elfmotat

That Lagrangian is not Lorentz invariant (which should be obvious given the formula for kinetic energy they used), so I'm not sure why you're trying to use four-vector notation. If an equation doesn't have Lorentz symmetry then putting it in four-vector form isn't going to look pretty! It's also probably not going to help very much. The next thing I should point out is that the second term in the Lagrangian you posted will not contribute to the action, because it's a total divergence (remember the divergence theorem + boundary conditions). I'll use the notation that the guy on stackexchange used. With signature (-+++) we have: [math]\mathcal{L}=\frac{1}{2} \left ( \mu_0 \, \dot{\vec{\eta}} \cdot \dot{\vec{\eta}} - \gamma P_0 \, (\nabla \cdot \vec{\eta})^2 \right ) = \frac{1}{2} \left ( \mu_0 \, g_{ij} \, \partial_0 \eta^i \, \partial_0 \eta^j - \gamma P_0 \, (\partial_i \eta^i)^2 \right )[/math] I'm going to drop the index notation now, because it's a hassle to use when the Lagrangian isn't relativistic. I'm sure you can work it out yourself by analogy if you really want it in that notation. So for the action we have: [math]S= \frac{1}{2} \int d^4x \left ( \mu_0 \, \dot{\vec{\eta}} \cdot \dot{\vec{\eta}} - \gamma P_0 \, (\nabla \cdot \vec{\eta})^2 \right )[/math] To get the equations of motion, we vary the action and set it to zero: [math]\delta S= \frac{1}{2} \int d^4x \left (2 \mu_0 \, \dot{\vec{\eta}} \cdot \delta \dot{\vec{\eta}} - 2 \gamma P_0 \, \nabla \cdot \vec{\eta} ~ \delta \left ( \nabla \cdot \vec{\eta} \right ) \right ) = \int d^4x \left (\mu_0 \, \dot{\vec{\eta}} \cdot \left [ \frac{d}{dt} \delta \vec{\eta} \right ] - \gamma P_0 \, \nabla \cdot \vec{\eta} ~ \left [ \nabla \cdot \delta \vec{\eta} \right ] \right )[/math] When we do the integral over time, we can integrate the first term by parts and set the boundary terms to zero. Similarly, when we do the integral over space we can integrate the second term by parts. What we get is: [math]\delta S = \int d^4x \left (-\mu_0 \, \ddot{\vec{\eta}} \cdot \delta \vec{\eta} + \gamma P_0 \, \nabla^2 \vec{\eta} \cdot \delta \vec{\eta} \right ) = \int d^4x \left (-\mu_0 \, \ddot{\vec{\eta}} + \gamma P_0 \, \nabla^2 \vec{\eta} \right ) \cdot \delta \vec{\eta}=0[/math] The above must hold for all [math]\delta \vec{\eta}[/math], so we find the following equations of motion: [math]\mu_0 \, \ddot{\vec{\eta}} = \gamma P_0 \, \nabla^2 \vec{\eta}[/math]

Are you being pedantic on purpose?

I'd recommend reading Griffiths' Introduction to Elementary Particles before anything else. It gives a general overview of the standard model without much of the theoretical basis. That may sound like a bad thing, but it's probably a good idea to get familiar with the notation and general concepts (Feynman diagrams, etc.) before jumping straight into QFT. For full-fledged QFT, the easiest introductory textbook I've come across is Klauber's. It takes the canonical quantization approach instead of the path integral formalism, so it will seem more familiar to you. He provides the first few chapters for free on his website: http://quantumfieldtheory.info/ . David Tong's lecture notes and video lectures are good as well, though he doesn't go into nearly the detail that Klauber does. He also uses the canonical quantization approach. You can find the notes here: http://www.damtp.cam.ac.uk/user/tong/qft.html , and the videos here: https://www.youtube.com/watch?v=8yplCob7_Ck&list=PL1C5310BB35555A1C . More advanced treatments of QFT usually make use of the path integral formalism though, so you'll probably want to eventually learn that. Zee's book is probably the easiest introduction to path integrals, though he can be a bit hand-wavy (which I personally can't stand). The first chapter is available for free: http://pup.princeton.edu/chapters/s7573.pdf . He also has a video lecture series, though it doesn't go into any great depth: https://www.youtube.com/watch?v=_AZdvtf6hPU&list=PLPtYfNT-VhvlB7kwjoHTqkHmhDibbl6Dr&index=1 . For a more formal and advanced treatment of QFT that goes into much more detail, you'll probably want Peskin and Schroeder's book. It goes through both the canonical (at the beginning of the book) and path integral (for ~ the latter 2/3 of the book) approaches. I wouldn't recommend it to a first-timer though. Yes, gauge symmetry gives rise to charge conservation.

I'm afraid I don't see any equations.

I'm not really sure what you're asking us to do. Could you elaborate on the puzzle?

He said "quantify." We know what "clumpy" means qualitatively.

Agreed. The math itself is not ambiguous - everyone agrees that the particle's state is a superposition of eigenstates, but what that actually means is up for interpretation.

I believe you're thinking of the ending to Men in Black:

Indeed. Pressure is not the same thing as density, the latter of which accounts for buoyancy. The pressure on the surface of Titan is about ~1.5 atm, which is pretty much what you'd experience in ~20 ft. of water like the OP says. However the density of Titan's atmosphere is ~4x the density of Earth's, meaning it's only ~0.5% the density of water. That means the average person would experience a buoyant force of ~0.75 lb., which is completely negligible. You'd sink like a rock, just like on Earth!

That's just your interpretation; you're making claims about what it's doing when nobody can see it, which is the definition of "untestable." There is absolutely no way to test whether or not it "really" does go through both, even in principle, without destroying the interference.

I'm not sure I understand. When we look to see which slit it goes through we find it only ever goes through one or the other. What it's doing before we measure it is untestable by definition.

I don't think there's anything wrong with saying "don't ask untestable questions." Questions like, "is the electron really in multiple locations at once before we measure it(?)" seem like exactly the sort of thing the 'shut up and calculate' philosophy advises against.

That's a good point. But there are also members that post in Speculations who have already typed up their ideas into a viXra (or similar) "pre-print." So there's no danger of stolen ideas because the timestamp on the archive is there for everyone to see.

Exactly!

Please tell us what that model is. We can't discuss its validity unless we know what its predictions are.

An observer in QM is really pretty much anything that interacts with the system you're trying to study. A camera constitutes an observer because many many photons must interact with it to form an image.

You don't seem to understand what the words "relative to" mean. You can't just say, "Bob is moving fast." You have to say, "Bob is moving fast relative to Alice." Why do we need this extra information? Well, the speed of Bob relative to Bob is zero! If Bob tosses a ball, the speed of Bob relative to Alice is not the same as the speed of Bob relative to the ball, etc. You can't just say that a plane is moving at 400 mph, you need to specify what the plane is moving relative to. This is precisely where your confusion is coming from. There is no such thing as absolute speed, only speed measured relative to something else.

You're making up nonsensical equations. The equation I posted applies exclusively to inertial observers with no gravitation. What you're posting has nothing to do with either special or general relativity.

That's interesting, but I'm looking particularly for threads in the speculations forum.

What does that mean? What do you mean by "we observe only spherical surfaces." I'm looking at my computer screen at the moment, and it certainly doesn't look like a sphere.

No, I'm genuinely curious. I sometimes enjoy the speculations section too (for the same reason I enjoy looking at viXra papers), but that doesn't mean I put any stock into it. Sounds like the type of thread we all wish happened more frequently.

Out of curiosity, I've been doing a bit of searching in the Speculations forum for anything that could be considered a "good" idea by mainstream physics. Really, I'm just looking for anything that isn't obviously nonsense. Unfortunately my search was unsuccessful: I couldn't find any. If anyone remembers any old threads that seem to fit my criteria I would be very much grateful. **Note: I'm unsure if this is the appropriate section for this thread. If not, please move it .

"What is the velocity of an electron(?)" is not a well-defined question in QM in the first place. Electrons do not have definite momenta.

I definitely don't think you're anywhere close to having "enough knowledge to be dangerous."

What are your thoughts? Imagine you're in a constantly accelerating train. What would it feel like?