spacelike

Note: I am familiar with (special) relativity and its implications. This is just a question about experimental results. I remembered hearing many years ago that data was showing that the speed of light in vacuum is getting slower. So, recently I decided to google it and I see a bunch of articles about the same thing. But I know from experience that articles on the internet can have very outdated information or just plain incorrect information sometimes. and the articles make it sound like it's not confirmed yet too, which doesn't make sense to me because isn't measuring the speed of light a relatively easy thing to do? I find it hard to believe that this can still be an open question. The only way I can imagine that we are still unsure is due to the possibility that the change is so small we can't measure it.... But it can't be that because scientists have claimed to measure that it is slowing down, so the amount of change in question is within our ability to measure. (I mean, the possibility of the change being so small will always exist of course... But either their measurements were wrong or they aren't, repeated experiments should easily reveal this, and it has been at least 5 years since I first heard this, hasn't anyone tried to repeat the experiment?) So what is it? Have those measurements been shown to be faulty? Are the slower measurements within the error margin? Has it been confirmed to be slowing down? Is 5 years not long enough for a repeated experiment to have finalized?

Maybe someone else can list a bunch of them for you if that's what you're after. But a general rule is if the observables are described by two operators that do not commute with each other, then they will have a relation like that. Two opperators (A and B) commute if: AB - BA = 0 (technically since these are operators you would need to operate on a test function "f" to prove that it works, ABf - BAf = 0) But if you find that it is not 0, then they will have some value which the product of the standard deviations must be greater than. For example, the commutator of 'x' and 'p' is 'i*h-bar' where "h-bar" is plancks constant divided by 2pi. xp - px = ih-bar Therefore the product of the standard deviations of x and p is non-zero [math]\sigma_{x}\sigma_{p}\ge\frac{\hbar}{2}[/math]

I understand that much, but the point I'm trying to make is what would the story be like from my point of view? Well you would say that I am always observing myself so I would find that I will be in the state [math]\{ (1, library), (0, class), (0, food room) \}[/math] for example, of course it could be any of the 3. However, if we still base our interpretation on the Copenhagen interpretation then before you measure my position, the story is just as you said before: [math]\{ (0.4, library), (0.35, class), (0.25, food room) \}[/math] according to you. So it depends on who's perspective we are considering. But how is this possible? Because don't forget that those probabilities are to be interpreted (by the particular interpretation we are discussing) as a literal statement about what CAN happen. How can it be that from my point of view I have a probability of 1 of being in the library (for example) and a probability of 0 of being anywhere else, whereas from your perspective I have a finite probability of being somewhere else. This means that according to me it is impossible for me to be anywhere but the library but according to you I can be at other places. I understand all of this mathematically when you consider a single point of view individually, but you still haven't discussed what I'm getting at, and that is when you put the two together. According to the Copenhagen interpretation even though I have a probability of 0 of being at the food room (according to me) it is still literally possible for you to actually observe that I AM at the food room! This is a paradox. A paradox to which the idea of many worlds has been proposed as a resolution.

But are those really different? The first one considers things from the cats perspective and the second one considers things only from our perspective. If you try and use the second one only and ask how do things appear from the cats side, don't you get again the same result as the first one? So I think they actually go together. One way I think of it is instead of like you said in the first one where there is only 2 cats, what if there are an infinite amount of cats and due to the probability (25% dead, 75% alive) 25% of the cats end up alive and 75% dead, which is equivalent to saying any one of those cats has a 25% chance of being in the "alive branch" and 75% in the "dead branch". The thing is if you only have one cat, then we know the cat observes itself and knows if it is alive or dead. We also know that according to our perspective the cat must have a 25% chance of living and a 75% chance of dying. However, the copenhagen interpretaion would say that this probability means that (even though let's say the cat observes itself to be alive) there is literally still a chance that we would observe a dead cat. Since these are independent observations, so considering all possible outcomes of both we see that technically it is a possibility that the cat observes itself to be alive and we observe it to be dead at the same instant. Or vice versa. So different perspectives would contradict each other, but can be reconciled if you consider that there are multiple cats like you were saying, and that is just the idea of many worlds isn't it? So 25% of the cats would end up in the "alive branch" in which we also measure the cat to be alive and the cat and the experimenters versions of reality are the same. and 75% of the cats end up in the "dead branch" in which we also measure the cat to be dead. So if there are many worlds like this then the cat and the human will always agree on the outcome (alive or dead) even though each is supposed to get a result independent of what the other gets.

no problem. Also, I don't really care too much for the interpretations anyway, so correct me if I'm wrong. But I don't think the many worlds thing is contrary to what you just said because I think the only reason the idea comes into the scene is because of the wave function collapse. As far as the evolution of the wavefunction with time is concerned there is no need for many worlds, but it is the collapse after a measurement that brings all of these things into question. But QM doesn't really say exactly what happens at this point, so it kind of seems that it is completely open to interpretation. I know mathematically we basically just write the new wavefunction as the eigenstate representing the value that was observed and see how it evolves from there with time again. But the thing is it's random which of the states it ends up collapsing to, so the idea is that the universe doesn't actually just somehow pick one possibility and that's it, but rather that all exist It's a bit outside of this discussion but I think the strongest argument for it is when you try and figure out how the Copenhagen interpretation would work in different perspectives. Say for example the Schrodinger's Cat thought experiment, replace the cat with a person if you like and then ask, what does the person observe? We observe him as a definite state which is a superposition of the two eigenstates "alive" and "dead". But the person is constantly observing himself/herself so he/she is already collapsed to one of those eigenstates. The only thing that seems to be able to save the Copenhagen Interpretation if we go on assuming that an "observation" or measurement is what collapses the wavefunction, is to introduce many worlds. That was my understanding and that was sort of what I was trying to say in my original post. But of course there could be other possibilities or explanations, but that's the argument in favor of many worlds I am most familiar with. There is probably just as many against it though.

I didn't make up "orthodox" that is straight out of David J. Griffiths book on quantum mechanics as an alternative name for the "Copenhagen interpretation". I care nothing for religion, but if you say it has to do with christianity than thank you I'll try and avoid that particular name for it in the future, but I did not make it up.. Copenhagen sounds better anyway. I am familiar with basic quantum mechanics. I am aware that the mathematics of quantum mechanics does not lead to any such claims. It is only from thinking about different interpretations of quantum mechanics that leads to things like many worlds. But don't tell me to read basic quantum mechanics as if I don't know any physics and I am actually just making all of this up based on something I read on wikipedia or something. I am not saying this is what quantum mechanics tells us, I am just putting forth one possible interpretation that supports what OP was asking. Furthermore basically everything I said has also been stated by Stephen Hawking. I am unbiased though, I don't care one way or another and I keep an open mind to all possibilities, but one cannot deny that many worlds does not only not violate any laws or theories, but is actually supported by some, and therefore should not just be dismissed by any serious physicist as far as I know. I'm just an undergraduate so perhaps my information is incomplete but this is the best I can say on the matter with the information I have.

I'm sorry, I don't understand why the length of the wire doesn't count. Say we are looking at the case of points along the plane cutting halfway through the length of the wire (so a circle about the origin, where the wire goes through it and extends from -L/2<z<L/2), the axis of the wire is the [math]\hat{k}[/math] direction. Then [math]\vec{B}=\int\frac{\mu_{0}}{4\pi}\frac{Id\vec{l}\times\hat{r}}{r^{2}}[/math] [math]d\vec{l}=dl\hat{k}[/math] [math]dl\hat{k}\times\hat{r}=dl \hat{\phi}[/math] So now we have: [math]\vec{B}=\frac{\mu_{0}}{4\pi}\int\frac{I dl}{r^{2}}\hat{\phi}[/math] [math]\vec{B}=\frac{\mu_{0}I}{4\pi r^{2}}L\hat{\phi}[/math] So we can clearly see that the magnetic field will wrap around the wire in the direction of [math]\hat{\phi}[/math] (consistent with the right hand rule) and also that it's magnitude [math]\frac{\mu_{0}IL}{4\pi r^{2}}[/math] is directly proportional to the current and length of the wire and inversely proportional to the distance from the wire squared. (unless of course I made a mistake, then please correct me anyone) EDIT: I think perhaps in the limit of an infinitely long wire this might reduce to [math]\frac{\mu_{0}I}{4\pi r}[/math].. It would make more sense to me if it did, I can't see how this would happen at the moment though. But it does not make sense to me that the magnetic field would not depend on the length of the wire if you had a wire of finite size, so I am fairly confident in the result I obtained above for a finite sized wire. Perhaps you could argue with your teacher that they didn't specify if the wire was infinite or finite.

I didn't mean it as a separate interpretation and that it was also "orthodox". I was only referring to the Copenhagen Interpretation which is also known as "the orthodox interpretation" it's just what it is called. But it also happens to be the most popular interpretation. So what I meant was copenhagen interpretation implies many worlds. But I'm glad you brought that up actually because I may have said that too strongly.. Personally I don't see how it can be any other way, but I can't say for sure if other possibilities exist or not. But in any case, I can say that the concept of many worlds can be shown to be logically consistent with the copenhagen interpretation. I should have just worded it that way in the first place.

Right >.< Sorry I really don't know what I was thinking when I wrote that, thanks for catching it. and I really don't think I should comment any further on the string theory aspect of this

(I do not know string theory, only vague concepts, so take this with a grain of salt) A particle is classically supposed to be a "point particle" and in purely mathematical terms this can never be 2-dimensional because it is defined as something with zero width, height, and depth. So in classical physics there are no 2-dimensional particles (or 3-dimensional or 1-dimensional) The 2d and 3d objects would only be due to collections of 0-dimensional point particles in a 3-dimensional space. But we are starting to move away from true point particles, we realize that localizing a particle to a single infinitesimal point would be impossible. However, even though we know this, even when discussing quantum mechanics we often still refer to them as "particles". A 2-dimensional object would be a line, so yes a string could easily be called 2-dimensional. The thing is to keep in mind is what area of physics you are in and also that nobody is really certain. The best we could do is answer your question based on what theory or area of physics you are talking about at that moment. I have answered it for classical physics (and the answer was "no"), but I can't truly say what the answer would be for string theory. Perhaps someone else on this forum is well versed in string theory and could answer your question from that perspective. But neither of them could be considered as the "definitive answer" to your question. So you may have different (conflicting) answer, depending on what regime of physics you are in. But just keep in mind that the word "particle" is probably used to imply different things. In mathematics it almost always means something with 0-dimensions. But, for physics in general I would just assume the word particle refers to the physical manifestation of the fundamental object (electrons, quarks, neutrinos, etc...), which I suppose could be 2-dimensional in string theory (but again, I do not know string theory). Sorry for all the editing.

I think it would actually be a combination of what both of you wrote because of the Biot-Savart Law: [math]\vec{B}=\int\frac{\mu_{0}}{4\pi}\frac{Id\vec{I}\times\hat{r}}{\vec{r}^{2}}[/math] So you see that it does go as your classmate said. I is on top, and r is on bottom. However the r is squared, so I would probably reword what your classmate said as ... inversely proportional to the square of the distance... Notice that the Biot-Savart law is not just for a single point, but is general of all points, it is the equation of the field itself. So you could also reword what he wrote by saying that the magnetic field itself is proportional to current and inversely proportional to the square of the distance, not just the field at a single point. Now, this is not the whole picture because we are forgetting the integral, which is over all space (or equivalently, just over the relevant region which is the conductor), so that the magnetic field will depend on the shape and size of the conductor. If it's a wire, then it would depend on the length as you said. So it would really be 3 things. Proportional to current and length, and inversely proportional to the square of the distance.

Not entirely. The orthodox interpretation of quantum mechanics basically requires the existence of many worlds. However this isn't the "multiple universes" you are probably talking about because these 'many worlds' are not independent, they would branch from our universe at every instant. If we look at simply the amount of different possible initial configurations for the big bang alone, that could easily give rise to essentially an infinite amount of different realities. As far as we know it may even have been possible for the result to yield different laws of physics in some of these realities. So, it really is a short leap from there to "multiple universes"... I think what you have in mind would be universes that pop into existence independently without a common origin. But is this really so far-fetched now? It seems that time and time again in physics we realize that unless there is a specific law to prevent something from happening it almost always happens, or we eventually find a law prohibiting it. As it stands, we know one universe was able to somehow form, so really in some respects it would be more amazing if this was the only universe. Just because the idea of multiple universes seems more strange, or more foreign, or more difficult to digest, does not in any way imply that it is less likely. Also, who said the existence of multiple universes would mean we would have no big bang? You could definitely still have a big bang with multiple universes.

Hello, I'm new here. Just another lowly physics undergraduate reporting in