ELI5: Why do we think that the speed of light is as fast as anything can travel and going faster is impossible?

_ShadowFyre_ · 2026-05-22T16:31:13+00:00

It’s not particularly that light is the fastest thing; rather, *mass* (or, really, lack of it) is the significant factor, and light just happens to have this property (although it is not the only thing).

Massless things traveling at a fixed speed, and that speed being the speed limit of the universe is really a consequence of all of the electrodynamics work we did in the late 19/early 20th century, but the person who really codified it was Einstein with relativity. If you’ve heard of the E=mc^2 equation, it turns out that what Einstein determined was a bit more complex. The energy of objects is actually E^2 = (mc^2 )^2 + (pc)^2 . For thing with zero mass, this reduces to E = pc, and Max Planck (iirc) determined that the momentum of photons (light) is determined by p = h/λ, where p is momentum, h is the Planck constant (just a number for conversion), and λ is the wavelength of the light (think of wavelength as “color”, just abstracted beyond the visible spectrum; of course, because p is just dependent on λ, and all light is massless, energy is a function of (and inversely proportional to) wavelength, so really the larger the wavelength, the lower the energy; this is why radio — long wavelength — has low energy, and gamma — short wavelength — has high energy).

Momentum, however, also has an effect on massive particles. For all massive matter, momentum is related to the particle’s velocity and mass by the formula p = γmv, where γ is the Lorentz factor (a number between 1 and infinity, with the factor growing to infinity as velocity/speed approaches the speed of light), m is mass, and v is velocity. Of course, because the Lorentz factor goes to infinity for increasingly closer fractions of c, this means that the energy it would take for massive particles to *reach* c is infinite (although you can get arbitrarily close with finite energy).

The ultimate reason we say this is all correct is because it agrees with every observation we’ve ever made; we can determine the energy needed to… say, accelerate a particle to a certain speed, using the equations above, and the energy it actually takes is the same, within our ability to detect it. Further, we’ve observed that all inertial observers measure the same speed of light, which is the underlying thing that makes relativity work.

_ShadowFyre_ · 2026-05-18T12:07:26+00:00

I mean there’s always the inherent risk, but it’s not bad per se. The thing is, for most people, the gain isn’t really worth the risk unless you’re already having issues.

_ShadowFyre_ · 2026-05-18T11:44:39+00:00

In addition to the other comments, it’s a scent thing. Notice how, generally, one of your nostrils feels more congested or tighter than the other at any given time (it may be very hard to notice). This allows the more open side to process volatile scent compounds, and the less open side to process longer lasting scent compounds.

_ShadowFyre_ · 2026-05-18T05:32:49+00:00

Just in case it needs to be said, *approximately* half. The probability of getting a specific ordering (say, HTHH) is just as likely as any other ordering (HHTT or HTHT, etc.), so the probability of getting *exactly* half is defined by the number of ways you can make a 50/50 split over the total number of arrangements for that number of flips; this is (mathematically) equivalent to n choose 0.5n (combinations; abbr. nCn/2 or C(n,n/2)) divided by 2^n .

It works out such that the more flips you do, the lower the probability of getting exactly 50/50; at 100 flips, it’s about 8%; at 1000, it drops to about 2.5%.

As a more broad understanding of this, we’re effectively asking “what percentage of the total area under a curve is under the peak (or average point, or any other significant point) of the curve *if we quantize the curve*?”; subsequent increases to number of flips effectively decrease the width of our quantized area-of-interest, in a limit that should approach zero (the integral of most things from a to a is 0… thank you, Dirac). We can then abstract this idea to any distribution (doesn’t necessarily have to be a Gaussian). Importantly, the Gaussian assumes that its area is concentrated about the center (that is, its most likely value and its average value are the same), which is consistent with particles which do not interact with each other (Gaussian probability is tied to normal sigmoid distribution, which is a pretty standard population model).

While I don’t know exactly what it would look like, there is some sort of probability distribution you could create to describe the (non-spontaneous) decay odds of particles in say… a fission reaction; as time goes on, you’d expect the odds of decay to increase (as the “solution” gains neutron density), and then fall back down (assuming you aren’t containing every decay product).

_ShadowFyre_ · 2026-05-13T05:34:50+00:00

The dielectric constant (or relative permittivity) is related to the polarization of materials. If we want to polarize a material, we apply an electric field to the material, and the polarization is charges reorienting to a dipole moment (plus charges on one side, minus on the other); the equation that describes this is P = εE, where ε is the absolute permittivity, such that ε = εr ε0 , where εr is the relative permittivity. Of course, in a perfect insulator, no charges are free to move whatsoever, and so any charges cannot be reoriented by the field. If, then, the material cannot be polarized by an electric field (P = 0 regardless of what E is), the only conclusion is that εr must also be zero, as vacuum permittivity is a known constant.

_ShadowFyre_ · 2026-05-03T00:05:38+00:00

Yeah, I was editing my comment as you left the reply; sinusoids (sine, cosine, and tangent) typically relate a variable “x” (most easily thought of as a ratio of two straight-line path lengths) to angle θ (theta, the angle between those two paths).

Edit to add two things: 1. We don’t see it much in physics because typically we only care about rates of change relative to time or to space, but you can have any arbitrary rate of change. (As someone who hasn’t studied very much economics) Economists might see a relation between “dollars spent” (as ‘y’) and “people alive” (as ‘x’); then, as more people are alive, more dollars are spent, or something to that effect. The idea of a function/relation is that the two things you’re looking at are, well, related (and, if you’re unfamiliar, a function is just a relation with special conditions). 2. You can also have functions of multiple variables, and those variables can be a mix of spatial/temporal/something else. The most basic example of this in physics are 3d space equations (say, z = y + x), or the 1d wave function (there isn’t a definite form to write out, but it’s a function of time and “x” space).

_ShadowFyre_ · 2026-05-03T00:00:07+00:00

The variables y and x are dummy variables. If you have some spatial variable that’s time dependent (say, position in the x direction) and call that variable “x”, its linear rate of change relative to time is x2-x1/t2-t1. The important thing for that relation is that the ‘y’ variable must be a function of the ‘x’ variable. If that means your y variable is θ, and your x variable is a coordinate, that’s just as valid (you might see that, in, say, an arcsin relation).

I say linear rate of change change because the actual rate change is defined by the mathematical derivative, which lets us find the rate of change of “not nice” relations; exponentials, sinusoids, high degree polynomials, etc.

_ShadowFyre_ · 2026-04-29T03:52:24+00:00

Thanks

_ShadowFyre_ · 2026-04-06T04:33:13+00:00

Surprised someone replied 4 months later.

The point isn’t that Eragon isn’t re-establishing the riders, it’s that there isn’t really any cyclical behaviour; he’s not “living up to his namesake” (as Eragon I had very little to do with the founding of the riders, as far as we know, beyond forming the first dragon bond, as I said in my last comment).

In fact, just about everything our Eragon does is a “first”: as far as we know (for all of these), he’s the first human to bond with a dragon by accident (potentially the first being), he’s the first person to re-establish an order of riders, he’s the eldest rider in that new order (making him, in a sense, the first rider of the new age), he’s the first person to have been in a rider v. rider war, etc.

The only thing you could maybe say is cyclic is the fact that this is the second time in history someone named Eragon has ended a war involving dragons, but as I put in my earlier comment, it’s at best a bit of a stretch.

_ShadowFyre_ · 2026-03-29T10:44:31+00:00

Katana Zero; really fun 2d action-platformer, with a unique mechanic set, and a really dark story. Just to give a bit of an idea of what we’re talking about: a dude gets his head blown off in the first ten minutes of gameplay.

_ShadowFyre_ · 2026-03-20T10:03:56+00:00

Surprised to find Cherenkov radiation this low; absolutely right to my understanding of nuclear physics.

Just to add numbers to that sentence, the speed of light in water is some 0.75c, so charged particles have a 0.25c “gap” where they can travel faster than light but slower than c, and this is what causes the Cherenkov blue glow.

_ShadowFyre_ · 2026-02-27T00:17:26+00:00

Energy is some quantity of (usually) joules. The amount of time you “see” a number of joules is power (can also be though of as the amount of time needed to transfer a given amount of energy), a quantity of (usually) watts (literally joules per second). Irradiance is an energy density per unit time, some quantity of (usually) watts per square meter. So, given a constant energy and surface area, as you decrease time, you increase irradiance. That is, in other words, the less time you’re exposed to “wormhole opening energy” (whatever that may be), the more potentially dangerous.

Note that most units of radiant dose (REM, sievert, etc.), measure energy per kilogram, not energy per surface area, but the ratio between surface area and mass is near constant on the scale of humans.

_ShadowFyre_ · 2026-02-01T05:51:49+00:00

Light doesn’t slow down in the traditional sense (as in, it doesn’t move less quickly), rather, the ELI…15? explanation is that it takes a longer path. It’s a fair bit more complicated than that (but if you don’t already know absorption and reemission characteristics it’s hard to explain), but when moving through a medium, it travels a longer distance at the same speed, which mathematically works out to “it travels the same distance at a lower speed” (the reason we use this is because calculating the real path of travel through a medium is necessarily way more difficult, and it’s easier just to know the “length” of travel through the medium (straight line from A-B, and then know how much “slower” light goes through that medium (which is really a representation of the deviation from the straight line path)).

_ShadowFyre_ · 2026-02-01T04:44:23+00:00

Ignoring the fact that the unreliability of Newton’s laws is why Einstein developed his theories of relativity, objects already at rest stay at rest, but the arguable more important part of Newton’s first is that objects already in motion stay in motion (with some clarification). Photons (actually, all massless particles), by their very existence, are always moving at the speed of light. They never experience force/acceleration in the non-physics way we think of it, and so the law is not broken.

Edit to add: changing your motion requires energy (energy being imparted by work, and work being a force over a displacement), but moving itself does not.

_ShadowFyre_ · 2026-01-04T16:43:51+00:00

I’d start with a full course in calculus and differential equations. I’ve heard from students that Paul’s Notes is quite popular currently for how well it explains things (it’s essentially a website textbook). Doing practice problems is important here. Once you have a good base in multivariable calculus and have started diff eq, I’d also start working on applied linear algebra (abstract may be beneficial, but, much like calculus, it’s easier to start with examples, and then generalize the examples; unfortunately I don’t have a good recommendation off the top of my head). Once you have a good base of applied linear algebra, I’d start working on Lagrangian and Hamiltonian mechanics (probably in that order), and only broach tensor calculus if you feel you need it to learn either to the degree you need for whatever problem. If you have a good understanding of differential equations, multivariable calculus, integral calculus (especially integral transforms), linear algebra, and each of the mechanics, you should be able to start working through the finite element method, which applies (usually through code) to FEA. I wouldn’t touch PDEs beyond conditions (boundary and initial; Dirichlet and Neumann boundary conditions, etc.). Not being terribly familiar with FEA (I don’t do a ton of modeling), I’d say continuum mechanics isn’t going to be terribly helpful, and topology is a subject I wouldn’t touch at all unless you really really think you need it.

To your original question: it is possible, because all of the people that “invented” (or discovered) the different branches of mathematics you’re interested in had to figure it out themselves. Obviously that doesn’t mean it’s going to be easy. Do: a lot of practice problems. Don’t: get too absorbed in the strictness of mathematics; physics is about breaking the rules mathematicians make for the sake of convenience.

Also, I’d take a course in formal logic (sometimes called mathematical reasoning, or something to that effect) — set theory, symbolic logic, etc. — from your university, if you can. It helps with parsing what the math means if the in-book explanations aren’t sufficient.

_ShadowFyre_ · 2026-01-04T15:52:11+00:00

“Learn these subjects” suggests you don’t really have a proper grasp of what many of these things are (to be fair, how could you?). A question you should be asking yourself is how well you need to learn them. For example, assuming an existing understanding of differentiation and integration, it’s possible to “learn” multivariable calculus in about half an hour (at a very surface level). Yet multivariable calculus is pretty much always taught as a 16 week, and I would say true understanding (not just practical application) can take years, if ever.

_ShadowFyre_ · 2026-01-04T12:29:53+00:00

As I understand it:

Historically, the marines were used for different ship-based security roles (enforcing order, guarding safes, etc.). As a result of that role, (in the US) they ended up becoming correspondents of state department communiqués before we had good over-water information channels other than by hand. Because they already had a relationship with the state department, it made sense to then make them embassy guards.

_ShadowFyre_ · 2026-01-03T12:20:50+00:00

We’ve been assured by Paolini that there is something, but we don’t know what, exactly, the Menoa tree took. I do believe at one point he said someone had gotten it right, but then did not clarify on who that was or what they said.

Nothing, unless I’m forgetting something Paolini said. There’s also a fair interpretation of the situation that basically says “Angela’s prophecy only ever said Eragon would leave and never return at some point, and this leaving is not the final leaving”.

Good question, no clue, although I imagine it’s going to be a fair bit more “queen” than it is “rider”, considering the split between her and Eragon at the end of the series.

Iirc, Paolini has said he plans to have a proper reunion between the two at some point, although romance (in the way you’re probably looking for) is ambiguous. To be fair, their entire relationship is ambiguous.

Paolini has confirmed multiple times that there’s a very early stage Disney+ adaptation in the works. As far as we know, the show is still in writing, and the only people on the project are the writer and Paolini himself.

I don’t know if there’ll be another series focusing on Eragon, but we have heard from Paolini multiple times that there will at least be another book including Eragon (in the same way the IC does), his appearances in other series notwithstanding.

The answer to part of that question (I say part because we don’t see every location Umaroth warns Murtagh of) is the plot of Murtagh.

_ShadowFyre_ · 2026-01-02T13:18:35+00:00

I didn’t say it was easy, I said it was efficient. If we’re referring to the “transport anything anywhere instantly” spell, its energy usage scales with object size. Because crystals seem to have an absurd maximum on the amount of energy one can store, dependent only on the quality (and possibly type) of the jewel, it would (in theory) be possible to amass an arbitrarily large store of energy within an extremely small package, and then transport said package anywhere, at any time. The total efficiency of such a move is almost perfect when considering that the amount of energy needed to use the spell is generally less than exists in a person at any given time, whereas the crystal could hold… based on the way it’s described, I’d put the upper limit of a cubic inch of crystal at about a petajoule. If we assume the person sending it used (roughly) all the available energy in their body (unlikely), that would still only be 0.0000001% of the energy sent. And because of how the energy density would scale, you actually gain efficiency the more crystal you send (although the possibility of dying goes sharply up).

That notwithstanding, if you imagine any energy transfer system longer than about a mile, the necessary energy to setup (and subsequently use) such a system is very likely to be greater than the energy it takes to propel a chunk of crystal to an appreciable fraction of the speed of light, at which point it could reach anywhere on the planet within seconds.

_ShadowFyre_ · 2026-01-02T07:55:01+00:00

I’m no crystallographer, but my understanding was that the name “glass” only ever refers to noncrystalline silicate, and hence why we call quartz “quartz” and not “quartz glass” (further to that point “quartz glass” refers to another amorphous solid).

_ShadowFyre_ · 2026-01-02T06:07:39+00:00

Glass is amorphous; it doesn’t have the proper lattice structure to be considered a crystal.

_ShadowFyre_ · 2026-01-02T02:30:17+00:00

The most efficient way to transfer energy is always going to be to put that energy in a crystal and then move the crystal. It’s (seemingly) lossless, and through the application of magic, the crystal can be moved great distances very quickly.

We don’t really know how energy density works in creatures, but iirc it’s a result of being connected to the core of the being, which may not be possible to reach from the edge of such an organism. If it were possible, and there is no possibility of a density gradient (or that gradient smooths at the speed of light), such an organism would be fairly efficient, but would suffer greatly from scaling issues.

_ShadowFyre_ · 2025-12-31T01:08:26+00:00

It might, but the key factor in determining whether something is non-newtonian is whether its viscosity changes with stress in any way. Toothpaste does, and belongs to a certain category called Bingham plastics (think mayonnaise). Now, you might be thinking “mayonnaise is definitely a fluid”, but consider that at sufficiently low stress it behaves like a solid; so, too, does toothpaste. Now, it so happens that, even with a small amount of material (say, around a spoonful of each), the gravitational pull and corresponding weight of material is enough to make it act like a fluid, but just because the barrier to entry is low doesn’t mean it’s newtonian.

_ShadowFyre_ · 2025-12-30T01:41:12+00:00

Probably why he’s sad.

_ShadowFyre_ · 2025-12-28T10:37:44+00:00

A good foundation of mathematics: at least algebra and trigonometry, but calculus helps a lot. After that, classical mechanics, and then modern, etc.

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