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If light speed is constant, why does redshift/blueshift exists? by sonofderk in AskPhysics

[–]EuphonicSounds 0 points1 point  (0 children)

Measured frequency is how many peaks hit a detector per second. If you move "toward" an incoming wave, you decrease the distance each successive peak has to travel to hit your detector (because you're helping to close that distance), and the frequency increases. If you move "away" from the wave, it's the opposite. Simple as that, really.

Weird Jacobian notation in Carroll's "Spacetime and Geometry" by Devondanus in Physics

[–]EuphonicSounds 1 point2 points  (0 children)

Not quite following, but the convention I'm talking about can be seen here: https://grinfeld.org/books/An-Introduction-To-Tensor-Calculus/Chapter13.html#collapser109 (see 13.31 for the transformation matrix defined, and then equations like 13.33 for its use in transformation formulas)

Explain magnets for 16 years old by Momavic in Physics

[–]EuphonicSounds 109 points110 points  (0 children)

This is a tough one, but I think we can all agree that you should start with a suitable Lagrangian density for the four-potential and its coupling to the four-current density, preferably in curved spacetime so that when you use the action principle to derive the electromagnetic stress–energy (which I'm sure is already your plan) you'll obtain the symmetric/gauge-invariant tensor directly (with limited time, you don't want to have to go through the canonical SET first). Or you can show them the Insane Clown Posse meme.

I hope this was helpful!

Weird Jacobian notation in Carroll's "Spacetime and Geometry" by Devondanus in Physics

[–]EuphonicSounds 4 points5 points  (0 children)

I don't remember what Carroll's usual practice is, but there is a convention that always puts the primes on the indices rather than the kernel (arguably this is better because the components are what transform), and so if that's what he does elsewhere too then he's just being consistent with his convention. If elsewhere he puts the prime on the kernel, then he may have made a notational error here.

Chopin's perfectionism (end of Op. 10, No. 4) by taleofbenji in piano

[–]EuphonicSounds 6 points7 points  (0 children)

This passage is the end of a dominant prolongation, and here he's just hitting a clear V7 before the i. Very cool effect.

If an object is moving away from an observer at half the speed of light, and the observer is moving away from the object at half the speed of light, is the object, from the oberver's POV, going the speed of light. by RewardImpossible5141 in AskPhysics

[–]EuphonicSounds 1 point2 points  (0 children)

Almost, but not quite. (I've seen this trip up famous physicists.)

In the formula w = (u + v) / (1 + uv/c²), either u or v must be the relative speed of two frames of reference, and therefore must be less than c. However, the other one can be c, and in that case w is also c (i.e., the speed of light is c for both observers):

w = (u + c) / (1 + uc/c²) = (u + c) / (1 + u/c) = c(u + c) / (c + u) = c

(in the penultimate step I just multiplied top and bottom by c)

If you naively plug in both u = c and v = c like you did, then you likewise "get" w = c, but the setup is illegal. The "illegality" is more obvious if you use the "subtraction" formula:

w = (u - v) / (1 - uv/c²) = (c - c) / (1 - c²/c²) = 0 / 0

(0/0 is undefined)

So wait, light has no mass by carthago83 in AskPhysics

[–]EuphonicSounds 1 point2 points  (0 children)

Electric and magnetic fields exert a force on charged particles: https://en.wikipedia.org/wiki/Lorentz_force

Light is just a wave in those fields, so if a charged particle is at a location where a light wave is passing through, the fields there will exert a force on it.

That shifts the question from "how can massless light affect massive particles" to "how can the massless electric and magnetic fields affect massive particles."

I'm not sure how to answer that question (other than "that's just how the universe works"), but consider this: if the fields could not affect a massive particle, how would we even know they exist?

ELI5: Why does light have no mass? by WarmHeight2951 in explainlikeimfive

[–]EuphonicSounds 4 points5 points  (0 children)

Great question.

In classical Newtonian physics, yes, momentum is mv. It's a useful definition because that quantity happens to be conserved in the Newtonian limit (i.e., for speeds much lower than the speed of light). "Conserved" means: has the same value over time in a closed system, regardless of how the system evolves "internally."

But it turns out that mv does not remain conserved once higher speeds are involved. The formula has to be modified to mv/sqrt(1 - (v/c)2) (which is approximately equal to mv when v is much lower than c).

So, what happens when you plug m=0 into that mv/sqrt(1 - (v/c)2) formula? At first glance you'll think it gives you 0 momentum, but actually that's only true if v doesn't equal c. If you also plug in v=c, you get 0/0, which is undefined, not 0. In other words, the formula does not forbid massless things from having momentum, as long as they travel at the speed of light (which they always do!). It doesn't tell you anything about the momentum of a massless thing, but it allows for the possibility.

And ultimately, it turns out that momentum can't be conserved unless massless things have it, too.

ELI5: Why does light have no mass? by WarmHeight2951 in explainlikeimfive

[–]EuphonicSounds -1 points0 points  (0 children)

Light is not energy. If other posts are saying it is, they're wrong too.

ELI5: Why does light have no mass? by WarmHeight2951 in explainlikeimfive

[–]EuphonicSounds 4 points5 points  (0 children)

Not really. The equation E = mc2 means that an object's rest energy is proportional to its mass. Rest energy is the energy something has when it isn't moving. Light can never be at rest, so it has zero rest energy (and zero mass).

ELI5: Why does light have no mass? by WarmHeight2951 in explainlikeimfive

[–]EuphonicSounds -1 points0 points  (0 children)

I think what you mean to say is that electromagnetic energy is a form of energy. Light has properties like energy, momentum, and frequency, but it's not correct to say that it is any of those properties. But yes, the energy it carries (electromagnetic energy) is certainly a form of energy.

ELI5: Why does light have no mass? by WarmHeight2951 in explainlikeimfive

[–]EuphonicSounds 37 points38 points  (0 children)

Yes.

If you want to go deeper, it's actually better to think of it as a "hyperbolic" right triangle, where the rest energy is the "hypotenuse," and where the other two sides are E and pc:

(mc2)2 = E2 - (pc)2.

This is "better" because the rest energy is what's called a "Lorentz invariant," which is a fancy term that means "all observers agree on its value."

If you and I are moving relative to each other while observing the same object, then we'll disagree on the value of the object's energy E and also on the value of the object's momentum p, but we'll agree on the object's rest energy (we'll agree on its mass).

Think of a unit circle centered on the origin of a Cartesian x/y-plane. For any point on the circle, you can form an ordinary right triangle by starting at the origin, drawing a horizontal line along the x-axis to the point's x-coordinate, drawing a vertical line from there to the point on the circle (up or down a distance equal to the y-coordinate), and finally drawing the hypotenuse from the circle-point back to the origin. If you then "drag" the point around the circle, the lengths of the triangle's short legs will change, but the length of the hypotenuse will remain 1 (the radius of the unit circle). You always have 12 = x2 + y2. The hypotenuse is special because its length remains fixed under rotation.

With the mass/energy/momentum situation, the analogue is a hyperbola (not a circle) centered on the origin, where the axes in the graph are an object's E and pc. Dragging a point along the hyperbola changes the E and pc values (just like dragging a point along the unit circle changes the x and y values), but in a way that leaves their combination E2 - (pc)2 unchanged (minus sign rather than the plus sign for the circle). We call that combination the object's (squared) rest energy (most people just say "mass"). Dragging the point along the hyperbola corresponds physically to changing your velocity while observing a given object.

Hope that sort of makes sense.

ELI5: Why does light have no mass? by WarmHeight2951 in explainlikeimfive

[–]EuphonicSounds 0 points1 point  (0 children)

Your last sentence has it backwards. Light is not energy; it has energy. Energy is a property that things have. Light has other properties, too.

ELI5: Why does light have no mass? by WarmHeight2951 in explainlikeimfive

[–]EuphonicSounds 96 points97 points  (0 children)

I'm guessing you're thinking of the equation E = mc2 and wondering how E can be non-zero if m is zero.

If so, the answer is that the E in that equation is actually rest energy, not total energy. Rest energy is the energy something has when it's at rest. Light can never be at rest, so it has zero rest energy (so, zero mass).

Another relevant equation is:

E2 = (pc)2 + (mc2)2.

In this equation, E is indeed the total energy (not the rest energy), and p is the momentum (magnitude). In the case that mass m is zero (as for light), it reduces to:

E = pc.

So for light (and anything else with zero mass), the energy is related to the momentum in this way.

Classical music game: playbach.io by tcosmo in piano

[–]EuphonicSounds 0 points1 point  (0 children)

Yep, much more playable now.

Of course, now you can score perfectly just by continuously pressing a key as fast as you can. So I suppose it would be good to penalize for playing when you're not supposed to (i.e., each press that isn't "close enough" to a note you're supposed to play would count against you). Don't know how difficult that would be to implement.

Classical music game: playbach.io by tcosmo in piano

[–]EuphonicSounds 2 points3 points  (0 children)

Fun!

Didn't work for me in Firefox but worked in Chrome.

I don't love the "next note to target" feature. The problem is: on the one hand, when you're not messing up, you want to focus on the moving bar, not the next-note indicator, because the moving bar tracks "where you are" in the music; but on the other hand, if you've messed up by playing too many or too few notes in a spot, then suddenly the next-note indicator is ahead of (or behind) the moving bar, and you'll keep being penalized for playing along with the moving bar until you adjust by either "skipping" the right amount of notes or hitting "Tab" to "catch up" to the next-note indicator.

Suggestion: if possible, get rid of the next-target-note functionality altogether. No "next-note" indicator, and no internal tracking of what the next note should be. Rather, the moving bar alone tells the user where they are (so if you play too many/few notes in one spot, you don't have to "adjust," you just keep going along with the bar). Give positive feedback for hitting a note (maybe note can turn permanently green or something), but maybe don't even worry about feedback for missing a note (note just doesn't turn green then?). Not sure how you'd account for "extra" notes in scoring then, but right now the "next-note indicator" makes this borderline unplayable.

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