LAST Problem from the International Physics Olympiad

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Күн бұрын

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@zhelyo_physics Жыл бұрын

The rest of the problem. Hope this is useful! Dimensional Analaysis part: kzbin.info/www/bejne/onm4laCkaNyJeas Black Hole Physics part: kzbin.info/www/bejne/qYe7k3d9draLl9k Hawking Radiation: kzbin.info/www/bejne/opOkqqqii69jiJo

@bhibuthibhusanpatel6210 Жыл бұрын

Thus in nature black hole is in equilibrium with CMB radiatio.

@Zodiaczero2 Жыл бұрын

Absolutely a cool problem! I replaced all the terms given by Olympia by the actual terms in standard physics I found σ = π⁵/60 [(8 kB⁴)]/(c² h³) is Hawking constant T = hc³/(16π² kB GM) is Hawking temperature (in your video is theta) A = (16π G² M²)/c⁴ is the event horizon's surface area after doing the exact process I obtained M* = c³h/(16π² G T_cmb kB) where T_cmb is the cosmic background temperature. it is almost the same as the given problem by Olympia except for the π. Very cool! I found on google the current cmb temperature is approximately 2.726 K. When I plugged this value into the formula, I calculated a mass of approximately 4.5 * 10²² kilograms, which is significantly smaller than that of Moon!

@zhelyo_physics Жыл бұрын

Glad you enjoyed it! Amazing research!

@Zodiaczero2 Жыл бұрын

@@zhelyo_physics Thanks!

@imranmohammed279 Жыл бұрын

HOW DID YOU MAKE IT LOOK SO EASY 😢😢?? I swear, the minute I see differentiation/integration in an Isaac Physics question myself, I know I'm about to spend 2 hours on it

@zhelyo_physics Жыл бұрын

I was just like that when I first came across calculus, don't worry! : ) Also this is the last part of a very long IPhO problem and this part is pretty much identical to the derivation in an earlier part of the problem minus the CMBR. Good effort spending this time on problems, it's a sign you really want to understand them!

@shawns0762 Жыл бұрын

Most people don't know that Einstein said that singularities are not possible. In the 1939 journal "Annals of Mathematics" he wrote "the essential result of this investigation is a clear understanding as to why the Schwarzchild singularities (Schwarzchild was the first to raise the issue of General relativity predicting singularities) do not exist in physical reality. Although the theory given here treats only clusters whose particles move along circular paths it does seem to be subject to reasonable doubt that more general cases will have analogous results. The Schwarzchild singularities do not appear for the reason that matter cannot be concentrated arbitrarily. And this is due to the fact that otherwise the constituting particles would reach the velocity of light." He was referring to the phenomenon of dilation (sometimes called gamma or y) mass that is dilated is smeared through spacetime relative to an outside observer. This is illustrated in a common 2 axis relativity graph with velocity (from stationary to the speed of light) on the horizontal line and dilation on the vertical. General relativity does not predict singularities when you factor in dilation. Einstein is known to have repeatedly spoken about this. Nobody believed in black holes when he was alive for this reason. Wherever you have an astronomical quantity of mass, dilation will occur because high mass means high momentum. There is no place in the universe where mass is more concentrated than at the center of a galaxy. According to Einstein's math, the mass at the center of our own galaxy must be dilated. In other words that mass is all around us. This is the explanation for the abnormally high rotation rates of stars in spiral galaxies, the missing mass is dilated mass. According to Einstein's math, galaxies with very, very low mass would show no signs of dark matter because they do not have enough mass at the center to achieve relativistic velocities, therefore they are not infused with dilated mass. This has been confirmed with galaxy NGC 1052-DF2. A simple way to confirm this would be to calculate the star rotation rates of a large number of galaxies. This would show that all the high mass galaxies would have star rotation rates that defy the known laws of physics and all the low mass galaxies would have predictable star rotation rates.

@shawns0762 Жыл бұрын

The shape of a galaxy is common in nature. From atoms to our solar system, the overwhelming majority of the mass is in the center. The same must be true for galaxies. Where there is mass there is energy. The night sky should be lit up from the galactic center but it isn't. The modern explanation for this is because gravitational forces there are so strong that not even light can escape, even though the mass of the photon is zero. Einstein's answer would be because the mass there is dilated relative to an Earthbound observer. This was the accepted explanation until television and movies popularized black holes in the 1960's. Belief in them gradually came to be despite the fact that Einstein said that they cannot exist and there was no evidence. The reason why we cannot see light from the galactic center is because there is no valid XYZ coordinate we can attribute to it, you can't point your finger at something that is smeared through spacetime. Or more precisely everywhere you point is equally valid. The modern idea that there is some way to take a "picture" of the galactic center is absurd. The interference alone, dilation alone or gravitational lensing alone would make that virtually impossible. As per relativity, an observer would have to exist at or near it's momentum.

@indianbeast644 Жыл бұрын

Sir I also have a doubt apart from this session . Air they say boomerang nebula is coldest thing in universe with 1 kelvin temperature but in ur video u said temperature of black hole is millionths kelvin.Isn't that mean it is the coldest thing.Could this also be the reason the gases of star almost occupy 0 volume thus a black is able to absorb anything with more storage.

@zhelyo_physics Жыл бұрын

Yep Black Hole thermodynamics predicts that temperature, but we have no experimental evidence for this. Mind you in labs on Earth we can get way below 1 K for low temperature experiments. I think the LHC magnets even are at 1.9 K. Hope this helps!

@garano_ Жыл бұрын

Why is the area of event horizon of black hole equal to m^2 G^2 /c^2 ? If Schwarzschild radius is 2GM/c^2 and area of sphere is 4Pi r^2 should not it be A = 8Pi G^2 M^2 /c^4

@zhelyo_physics Жыл бұрын

Excellent question. It is proportional to 1/c^4 in the question as well as written on my board. This is a semi-classical derivation from dimensional analysis as given for an Olympiad problem. It's a pretty neat way of deriving everything except the 8pi factor. I have derived it here: kzbin.info/www/bejne/qYe7k3d9draLl9k

@garano_ Жыл бұрын

@@zhelyo_physics Thank you

@Miftahul_786 Жыл бұрын

Hi isn’t the Stefan-Boltzmann constant given by 2π^5k^4/(15h^3c^2)?

@zhelyo_physics Жыл бұрын

Nope, you can see the derivation in an earlier part of a question if it helps: kzbin.info/www/bejne/onm4laCkaNyJeas Hope this is helpful!

@Miftahul_786 Жыл бұрын

@@zhelyo_physics Ah is it because it is stated that the value of “a” is insignificant and so therefore the 2π^5/15 is just a constant that doesn’t really affect the end result I assume. Because I plugged what you put in for σ and it didn’t give the actual value of the constant.

@DhiraDisrattakit 10 ай бұрын

But is M* is rate of change in mass of black hole is it so you can't not use it to determine a mass

@DhiraDisrattakit 10 ай бұрын

i mean directly

@zhelyo_physics 10 ай бұрын

excellent question, the mass is typically determined by astronomers via many other methods.

@anushjadhav5050 Жыл бұрын

Hi pls try solve jee advanced exam (India) tough questions

@zhelyo_physics Жыл бұрын

For sure, I have already filmed lots! More coming this week.

@maheenghayasrafique5468 Жыл бұрын

Would that mean at thermal equilibrium theres no mass) no gravity of black hole

@zhelyo_physics Жыл бұрын

excellent question. Nope, just the rate of change, dm/dt=0 meaning that it m doesn't change.

@ANUJ.5 Жыл бұрын

I have just completed my high school graduation and I also want to open a KZbin channel in which I will teach Maths, can you give me any tips?

@zhelyo_physics Жыл бұрын

Lots - follow your passion and try your videos to be as useful as possible! Good luck it is very rewarding. Comment with a link to a few videos when you make them!

@ANUJ.5 Жыл бұрын

@@zhelyo_physics defenetaly sir , I will keep physics major and maths minor in my college because i want to become a physicist, I will share with you when I start it , And I also have a question that why dark matter does not interact with everyday life.

@zhelyo_physics Жыл бұрын

wish I could answer that, I'd be a Nobel Prize Winner! : ) All we know sadly is that whatever it is, it does not fit the Standard Model of Particle Physics.

@gogetaroyale1754 Жыл бұрын

@@zhelyo_physics I really appreciate how humble you are and how you help those in need, I’m glad there are people like you in this world, thank you and quite honestly I barely comment, this is probably my first comment since a whole year, Once again thank you

@zhelyo_physics Жыл бұрын

@@gogetaroyale1754 wow thank you so much for the kind words and for following my channel for a whole year, and great to hear from you! Comments like these genuinely make my day, thanks!