121

"Physics breaks down" is a bad way of saying what people are trying to say. It's the sort of thing that sounds cool at first, but then it starts misleading people. What scientists mean is "our best theory produces non-sensical or contradictory results in this situation, so we know the theory doesn't make good predictions there." They do ...


94

Microgravity is used because zero gravity is inaccurate. The ISS, at 400 km, experiences an average atmospheric density of 4 nanograms per cubic meter. It's frontal area varies from 700-2300 square meters. At 1000 m$^2$, the drag force is $ \frac 1 4$N. With a mass around 250,000 kg, that's $10^{-6}$ m/s$^2$, or 0.1 $\mu$g. Hence: microgravity, literally. If ...


50

Let me give an example of a very, very mild case of 'theory breaks down'. Boyle's law is stated as follows: $$ P_1V_1 = P_2V_2 $$ Expressing that for a given quantity of gas the pressure and volume are inversely proportional to each other. At low pressures Boyle's law holds good. The reason that it holds good is that at low pressure the gas molecules take up ...


40

I disagree that you feel centrifugal force. A person in a centrifuge actually feels their reaction to the centripetal force. If you sit in a car that is subject to harsh acceleration, you 'feel' as if you are being pushed back in your seat. There is no force pushing you back- it is simply the result of your inertia.


36

A force is fictitious if it doesn't obey Newton's three laws of motion. Recall Newton's first law: The first law states that an object at rest will stay at rest, and an object in motion will stay in motion unless acted on by a net external force. Mathematically, this is equivalent to saying that if the net force on an object is zero, then the velocity of ...


32

Generally when physicists talk about the universe being finite, they are talking about the existence of an upper bound $R$ on the distance between any two points in space. Such an upper bound could arise in several ways - perhaps the universe has an edge - a boundary which cannot be crossed - or perhaps the universe has the topology of a 3-sphere, and so if ...


32

Infrared region is a part of electromagnetic spectrum that is mostly responsible for the radiative heat transfer in our everyday life. It is expressed by the fact that the peak of the Planck distribution at room temperature lies in the infrared range: Planck radiation has a maximum intensity at a wavelength that depends on the temperature of the body. For ...


27

Don't all the wavelengths of electromagnetic radiation carry energy? Yes. And that photon energy $E$ is given by $$E=h\nu$$ Where $h$ = Planck's constant and $\nu$ = frequency. But not all frequencies interact with matter in the same way. Judging by how Gamma rays are highly penetrating and are dangerous when absorbed by tissues Very little of the energy ...


26

A mollusk is an animal like a clam, oyster, or snail, with a curved shell, or even an octopus without a shell. Einstein is using the word "mollusk" simply to convey the idea that the coordinates need not be flat Cartesian coordinates but can be curved almost arbitrarily like the shell or skin of a mollusk and even that they can deform over time ...


26

As Dale notes, a mollusc is a kind of animal — specifically, one of the many kinds of animals belonging to the phylum Mollusca, which includes many well known types of animals such as slugs, snails, clams and even squids and octopuses, as well as a large number of less commonly known (mostly marine) lifeforms. The name "mollusc" comes from the ...


22

"Physics breaks down" sounds good, but it is confusing. A better phrasing would be "known physics breaks down." Physics attempts to model reality using mathematics. In this sense, physics has no "laws." In the famous words of Captain Barbossa, "They're more like guidelines." However, we have many of these ...


22

For two electrons separated by distance $r$, we have $$F_g = \frac{Gm^2}{r^2}$$ and $$F_e = \frac{1}{4\pi\epsilon_0}\frac{e^2}{r^2}$$ The ratio is $$\frac{F_e}{F_g} = \frac{e^2}{4\pi\epsilon_0 G m^2}$$ Now choose a unit system in which $4\pi\epsilon_0 G = 1$, yielding $$\frac{F_e}{F_g} = \frac{e^2}{m^2}$$ So the constant Feynman is referring to is the charge-...


21

In general, taking the non-relativistic limit for a moving particle is to assume that its velocity is much smaller than the speed of light, i.e. that $$\frac{v}{c}\ll 1.$$ In this limit, the laws of Special Relativity coincide with the laws of Newtonian physics, and (most) relativistic effects can be ignored. For example, in Special Relativity the equations ...


20

According to the basic Newtonian formulation of mechanics, "real" forces come in couples: a force (action) and its reaction acting on the source of the action. Furthermore "real" forces are independent of the used reference frame. Fictitious forces, as centrifugal or Coriolis one, violate both conditions. This is the reason why they are ...


19

The picture of "four forces" comes from particle physics / quantum field theory (it's also kind of a lie but that's a different story). Within this framework, we can think of gravity (at least, perturbatively, when the gravitational effects are small) as being mediated by a massless spin-2 particle. In this sense, gravity is simply another ...


18

Microgravity doesn't mean that the gravitational field is negligible, just that the system in question does not feel its effects due to being in free-fall. The interior of a freely-falling elevator is a microgravity environment - at least until it hits the ground.


18

The phrase "in principle" means that the action being described is hypothetical, usually assuming certain ideal conditions. It contrasts to an action performed "in practice", which refers to actually carrying out the task with all the real-world complications that arise. The use of "in principle" implies that the task may be ...


14

The question has two parts: (1) What does "tree level" mean, and why are tree-level effects said to be classical in nature? (2) Is the Higgs mechanism classical in nature? Tree level $\to$ classical Solving linear differential equations is easy. Solving nonlinear differential equations is hard, usually too hard. If the nonlinearities are small ...


12

What he means when he says it's a fundamental constant is just that you can measure it anywhere in the universe and you'll get (as far as we can tell) the same value anywhere. The ratio of the volume of the earth to the volume of a flea can only be measured here, and also depends on the flea. If it has a name, I don't know it. Rodney Dunning's answer calls ...


12

The object at the non-inertial frame really feels the centrifugal force! So, it is a real force for the object. This is actually incorrect. An accelerometer mounted on the object detects only the sum of the real forces. There is no experiment by which you can “feel” any fictitious force. They only exist in non-inertial frames and their existence or non-...


11

This constant is the ratio between the fine structure constant $\alpha$ and the gravitational coupling constant $\alpha_G$. It is denoted by $N$ in Martin Rees's Six Numbers, but he mostly calls it "the big number". It has pretty important effects on what kind of structures are possible in the universe. Basically it sets the size hierarchy scale ...


10

"In principle" things are things which can easily be derived from the fundamental principles of the model. This tends to get used in situations where the real life application of this is more complicated. As an example from my computer science background, if given a matrix problem $Y=MX$, it is, in principle, possible to solve for $X$ given $Y$ by ...


10

It is called the « Unschärferelation ». Some people prefer that to the english version because uncertainty makes you think that if you made better measurements, you wouldn’t get this uncertainty, which is not the case. In fact, it is better to think about it as relation between the dispersion of the momentums and the dispersion of the positions of a particle,...


10

When cosmologists talk about an infinite Friedmann universe, they mean one with infinite spatial volume, finite and uniform matter density (averaged over cosmological scales), and thus infinite matter. There would be galaxies as far as you care to go, even if you could go far beyond what we call the “cosmological horizon”.


10

In advanced physics circles, "classical mechanics" always means something very specific, and it doesn't mean "Newtonian." Classical means not quantum. Newton's theory of gravity is just one example of a classical theory. Einstein's general relativity is also a classical theory. Any theory which says gravitation is due to the exchange of ...


9

You are not the only person who has problems with the term microgravity. I doubt there is any record of how or why the term was coined. My guess is that NASA introduced the term microgravity because it sounds more scientific that "zero gravity" (which is just plain wrong) but less scary than "free fall", which is accurate but might ...


9

A broad class of Lagrangians is of the form $$L(\mathbf q,\dot{\mathbf q})= \frac{1}{2}\sum_{i,j}g_{ij} \dot q^i \dot q^j - V(\mathbf q)$$ where $g_{ij}$ are the components of a (generally $\mathbf q$-dependent) symmetric bilinear form; this is the "kinetic matrix" to which the other question refers. In this class of Lagrangians, the canonical ...


9

I'll give a brief answer that is somewhat at odds with Chiral Anomaly's answer. When we do quantum field theory we expand about some 'saddle point' of the action, i.e. some place where the variation of the action vanishes and thus we can think of it as classical. When you are playing around with just the Lagrangian in quantum field theory, you are looking at ...


9

"Fictitious" is a loaded term. It is better to use the alternative terms "pseudo force" or "inertial force", which avoid implying that the force is not real. Whichever label is used the key point is that centrifugal force (and, similarly, Euler force and Coriolis force) arises purely from the fact that we are measuring the ...


8

Your intuition is correct. All the points along the axis of rotation share the same motion. In fact, defining the center of mass by means of the rotation axis isn't sufficient. It is possible to define the center of mass as the only point where all possible rotation axis pass through for a freely rotating rigid body. So you have to consider all possible ...


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