in physics must comply to special relativity, otherwise it is just an empirical approximation.

Of course it has. You are supposing that c is the same for the observer in the spaceship and for the observer on earth. But that is not according to Newton. According to classical mechanics, you must take into account that the velocity of light that the earth observer sees is the vector sum of the speed of the light between the mirrors plus the velocity of the spaceship. If you do the calculation you would see that for the earth observer the clock still has the same ticking rate as his own local clock.

No. 2 Points: We do not know that the universe started 13.8 billion years ago. We only know that our theories break down at that point in time. What we do know is supported by observation, and not based on reasoning alone. Then, just citing Markus: I would say this differently: Nature is even stranger than we can imagine.

This looks like outdated philosophy, namely rationalism. Rationalism is the idea that one can derive how the world is, based on thought alone. This idea was already refuted by Immanuel Kant in his Critique of pure reason in 1788. (Just reflect for a moment what Kant could have meant with that title...). Your idea is discussed in the chapter called The antinomy of pure reason, namely that of boundaries of (time and) space. Kant proofs both "The world has a beginning in time, and in space it is also enclosed in boundaries", as its opposite "The world has no beginning and no bounds in space, but is infinite with regard to both time and space", showing that by reason alone it is impossible to know what is true. Kant tried to overcome the tension between pure empiricism and pure rationalism. Both on itself do not lead to any justified truths. In modern day speak: in science we need theory building and observation.

Just found this in the Wikipedia entry of 'Spacetime':

It seems to me that you see spacetime space as a fluid, as something in itself, that has influence on objects in it. Many physicists here already explained that this view on space is wrong. It it were true that galaxies are accelerating one would be able to measure the fictitious force caused by the acceleration. But we don't. Now you could think that therefore our galaxy is exactly in the middle of the universe, every other galaxy (except maybe the galaxies that belong to our cluster) recedes from us, so these would be able to measure acceleration. But that is against the idea of the cosmological principle, that we have no preferred place or orientation in the universe. Spacetime is an abstraction of measuring of distances and periods, it is not a physical substance. So saying 'space expands' says nothing more than that distances become bigger. General Relativity can describe this without the idea that galaxies recede from each other due to some local forces. So spacetime does not exert any force on galaxies. Your understanding of space expansion is flawed.

I've lived one year long in Ireland. The risk there seems very real to me... Markus, I would like to (mis)use this opportunity to thank you for your very clear postings everywhere on these fora, bringing in your deep expertise, and in name of some others, for your patience explaining the nearly impossible. @Quantum321: I have two analogies. The first is the balloon again. But look from this side: the balloon is inflating because of the pressure from the inside, so there is a force in the outward direction. But there is no force between the dots drawn on the surface. The second is two people on the north pole of the earth: say they walk to the south, but under a slight angle. Given their experience that the earth is locally flat, they expect that their distance increase with time uniformly: if they have walked two kilometer, their distance will be twice as much as when they had walked for one kilometer. But to their astonishment, they measure that the distance between them increases less and less the farther they walk. So they conclude there is some force that tries to push them to each other. But we know there is no such force: it is a consequence of the curvature of the earth. (So in this example, their universe accelerates less and less. The curvature of the earth is positive, but if you imagine a negative curvature (the form of a saddle) they will get away from each other faster and faster, without any force.) Just imagine that the direction they are walking, is the time dimension.

Ha! Very good! That was what my physics teacher used to say when he called somebody for the blackboard, and he/she stood there hopelessly how to solve the problem: 'Think loud, please!'. Most of the times absolute silence was the result...

I don't think you have to refer to mental illness: in many organisations finger-pointing is a normal practice, meaning 'I am not responsible, (s)he is!'. I do not see this as the essence of your examples. Or you have given not the kind of examples of what you really have in mind.

I am not sure if this is a fallacy. The only thing that comes close I know of is bad faith. At least it is lying about who really is responsible for the situation, denying one's own responsibility.

Hi geordief, I think in Why does E=mc2 (Brian Cox and Jeff Forshaw) does a very good job in explaining this. It first argues that because of causality only a Minkowski-space works, i.e. there is an 'absolute universal speed-limit'. Only afterwards it identifies that this speed limit is the same as the speed of light, with two arguments: the formula for time dilation previously derived with the 'light clock' is the same as the formula derived from the Minkowski-space, which means that c must be the light speed. After showing that E=mc2, it shows that massless particles must move at exactly this speed limit. It is a good read for lay people, with Pythagoras as one of the most advanced mathematics you need. I made a quick reread of the book specially to be able to react on your thread, so better read it!

Maybe this helps. This is the Windows color-Applet: As you see, red/green/blue are at their maximum, which produces white (see the arrow). As several people here have said, blue and red light are absorbed by a green leaf, maybe not totally, I don't know but you can see the result by decreasing the red and blue components. Then you get this: And please confirm that you understand that - the Bohr model only applies to hydrogen - it only explains the main transitions, so it is a out-of-date model - Atoms in molecules form totally different electron orbitals then the atoms a molecule is build off (so the colours of molecules is not just a mix of the colours of the atoms on their own). If you do not acknowledge this, further discussion seems useless.

The inside of a rainbow is always lighter than the outside. But these pictures were made when the sun was low above the horizon, so it was shining red. Therefore also the rainbow itself is mainly red. See this picture, that was obviously made when the sun was still higher above the horizon: I just looked it up: the raindrops reflect both from the backside as from the frontside. The light that reflects from the backside of the raindrops makes the rainbow itself, the light that reflects from the frontside are just reflected, and therefore has the same colour as the incoming light, mainly red in your case. See here.

Sounds like Cyclosophy... The original article is in Dutch: Velosofie. Maybe you can use some Webtranslator to read it. What he derives from his bicycle: distance sun - earth vacuum velocity of light constant of gravity fine structure constant age of the earth age of the universe (which was estimated at 18 billion years those days. The article is from 1990. But it surely is possible to get at 13.8 billion years) Praise the holy bicycle!