Just wondering about the definitions and usage of these three terms.

To my understanding so far, "covariant" and "form-invariant" are used when referring to physical laws, and these words are synonyms?

"Invariant" on the other hand refers to physical quantities?

Would you ever use "invariant" when talking about a law? I ask as I'm slightly confused over a sentence in my undergrad modern physics textbook:

"In general, Newton's laws must be replaced by Einstein's relativistic laws...which hold for all speeds and are invariant, as are all physical laws, under the Lorentz transformations." [emphasis added]

~ Serway, Moses & Moyer. Modern Physics, 3rd ed.

Did they just use the wrong word?

I'd like to create a very rough animation of a wave crashing on a beach. I'm guessing it would have to be a particle simulator, where you code in the forces between the particles and then integrate forward in time. I've done similar things, like simulations of charged particles, but there the forces are pretty straightforward, whereas here I guess I'd have to account for 1) tides 2) gravity 3) water surface tension. These seem like widely different forces acting on different scales. I don't even know where to begin. Any hints or links to papers related to this topic?

illustrated a procedure to forecast the decay rates of isotopes with known long average lifetimes. Lifetimes of the many U isotopes vary from micoseconds to gigayears. F has only one stable isotope while Sn has 10. Can Standard Model principles be used to predict the stability of isotopes and the average lifetimes for unstable isotopes, or can this only be done by measurement?

I need to create an online service displaying latest Kp index.

Where I can take the data?

The data should be in machine-readable format, i.e. text files, XML, or CGI gateways, for instance. No graphical plots!

I found this: http://www.swpc.noaa.gov/wingkp/wingkp_list.txt

Is Est. Kp what I need? I compared the data with plots covering several last days and found that kp values in this file are lower that on the charts.

A-Calculate the speed of a proton after it accelerates from rest through a potential difference of 220V .

B-Calculate the speed of an electron after it accelerates from rest through a potential difference of 220V .

I'm interested in the extent to which quantum physical effects are seen at a macroscopic level. I might get some of the physics wrong, but I think I'll get it close enough that I can ask the question:

Let's sat that we create a bonfire and let it burn until it burns out. As the smoke rises from the fire, turbulence takes over and the smoke particles and steam and hot air all mixed together. By the end of the night when the fire has burned out, the collection of molecules in the system are in some position/velocity X.

My question: Let's assume the multiverse interpretation of quantum physics. How many possible end state superpositions can there be in this situation? Ok, that's imprecise and incorrect because it would actually be an uncountable infinitude of possible end states. How about this: Given the end state that we observed, what percentage of the end state superposition would be "visually" indiscernable from the end state that we observed so that each molecule would be in nearly the same end state across that portion of the multiverse?

Or put another way: Do quantum effects sneak into everyday life fast enough that we can observe them? If we are effected by quantum physics at all, I imagine this is roughly a function of the timescale of the chaos effects.

Schwarzschild singularities are described by the Kantowski-Sachs metric with a contracting S². Of course, T-duality doesn't apply to S². But what about a Kasner-type singularity with two contracting spatial dimensions compactified over a torus T², and an expanding spatial dimension? The T-dual of the torus gives rise to a geometry which is expanding in all spatial directions

There is no tunneling in the case of infinite potential barrier, but there is when we have a finite well. In the classical analog, in the first case we have a particle bouncing between to infinitely rigid impenetrable walls and there is no tunneling, same as the quantum case. But if we have a finite barrier, means we have walls of finite rigidity, say made of cork or something. Then the particle would just break through some of the cork and it's probability of being found further in the cork wall will decay steadily.

I can understand discrete energy levels being a new thing, because they behave like a wave that's confined and not like particles confined, but why tunneling?

Who hasn't heard about the double-slit experiment? It figures in any book of quantum physics. But there is something no one can explain to me : I understand why the light cannot be described only as a wave, but I do not understand why it cannot be explained only in terms of a particle, having some trajectory, following other laws of phyisics we may not know. Usually, every book in which I have tried to look for an answer considers that if it cannot be described as a classical trajectory (which is clearly the case in this experiment), then it is not a particle, that is, a material point. Could it not be a particle following new laws?

By what mechanism do quantum effects become observable in normal life at the macroscopic level? For instance, when two molecules "collide" is the momentum a probabilistic event wherein the end state is not unique? Another example, during a chemical reaction, it is a probabilistic event at the quantum level whether or not any particular molecule within the solution interacts with another molecule?

Why is there a consistent theory of continuum mechanics in which one just consider things like differential elements and apply Newtons laws? Is there a deeper reason for it. Is it the nature of newtonian framework that makes it happen or is it somehow related to nature of bodies (topological spaces with borel measure etc)?

I've been looking for questions about dark matter, and I've read some very interesting answers. However, I desire too look into it deeply.

This is not actually a question. I'm asking the community to recommend interesting references to understanding dark matter and dark energy.

I accept all sort of references: notes, books, scientific papers etc.

Let us assume some background on classical physics, thermodynamics and basics about quantum theory.

Ilya and Anya each can run at a speed of 8.80mph and walk at a speed of 3.70mph . They set off together on a route of length 5.00 miles. Anya walks half of the distance and runs the other half, while Ilya walks half of the time and runs the other half.

A. How long does it take Anya to cover the distance of 5.00 miles? Express your answer numerically, in minutes.

B. Find Anya's average speed. Express Anya's average speed numerically, in miles per hour.

C. How long does it take Ilya to cover the distance? Express the time taken by Ilya numerically, in minutes.

D. Now find Ilya's average speed. Express Ilya's average speed numerically, in miles per hour.

The solar neutrino problem has been "solved" by discovering that neutrinos have mass and they oscillate. So how accurate are now our predictions about the number and types of solar neutrinos that reach the earth?

It is well accepted that quantum theory has well adapted itself to the requirements of special relativity. Quantum field theories are perfect examples of this peaceful coexistence. However I sometimes tend to feel little uneasy about some aspects. Consider an EPR pair of particles light years apart. Suppose there are 2 observers moving relative to each other with constant relative velocity. Let us consider, there are spin detection mechanism at both end for each particle. Now suppose one of the observer is at rest w.r.t. the detector for the first particle. As soon as the detection made, the wave function of the 2 particle entangled system will collapse instantaneously and the second particle must realize a definite opposite spin value. Now due to relativity of simultaneity, the second observer may claim that the collapse of the wave function for the two particle system is not simultaneous. He may even claim that the second particle is measured first. In that case a special frame of reference will be privileged, the frame at which the wave function collapsed instantaneously. This will cause a significant strain on the core principle of special relativity.

I am sure the above reasoning is flawed. My question is where?