Anonymous at Mon, 14 Oct 2024 08:22:52 UTC No. 16430492

>>16430483
The massive the particle the more energy it has. That's all

Anonymous at Mon, 14 Oct 2024 08:26:58 UTC No. 16430496

>>16430483
That it correctly captures a measure of the total, non potential energy of an object when considering that it moving at relativistic speeds can affect its total mass, as opposed that energy merely being captured by the kinetic energy alone. It won't mean anything to you unless you understand how it was derived, what energy is a measure of, and what value it's intended to replace.

I actually hate that this formula is specifically famous, because its simplicity and abstractness makes it hard to understand. Conversely, the Lorentz Contraction formula is much more obviously meaningful and has a far clearer and more intuitive geometric interpretation, but it's not well know in pop culture because its formula just looks more messy.

https://www.fourmilab.ch/cship/lorentz.html

Anonymous at Mon, 14 Oct 2024 08:27:20 UTC No. 16430497

>>16430483
The central topic of special relativity is Poincare symmetry. Poincare symmetry is a simple statement that measurements don’t care about what coordinate frame you choose. So measurements must be Poincare invariants. Such invariants are described using group theory. The classification of invariants for the Poincare group was done by Wigner. He showed that the two fundamental invariants are mass and angular momentum. E^2 - p^2 = m^2 is the invariant expression for the former. The square of the Pauli-Lubanski pseudovector is the invariant expression for the latter.
https://en.wikipedia.org/wiki/Wigner%27s_classification

Anonymous at Mon, 14 Oct 2024 08:28:32 UTC No. 16430499

That mass IS just energy. We live in a universe of energy where mass is just a property of that energy.

Anonymous at Mon, 14 Oct 2024 08:30:30 UTC No. 16430503

>>16430499
massless particles exist and they have energy

Anonymous at Mon, 14 Oct 2024 11:25:20 UTC No. 16430686

>>16430497
Ok, but assume I’m an undergrad and group theory is hard for me, why is e=mc^2 significant

Anonymous at Mon, 14 Oct 2024 11:26:54 UTC No. 16430690

>>16430492
and mass has a lot of energy

Anonymous at Mon, 14 Oct 2024 11:30:24 UTC No. 16430700

>>16430686
I need to know what I can meaningfully measure as an experimentalist. Relativity says that the only things two observers agree on is mass and total angular momentum. The former has to do with linear movement (intertia in Newtonian terms) while the latter is about rotational movement.

If you introduce other symmetries such as gauge, you add charge or something else to that list. Noether’s theorem.

Anonymous at Mon, 14 Oct 2024 11:32:27 UTC No. 16430705

>>16430700
*the only two things about a particle
You can of course introduce auxiliary things that are also Lorentz invariant, but only mass and angular momentum pertain directly to particles themselves.

Anonymous at Mon, 14 Oct 2024 11:37:58 UTC No. 16430716

>>16430503
No they don't exist. Prove to me that photons are particles.

Anonymous at Mon, 14 Oct 2024 11:39:32 UTC No. 16430720

>>16430716
See Wigner’s classification, specifically the massless case. Massless spin 1 particles gauged under a U(1) group are photons. You can derive Maxwell’s equations from these basic assumptions.

Anonymous at Mon, 14 Oct 2024 11:51:46 UTC No. 16430740

>>16430720
lmao

🗑️ B00T at Mon, 14 Oct 2024 11:53:34 UTC No. 16430741

>>16430740
luhmayo

Anonymous at Mon, 14 Oct 2024 11:53:39 UTC No. 16430742

>>16430740
If you don’t like this elegant theoretical explanation, see the photoelectric effect.

Anonymous at Mon, 14 Oct 2024 12:13:18 UTC No. 16430754

>>16430720
Particles don't exist in QM, you are only looking at wavefunctions.

Anonymous at Mon, 14 Oct 2024 12:40:56 UTC No. 16430781

>>16430754
Relativistic quantum mechanics is necessarily field theoretic. What I meant by a “particle” is a quantized relativistic field aka Poincare representation.

Anonymous at Mon, 14 Oct 2024 12:42:00 UTC No. 16430783

>>16430781
*unitary projective Poincare representation

Anonymous at Mon, 14 Oct 2024 12:45:29 UTC No. 16430793

>>16430492
Not true. By this logic photons have no energy. Back to /p*l/ with you

🗑️ PAPAB00T at Mon, 14 Oct 2024 12:50:03 UTC No. 16430799

>>16430793
It's not /p*l/ it's /pol/

Anonymous at Mon, 14 Oct 2024 14:10:44 UTC No. 16430910

>>16430793
Photons have no energy. Things that are affected by photons have energy. I invite you to measure the energy of a photon using only photons.

Anonymous at Mon, 14 Oct 2024 15:55:18 UTC No. 16431173

>>16430700
ok but that doesn't really tell me much about how the result was applied to broaden scientific understand of the world, then and now(and why ordinary people consider it significant, not just theoretical physicists)

Anonymous at Mon, 14 Oct 2024 16:11:19 UTC No. 16431234

>>16430910
Photomultiplier

Anonymous at Mon, 14 Oct 2024 16:29:15 UTC No. 16431301

>photons lose energy when they're refracted by a medium with a lower speed of light
thats whats observed in experiments

Anonymous at Mon, 14 Oct 2024 20:25:28 UTC No. 16431717

It's actually E = mc^2 + AI

Anonymous at Mon, 14 Oct 2024 20:27:05 UTC No. 16431721

>>16431173
>Give not that which is holy unto the dogs, neither cast ye your pearls before swine, lest they trample them under their feet, and turn again and rend you.
Matthew 7:6
I literally told you how. My job here is done.

Anonymous at Mon, 14 Oct 2024 20:28:38 UTC No. 16431726

>>16430700
I thought momentum was Lorentz invariant, not mass hmm

Anonymous at Mon, 14 Oct 2024 20:28:40 UTC No. 16431727

>>16431234
But that uses electrons.

Anonymous at Mon, 14 Oct 2024 20:31:24 UTC No. 16431734

>>16430483
Jewish cousin fucker is smart. Don't question it, goy.

Anonymous at Mon, 14 Oct 2024 20:37:31 UTC No. 16431754

>>16431726
look at a tree while standing. It has zero momentum. Now start walking. It now has non-zero momentum.