How does Mercury's orbit prove General Relativity?

Ғылым және технология

When Einstein proposed his new theory of gravity in 1915 - his theory of General Relativity that massive objects curve space - he came up with three ways of testing his theory. One of those ways was whether it could properly predict the orbit of Mercury, which up until then, no theory of gravity had been able to do. So why is Mercury's orbit so odd?
Measuring the speed of light with marshmallows in a microwave: physicamechanica.wordpress.co...
Galle (1846) - articles.adsabs.harvard.edu/pd...
Le Verrier (1859) - articles.adsabs.harvard.edu/pd...
Swift (1878) - articles.adsabs.harvard.edu/pd...
Einstein (1915) - www.kritik-relativitaetstheor...
Schwarzschild (1916) - articles.adsabs.harvard.edu/pd...
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👩🏽‍💻 Dr Becky Smethurst is an astrophysicist researching galaxies and supermassive black holes at Christ Church at the University of Oxford.
drbecky.uk.com
rebeccasmethurst.co.uk

Пікірлер: 2 100

  • @DrBecky
    @DrBecky4 жыл бұрын

    Whoops! Seems like I misspoke about how GPS works towards the end of this video. Your phone doesn’t send a signal to satellites, it only receives them. Thanks to everyone who pointed this out in the comments already 👍 Also to those who pointed out perihelion is Greek not Latin - but we’ve always known language isn’t my forte 🤪

  • @calinculianu

    @calinculianu

    4 жыл бұрын

    You also mis-spoke about the origin of the word "perihelion". It's 100% a Greek word. If it were Latin it would be "proxisolis". It's not Latin.. Becky. :)

  • @tonyelsom6382

    @tonyelsom6382

    4 жыл бұрын

    Who cares?..certainly not me 👍

  • @fazergazer

    @fazergazer

    4 жыл бұрын

    A rose by any other name Would smell as sweet

  • @Gpcas9

    @Gpcas9

    4 жыл бұрын

    @calin To celebrate this information I'll open a can of "perri air" for you too ;-)

  • @Markle2k

    @Markle2k

    4 жыл бұрын

    @@tonyelsom6382 "Who cares? " Literally every person who uses GPS and cares or wants to know how it actually works. "who cares?" is like saying "who cares that you don't actually project light out from your eyes to illuminate the world?"

  • @thestonewall30
    @thestonewall304 жыл бұрын

    Einstein just drop the mic on the end of that paper

  • @DaveRoberts308

    @DaveRoberts308

    4 жыл бұрын

    Michael Steffan Exactly. “Peace, out, bitches.” 🤣

  • @pianoraves

    @pianoraves

    3 жыл бұрын

    One of the biggest f*ng micdrops in history and noone got it. And i still don't get it 100 years later.

  • @elwoodzmake

    @elwoodzmake

    3 жыл бұрын

    @Enter the Bragn’ Spacetime is just a result of Gravity. Frankly, we need it, you know to wake up and stuff...

  • @elwoodzmake

    @elwoodzmake

    3 жыл бұрын

    @Enter the Bragn’ you're not entirely wrong, but you don't understand why, that's the funny part. :D

  • @jjsamuelgunn1136

    @jjsamuelgunn1136

    3 жыл бұрын

    Blackhole: Hold my beer

  • @chrisray1567
    @chrisray15674 жыл бұрын

    Science history is my favorite kind of history. Thanks for taking the time to make these types of videos. I love them!

  • @Reziac

    @Reziac

    4 жыл бұрын

    It's actually a really good way to understand the science, since we get to see it develop from nothing to the where it is today.

  • @Reziac

    @Reziac

    4 жыл бұрын

    No, not much patience for reading about it, would rather see it like this. But sounds like a good book, I'll keep an eye out for it, thanks.

  • @chrisray1567

    @chrisray1567

    4 жыл бұрын

    @4one14 I have read it. Actually, I think I listened to it as an audio book. Either way, it was excellent and is a book that I often recommend to others as well.

  • @ejmtv3

    @ejmtv3

    3 жыл бұрын

    except the science history of Medicine which is a very dark and scary journey

  • @jwaustinmunguy

    @jwaustinmunguy

    2 жыл бұрын

    I love astrophysics but how can it be better than the ncessant beheading of kings and queens in English history?

  • @carrickrichards2457
    @carrickrichards2457 Жыл бұрын

    I've heard this put as "Einstein destroyed the planet 'Vulcan' with just the power of his mind. Le Verrier found Neptune with just the power of his!". I do love how the film 'Einstein and Eddington' shows how the proofs were worked out. It gives Planck his proper credit too. Thank you for bringing this to life

  • @craigfowler7098
    @craigfowler70989 ай бұрын

    Shows what a genius Einstein was. Very interesting and detailed overview of his theory and first proof.

  • @Fenristhegreat
    @Fenristhegreat4 жыл бұрын

    Nothing could have prepared me for the Avril Lavigne smash cut.

  • @nathanlewis42

    @nathanlewis42

    4 жыл бұрын

    How about a warning that it was coming?

  • @Fenristhegreat

    @Fenristhegreat

    4 жыл бұрын

    I wouldn't have believed it.

  • @xilnes7166

    @xilnes7166

    4 жыл бұрын

    yup but its so avril...

  • @JDAxonn

    @JDAxonn

    4 жыл бұрын

    Not even reading this comment from the start prepared me for it...

  • @ChristianStran

    @ChristianStran

    4 жыл бұрын

    Hahahahahahahahahahahah 😂🤣

  • @murasaki848
    @murasaki848 Жыл бұрын

    16:21 For the younger viewers, the song she's singing is "Where You Lead" by Carole King, from her Tapestry album (1971). Carole King was an awesome songwriter, and that album won 4 Grammys including Album of the Year, as well as going 14x platinum by selling 30 million copies and having covers done by other singers such as James Taylor ("You've Got a Friend") that also charted, some that were released previously but Carole King co-wrote (Shirelles "Will You Still Love Me Tomorrow").

  • @camurgo
    @camurgo4 жыл бұрын

    Just found your channel. Loved it instantly. Everything so well explained! Keep up the good work!

  • @jimmarshall2757
    @jimmarshall27574 жыл бұрын

    Hi Becky, four years ago I had a stroke and lost 54 years of astronomy knowledge, after a lot of work I have regained quite a large amount of it , can I say this has been one of the best tutorials I have listened to in years. Nice clear speech at an easy pace in simple terms. I do have one question, whenever we talk about space-time it is always shown as a funnel in a flat plain, a spherical object in space-time is more like a ball in a block of jelly, it's effect on space-time is more liken to a field around any object with mass. Or have I forgotten something again. Once again, love your talk, more please.

  • @DrBecky

    @DrBecky

    4 жыл бұрын

    Jim I’m so glad I could help you reconnect again. All the best for your continued recovery. Your right that all the visualisations we see are in 2D rather than the 3D it should be. I love your metaphor of a block in jelly! Unfortunately representing that with the curvature clearly on a 2D image is very difficult

  • @jimmarshall2757

    @jimmarshall2757

    4 жыл бұрын

    Dr. Becky, thank you for your reply, when I started to relearn I started to remember the thing I had learnt at school in the 60s and 70s, I went back to Carolyn Crawford's lectures and lost the plot, I realised most of the thing learnt at school where Newtonian and not Einsteinian,, 😂😂😂 I have so many question on Space-tine, dark matter, dark energy, the expansion of the known Universe. May I contact you when I get stuck or hit a wall. Once again thank you so much for your reply. 👍

  • @spvillano

    @spvillano

    Жыл бұрын

    @@jimmarshall2757 it'd be much easier to visualize if we had full holographic moving displays. Well, for everyone else, that @#*! cataract would just make me see double... :/ I had the other eye done a while ago, they used an uncoated synthetic lens and now I can actually perceive a fair bit into UV. Although, I did consider holding out for a full body transplant...

  • @partymetroid

    @partymetroid

    Жыл бұрын

    See "A new way to visualize General Relativity" by ScienceClic English

  • @dimasgomez

    @dimasgomez

    Жыл бұрын

    Man, I will avoid complaining to be lazy or late to studies I lost during the years. If you can go through it all again, also can I learn whatever I haven't yet in this life. You inspire me, sir. 🙏

  • @BillMSmith
    @BillMSmith4 жыл бұрын

    Science science science science science SPIROGRAPH! science science science science science science science science MARSHMALLOWS! science science science... This is why Dr Becky is a great communicator. There's always going to be some fun thrown in.

  • @davidtoddhoward
    @davidtoddhoward4 жыл бұрын

    Excellent video on Mercury's importance in proving General Relativity.. Really cleared up some details for me. So glad I found your channel.. Thanks so much! 😀

  • @DrBecky

    @DrBecky

    4 жыл бұрын

    Glad you enjoyed it Todd 👍

  • @hjsalvage2

    @hjsalvage2

    4 жыл бұрын

    RELATIVITY was created because NO EXPERIMENT EVER DONE WAS ABLE TO PROVE THAT EARTH IS IN MOTION. RELATIVITY IS TOTAL HARRY POTTER 🐂🐂🐂🐂💩💩💩💩🤣🤣. N MERCURY IS ILUMANARY Watch "Stars are NOT what you think they are! Expectation vs. Reality" on KZread kzread.info/dash/bejne/nqF2yo-Qit3Qeco.html

  • @hjsalvage2

    @hjsalvage2

    4 жыл бұрын

    Satellites SUPPOSEDLY fly at 17500 or faster. So before a signal could receive or send. It would be out of range. So satellites actually float. Look up satellite falls in farm..an sec. GPS is ground based

  • @truthislam6481

    @truthislam6481

    4 жыл бұрын

    @@hjsalvage2 Beware of KZread science! Oops sorry, Dr. Becky!

  • @samuelhmullins2170

    @samuelhmullins2170

    3 жыл бұрын

    I like @Dr. Becky too, I'm just not feeling her explanation yet. I simply need to watch other/more teachings, and hope she'll understand. She could almost start a religion, as fine as all that is.

  • @JustMeinYoutube
    @JustMeinYoutube4 жыл бұрын

    Seems KZread has improved its recommendations algorithm! I just subscribed! Thank you Dr. Becky for your excellent videos! And you sing beautifully as well 🙂

  • @GameChanger-qi1uo
    @GameChanger-qi1uo4 жыл бұрын

    As much as I love learning from you, your out takes at the end and your singing makes the whole video seem like a perfect circle. Complete!

  • @keppela1
    @keppela14 жыл бұрын

    Thanks! Getting clear on the connection between Mercury's orbit and gen. relativity has been on my bucket list for years!

  • @AdamBurstein
    @AdamBurstein3 жыл бұрын

    Love your videos. Thanks so much for doing them and for making physics accessible to the masses.

  • @steveokay8810
    @steveokay88103 жыл бұрын

    This is the first time I feel I've gotten a complete walkthrough of what the whole problem with Mercury and how it was resolved esp. WRT the speed of light. Lots of other pop-science books, videos, TV episodes, etc. always wash over some bit of it and are just like "Oh, there was an error and it couldn't be resolved because Newton was wrong and then along came Einstein and fixed it..." So, thanks for getting in those minor but very important details.

  • @Joe-pz7cg
    @Joe-pz7cg4 жыл бұрын

    I just stumbled onto your channel and I love it! If I can make a request, can you do a video on the lagrange points? I can find a few that describe where they are and that L4 and L5 are stable, but not why. I know very basic orbital mechanics (thank you kerbal space program) and I'm not seeing the math. Please don't stop making videos. 🤩

  • @danaborgman8526
    @danaborgman85264 жыл бұрын

    I love these videos! You get all the interesting stories without having to memorize everything for an exam afterwards!

  • @ZoltanF1LH
    @ZoltanF1LH4 жыл бұрын

    I loved your vids on 60symbols, I'm glad I found your channel! 😊

  • @madhavsharma6643
    @madhavsharma6643 Жыл бұрын

    thanks dr. becky the way you explain and carry the video on and the images and gifs you show and how u explain really are a sign of a pro. I haven't really found a channel like yours where a PhD explains physics like that detailed

  • @Dappdude
    @Dappdude4 жыл бұрын

    I've never heard this problem explained so well, great video Becky!

  • @herblapp

    @herblapp

    4 жыл бұрын

    Today she is the best popularist of astronomy and keeps getting better.

  • @cortster12

    @cortster12

    4 жыл бұрын

    I honestly found it a bit confusing. I still don't understand the physical phenomena that causes it to happen, just the math behind it. What about curving space makes this different?

  • @jacobvandijk6525
    @jacobvandijk65254 жыл бұрын

    Very well done, Becky! Lovely presentation. I like the enthousiastic look in your eyes. Just great! By the way, you are the first English speaking person on KZread who pronounces Schwarzschild correctly ;-)

  • @jimarnn1938
    @jimarnn19383 жыл бұрын

    Loved the bit at the end of you checking your pronunciation, facts etc. Makes you very ralatable! I also love the enthusiasm in your presentations... doesn't seem like you have to rehearse that bit at all!

  • @dawienel1142
    @dawienel1142 Жыл бұрын

    Been watching your videos for quite some time and I just have to say you're amazing, keep doing what you are doing, and keep the singing and blurps at the end. God Bless :-)

  • @amasaro70
    @amasaro702 жыл бұрын

    Dr. Becky is one of those rare astrophysists who are very good at explaining abstract concepts. As a keen follower of astronomy, I find I can almost anticipate her next sentence. For this, I love her.

  • @sethsims7414
    @sethsims74144 жыл бұрын

    GPS receivers only listen. The satellites are screaming out what time their extremely accurate clocks say it is. The receiver compares all the times it's hearing to get the distance. It actually needs a minimum of 4 satellite locks, it's solving for x,y,z and the actual time where it is. That's why GPS receivers are some of the best clocks an average person can use. They are listening to atomic clocks orbiting above our heads.

  • @AthAthanasius

    @AthAthanasius

    4 жыл бұрын

    They 'scream out' both their idea of the current time *and* their position. Part of the maintenance of the GPS system is keeping very precise track of where each satellite is so it can be told this to pass it on. In an apocalypse scenario the GPS system would degrade. I've no idea just how quickly, but suspect that after a few decades it would likely be unusable for positioning (but would still be a good time source). That's assuming satellites would still be active of course. I've not looked at the details, but there's likely some scary looking math that allows a GPS receiver to take all the time signals it receives to work out a good idea of the current time to then compare to each sender to actually work out the position. You don't have an atomic clock in your smartphone after all.

  • @sethsims7414

    @sethsims7414

    4 жыл бұрын

    @@AthAthanasius yea I didn't mention the ephemeris (though I can't spell that word without looking it up), if we're really being specific the satellites mostly scream TICK, TICK, TICK, and only transmit the full time every few seconds, and their tracks every so often. The ground tracking stations update the GPS's ephemeris data pretty often from what I remember. Though I don't know either how long you could trust them without the update. The trilateration math wouldn't be that bad if you could trust the ranges you get from the signals. But there's a lot of sources of noise as they move through the atmosphere and bounce off buildings. A lot of the complexity is trying to correct for those errors. I heard the next round of GPS is going to be using multiple frequencies to allow the biggest source of error from the atmosphere to be measured and corrected. I think the projections are that we can get something like centimeter accuracy from the new system. You can do that with the current system if you have two close by GPS receivers. One isn't moving and it transmits corrections to the signals knowing that it isn't moving.

  • @kingblondie7075

    @kingblondie7075

    4 жыл бұрын

    @@AthAthanasius some of them scream out "I am in great pain, please help"

  • @quamrana

    @quamrana

    4 жыл бұрын

    They may be screaming out the time, but down here it is a whisper in a hurricane!

  • @anssihakkarainen5726

    @anssihakkarainen5726

    4 жыл бұрын

    @@sethsims7414 They scream Pseudo Random Noise...

  • @mikesnyder1788
    @mikesnyder1788 Жыл бұрын

    I have read several accounts of Einstein and his Mercury fixation and, now, finally, I kinda sorta understand! Thanks, Dr. Becky for yet another clear explanation on a complicated point of physics. Love your work!!!

  • @GaryWrightUtah
    @GaryWrightUtah3 жыл бұрын

    I always love the bloopers at the end. Even if I don't understand all the other stuff real well, I get a laugh at your bloopers ... your awesome.

  • @TheFeltbegone
    @TheFeltbegone4 жыл бұрын

    For as many times that I've heard Mercury's orbit mentioned in relation to relativity, this is the first time I have seen that extra term mentioned. Also, I have heard of gravity and speed affecting GPS, but had not heard it explained as a gravitational red shift. Super clear and interesting. Thank you for that.

  • @AthAthanasius

    @AthAthanasius

    4 жыл бұрын

    Whilst this gravitational redhsift will indeed be affecting the signals from the satellites (Becky made an oops in saying GPS devices ping the satellites, they don't, they're just passive listeners), I thought the major reason that General Relativity has to be taken into account is that the clocks on the satellites will run it a faster rate than those down here on Earth (as we're deeper in the gravitational well so experience some GR time dilation). Of course the satellites are also orbiting at a relatively high speed so a experience a little *Special* Relitavistic time dilation as well, but it's less than the inverse effect from GR time dilation so they do run faster. There's a neat graph of the combination of these two effects on Wikipedia: en.wikipedia.org/wiki/Gravitational_time_dilation#Experimental_confirmation

  • @MrLaptopus

    @MrLaptopus

    4 жыл бұрын

    @@AthAthanasius Wrong on both counts

  • @colinp2238

    @colinp2238

    4 жыл бұрын

    @@AthAthanasius Wiki states that it is not an accurate site and is open to amendments.

  • @danieloneal7137
    @danieloneal71374 жыл бұрын

    I do love the old-timey headlines ... “Men of science more or less agog”

  • @steve1978ger

    @steve1978ger

    4 жыл бұрын

    LIGHTS ALL ASKEW IN THE HEAVENS But Nobody Need Worry. This made me think of H.P. Lovecraft and it's actually the period where he came up with his "cosmic horrors".

  • @Varma414
    @Varma4143 жыл бұрын

    Today is Friday and this is the first Video I am watching and starting my day. I appreciate Your time and work Dr. Smethurst. Keep on going with speed of light(AU)🤩

  • @mohanpathak
    @mohanpathak3 жыл бұрын

    So useful and so full of knowledge. There's so much to learn here. Thanks for creating this video!

  • @timothymarchant9079
    @timothymarchant90794 жыл бұрын

    Thanks Becky. I've been grappling with flat earthers so I came here to restabilise my sanity. :)

  • @JLukeHypernova

    @JLukeHypernova

    4 жыл бұрын

    It's best to just not even engage them.

  • @nathanlewis42

    @nathanlewis42

    4 жыл бұрын

    @@JLukeHypernova I find that sending them images of satellite dishes and asking if they have ever seen one works pretty well. They don't have a comeback that can't easily be knocked down and in my experience they tend to go quiet after that.

  • @302Diane

    @302Diane

    4 жыл бұрын

    @@nathanlewis42 You seem to have encountered remarkably submissive flat-Earthers. In my experience, they never go quiet.

  • @nathanlewis42

    @nathanlewis42

    4 жыл бұрын

    Diane Miller maybe but try sending them a link to pictures of satellite dishes and ask if they have ever seen them on houses. Only one replied and said high altitude balloons and I pointed out that balloons move with the wind so the dishes wouldn’t have to move all around. I never heard back after that.

  • @robertb7293

    @robertb7293

    4 жыл бұрын

    /Pretending that someone totally tagged me in for trolling flerfers. They tend to get reduced to butt hurt mumbling quick enough if you can deconstruct the uses they have for their beliefs. Not easy, but I've deconverted a few. So yeah. It's possible. Did you know that you can track latitude, and locate the Earths poles, just by measuring the shadows on the moon? Turns out that someone who can locate their position on Earth, in the dark, without equipment is a pretty impressive flex to a person who can't operate a sheet of paper. The real challenge is to finish the demonstration before they block you.

  • @mcnultyssobercompanion6372
    @mcnultyssobercompanion63724 жыл бұрын

    Another really great, informative video. Lovely work. I am once again *a little* smarter than I was 15 minutes ago. Thank you. :)

  • @coeur8042

    @coeur8042

    3 жыл бұрын

    Intelligence has nothing to do with information!

  • @Wacoal34d
    @Wacoal34d Жыл бұрын

    Love your lively and informative videos Becky! You are a breath of fresh air in this otherwise stodgy area.

  • @billoetjen
    @billoetjen4 жыл бұрын

    This pushes all the other presentations back. Most excellent.

  • @MuMuKuh
    @MuMuKuh4 жыл бұрын

    "The Hunt for Vulcan" is a great read on everything covered in this Video

  • @roblouw1344
    @roblouw13443 жыл бұрын

    Dr Becky, I have only just viewed this excellent video. As you mentioned the clocks on the GPS satellites run faster than those on earth because of the reduced effects of gravity at their altitude. Special relativity also has a role to play. Because the satellites are travelling so fast their clocks run slower relative to us on earth. The general relativistic effect is however greater than the special relativistic effect. So the net result is that the satellite clocks are still running fast than clocks on earth.

  • @StinkyCashFlatEarth

    @StinkyCashFlatEarth

    2 жыл бұрын

    Tell me your brainwashed without telling me you’re brainwashed

  • @WilliamAndySmith-Romaq

    @WilliamAndySmith-Romaq

    2 жыл бұрын

    I recall seeing a page somewhere that explained in Layman's terms the interplay between "clocks on earth appear faster because of the gravity well" vs "clocks in the GPS fleet appear faster relative to clocks on earth because of their speed of travel in orbit". I recall reading the two effects "not quite cancel one another out, but close." I don't recall the gravitational redshift on the signals themselves even being considered. This "interplay of effects on GPS" seems like something that Dr. Becky might do as a follow up episode. I wish I could locate that link I read.

  • @AndreSomers

    @AndreSomers

    2 жыл бұрын

    Her explanation was also wrong in the sense that phones or other receivers don’t ping the satellites. They just, well, receive the signals the satellites are emitting constantly.

  • @WilliamAndySmith-Romaq

    @WilliamAndySmith-Romaq

    2 жыл бұрын

    @@AndreSomers Yup... She mentioned that fairly quickly in the comments.

  • @AndreSomers

    @AndreSomers

    2 жыл бұрын

    @@WilliamAndySmith-Romaq oh, sorry, missed that comment.

  • @toddarmstrong1167
    @toddarmstrong1167 Жыл бұрын

    I have told you before how much I love your videos and your singing. Can't wait for the album.

  • @RogerRosenquist
    @RogerRosenquist4 жыл бұрын

    OK, I'm hooked. Enjoyed the random text overlays and out-takes.

  • @clemstevenson
    @clemstevenson4 жыл бұрын

    Thanks to Albert Einstein, you now know what time it is when Cambridge arrives at your train.

  • @oopfpa

    @oopfpa

    3 жыл бұрын

    I think it will take a lot more than Einstein to predict British Rail service.

  • @clemstevenson

    @clemstevenson

    3 жыл бұрын

    @@oopfpa You can confidently predict that the result of the experiment will not match with the predicted value.

  • @labaguette2728

    @labaguette2728

    3 жыл бұрын

    I started traveling close to the speed of light right as this comment was posted. Now, only a few seconds later, I can post my response

  • @johnkanai4106

    @johnkanai4106

    3 жыл бұрын

    Elementary...

  • @clemstevenson

    @clemstevenson

    3 жыл бұрын

    @@johnkanai4106 Times they are a-changing :-)

  • @NewGoldStandard
    @NewGoldStandard4 жыл бұрын

    Great video, thanks. I'm always fascinated with the real-world applications for general relativity. It makes something that would otherwise be very abstract more concrete.

  • @YouTuber-mc2el
    @YouTuber-mc2el8 ай бұрын

    I understood all that you said...every word with complete clarity. I enjoyed the depth at which you took the subject. The presentation you put forth was exceptional without fault. No stumbling, no uhhs, no noticeable tripping of any kind. Very well Done. Then you had to include the edits and burst my bubble LOL.Thank you very much.

  • @sagsgalaxia7627
    @sagsgalaxia76273 жыл бұрын

    Wow your energy while describing it. Amazing. Thanks for explaining it so clearly.

  • @olly5764
    @olly57644 жыл бұрын

    looked up the Marshmallow in a microwave experiment, WOW, that's straight forward, I'll be trying that with my friend's twin sons in a couple of years!

  • @SigEpBlue
    @SigEpBlue4 жыл бұрын

    Missing the obligatory Spock when you mentioned Vulcan. ;)

  • @ChrisPage68

    @ChrisPage68

    4 жыл бұрын

    Highly illogical, Captain.

  • @ryanbrewer4785

    @ryanbrewer4785

    4 жыл бұрын

    @@ChrisPage68 thumbs up

  • @danuttall

    @danuttall

    4 жыл бұрын

    That fictional Vulcan around another star was named after the imaginary Vulcan around our star.

  • @bottlekruiser

    @bottlekruiser

    4 жыл бұрын

    Live long and prosper

  • @JimWarp93

    @JimWarp93

    4 жыл бұрын

    And I missed the fitting Back to the Future snippet

  • @freeflycoffey
    @freeflycoffey2 жыл бұрын

    Love your work Dr. Becky. Keep it up 😎

  • @Mrmohit2711
    @Mrmohit27113 жыл бұрын

    Thank you...that mercury part was so educative...looking forward to more such content

  • @LeutnantJoker
    @LeutnantJoker4 жыл бұрын

    Wow, Vulcan is a lot closer than I always thought it was... ;)

  • @jaygee6738

    @jaygee6738

    3 жыл бұрын

    IGNORE THOSE IDIOTS!!!

  • @TheDisabledGamersChannel
    @TheDisabledGamersChannel4 жыл бұрын

    You should have a singing channel as well, you've got such a lovely voice.

  • @jacksonstarky8288

    @jacksonstarky8288

    4 жыл бұрын

    I was thinking something similar. I love the singing outtakes. I think Dr. Becky should record some astronomy / cosmology songs.

  • @TheDisabledGamersChannel

    @TheDisabledGamersChannel

    4 жыл бұрын

    @@jacksonstarky8288 That'd be pretty cool.

  • @PixelatedPenfold

    @PixelatedPenfold

    3 жыл бұрын

    @@jacksonstarky8288 How about the Monty Python Galaxy Song? Even Stephen Hawking covered that one.

  • @jacksonstarky8288

    @jacksonstarky8288

    3 жыл бұрын

    @@PixelatedPenfold Yes!

  • @pokalorentz9363

    @pokalorentz9363

    3 жыл бұрын

    Dr Beckey could take some inspiration from Sabine Hossenfelder. She's a quantum physicist with her own singing channel

  • @nicholashuff4198
    @nicholashuff4198 Жыл бұрын

    Your whimsical attention to accurate articulation is adorable. 😘

  • @tarlach1280x960
    @tarlach1280x9604 жыл бұрын

    I simply love your videos... eloquent explained.

  • @rylian21
    @rylian214 жыл бұрын

    I love this stuff. I'm a layman, so while the specific math eludes me, I can grasp the concepts when they're explained to me so well.

  • @fredb2022

    @fredb2022

    2 жыл бұрын

    Ditto. The equations do not speak to me any more than if the text was presented in Latin or Greek.

  • @graphosxp
    @graphosxp4 жыл бұрын

    "In Space, No One Can Hear You...." Sing!

  • @marcuschauvin7039

    @marcuschauvin7039

    4 жыл бұрын

    No one can smell your farts either!

  • @ChrisPage68

    @ChrisPage68

    4 жыл бұрын

    @@marcuschauvin7039 Soace smells like burnt toast, apparently.

  • @graphosxp

    @graphosxp

    4 жыл бұрын

    @@marcuschauvin7039 Huh? Gas CAN travel through space. In fact if you have enough flatulence filling a volume of outer space it will carry sound waves. Let's compare! "Earth's atmosphere is 78% nitrogen, 21% oxygen, 0.9% argon, and 0.03% carbon dioxide with very small percentages of other elements." "A typical breakdown of the chemical composition of farts is: Nitrogen: 20-90% Hydrogen: 0-50% (flammable) Carbon dioxide: 10-30% Oxygen: 0-10% Methane: 0-10% (flammable)" "What Is a Fart Made Of?" : www.thoughtco.com/chemical-composition-of-farts-608409

  • @ZeedijkMike

    @ZeedijkMike

    4 жыл бұрын

    @@marcuschauvin7039 : Professor Farnsworth have made a "Smelloscope" (-:

  • @CaptWesStarwind

    @CaptWesStarwind

    4 жыл бұрын

    I want to like this comment, but since it currently has 42 likes, I'll wait.

  • @user-li7ec3fg6h
    @user-li7ec3fg6h Жыл бұрын

    Hi doc becky, you did a great job explaining that. Many, many thanks! Once again! And on top of that so charming as always. Looking forward to more such good explanations! (Showing the little mistakes with the shots at the end are great too. I think it's so great that all this is not a problem, because it's about more important things and the human is just part of us. Scientists and spacenerds show us again and again how much is feasible if we leave out the destructive and divisive stuff :-). All the best from Berlin, Germany

  • @Leap_of_Faithhh
    @Leap_of_Faithhh3 жыл бұрын

    You are so much fun to watch and to listen to. Thank you! ❤️🙏

  • @cristiangamboa2037
    @cristiangamboa20374 жыл бұрын

    Thanks a lot for this video, I tired of pseudo astrologist trying to tell me how Mercury will affect my life. Finally someone tells me something rational about it.

  • @hareecionelson5875

    @hareecionelson5875

    4 жыл бұрын

    Aren't all astrologers pseudo-astrologers? Astronomer or astrophysicist is the scientific name. Astrology is woo woo

  • @cristiangamboa2037

    @cristiangamboa2037

    4 жыл бұрын

    @@hareecionelson5875 Astrology is pure ignorance, that why I appreciate when someone says something about Mercury's orbit that is based on science.

  • @jeffwells1255

    @jeffwells1255

    3 жыл бұрын

    The practice of astrology should be treated as the obvious fraud that it is and treated as such by the legal system. While we're at it we should include as many other frauds in there, such as homeopathy and especially religion!

  • @essaboselin5252
    @essaboselin52524 жыл бұрын

    This mathematician will forgive your "divide by infinity" comment just because of the cute Pluto crying image. It'll always be a planet in my heart.

  • @Restilia_ch

    @Restilia_ch

    4 жыл бұрын

    Don't evict Sailor Pluto!

  • @huverdoose

    @huverdoose

    4 жыл бұрын

    Dwarf planets are planets also, and deserve the same rights and respect afforded to other planets.

  • @essaboselin5252

    @essaboselin5252

    4 жыл бұрын

    @@huverdoose I wonder if professional astronomers know they're fighting an uphill battle with the general public over Pluto? It's wild how attached people are to the idea that it is a planet. It's not like anyone has ever visited it; it's not like you can spot it with the naked eye (or even a cheap home telescope.) I do agree with Dr. Becky's colleague, Dr. Merrifield, that it's a bit moot how you classify it. Nothing about Pluto has changed because of the new designation. And astronomy is known for some vague definitions - planemos anyone? Having said all that: Cleared orbit, schmeared orbit! Pluto is a planet! :-)

  • @huverdoose

    @huverdoose

    4 жыл бұрын

    @@essaboselin5252 I live about a half hour from Clyde Tombaugh's hometown, so nearly everyone in my area takes it personally. I don't, but it's sometimes fun to pretend.

  • @SG-op6nc
    @SG-op6nc Жыл бұрын

    Awesome explanation. So clear and concise. Well done Dr. Becky 👏

  • @howarddelovitch1451
    @howarddelovitch14514 жыл бұрын

    OMG! Thank You! Finally , this has intrigued me for years now and nobody talks about this.

  • @Tanis161
    @Tanis1614 жыл бұрын

    Have you ever considered doing Star Talk with Neil? I would love to hear you two blow our minds.

  • @herblapp

    @herblapp

    4 жыл бұрын

    Maybe Becky has. But l'd suspect he wouldn't since he'd benout classed and certainly out shined!!

  • @jeffwells1255

    @jeffwells1255

    3 жыл бұрын

    @@herblapp Oh, I doubt that Dr Tyson's ego would be the least bit threatened by that since he loves a challenge and is no kind of an egomaniac anyway, although some might think so due to his enthusiasm.

  • @rainrope5069
    @rainrope50694 жыл бұрын

    11:36 Cliff Stoll is an astronomer too, I feel like he'll be kinder than the math professors

  • @LeoStaley

    @LeoStaley

    4 жыл бұрын

    Cliff stoll is earth's greatest treasure.

  • @irrelevant_noob

    @irrelevant_noob

    3 жыл бұрын

    And anyway she's not really wrong... Dividing any finite number by infinity can give NO OTHER RESULT than zero. It's not a singularity, not even an undefined term. The only caveat would be if the value would be merely "NEAR-infinite" and not an "actual" infinity, but that's really not worth griping about. :-B

  • @ronakpathak8376
    @ronakpathak8376 Жыл бұрын

    A very thorough video and very easy to follow explanation. Enjoyed watching it!

  • @usernname1
    @usernname14 жыл бұрын

    I always have heard about this but never knew why. This was great. Thank you.

  • @denomsolis4171
    @denomsolis41714 жыл бұрын

    Ooooh you have a lovely singing voice ! :D

  • @jimr8552
    @jimr85524 жыл бұрын

    Can you imagine just how far Einstein could have gone if he had the technology of today?

  • @dach829

    @dach829

    4 жыл бұрын

    @NowTV how so?

  • @wishusknight3009

    @wishusknight3009

    4 жыл бұрын

    @@dach829 Because NowTV is a flatard.

  • @jeffwells1255

    @jeffwells1255

    3 жыл бұрын

    I present to you Professor Stephen Hawking.

  • @theheadscout4356
    @theheadscout43563 жыл бұрын

    Thanks for sharing it so enthusiastically. Inspirational!

  • @Nabiry
    @Nabiry3 жыл бұрын

    Really awesome video, and very well explained. Thank you 👌

  • @luudest
    @luudest4 жыл бұрын

    9:40 Does this extra term explain a „new“ physical process in comparison with the Newtonian model? What is the physical explanation of this term???

  • @sleepy314

    @sleepy314

    4 жыл бұрын

    Game Changer _ yes, curved spacetime

  • @mursie100

    @mursie100

    4 жыл бұрын

    It's just that the closer you get to the gravitational center of a massive object, the less gravity acts like a force, and more like a curvature/stretching of the fabric of space around that object. You know how they say that if our sun instantly turned into a back hole, planetary orbits will not be affected... But if you decide to keep getting closer and closer to that black hole, space-time will get stretched deeper and deeper until it's infinitely stretched into a gravitational well. That "deeper" stretching of space-time as you get closer to a massive object's gravitational center, is what that "extra term" explains.

  • @Shenron557

    @Shenron557

    4 жыл бұрын

    Dimensional analysis on the term does not give the dimensions of Force, Potential or Acceleration. It gives [length]^(-2), which is m^(-2) in SI units. I'm not aware of any physical quantity with those dimensions.

  • @zoltankurti

    @zoltankurti

    4 жыл бұрын

    @@Shenron557 curvature is 1/length^2.

  • @luudest

    @luudest

    4 жыл бұрын

    mursie100 how does the „deeper stretching“ lead to the mercury perihelion precession?

  • @Skukkix23
    @Skukkix234 жыл бұрын

    Schwarzschild pronounciation is almost right, but the "i" is the same as in "build".

  • @stuartajc8141

    @stuartajc8141

    4 жыл бұрын

    Ironically it is "pronunciation" - the way a word is pronounced

  • @Skukkix23

    @Skukkix23

    4 жыл бұрын

    @@stuartajc8141 wow. And I thought German was hard, at least we have continuous rules

  • @stuartajc8141

    @stuartajc8141

    4 жыл бұрын

    @@Skukkix23 English is crazy like that

  • @elevown

    @elevown

    4 жыл бұрын

    @@stuartajc8141 English just proffers to go with 'whatever' lol. Its a case of just learning each one that differs as you come across them.

  • @fazergazer

    @fazergazer

    4 жыл бұрын

    Skukkix23 most Germans prefer non-native speakers to pronounce German words in whichever regional specific language phonemes that speaker uses. So it is actually preferable to anglicize the German -child. Otherwise it is considered rude or creepy.

  • @damerval
    @damerval3 жыл бұрын

    Dr. Becky, wow, what a cool channel, thank you. You have the gift for explaining things, and an evident passion for science. Not being a scientist myself I love to hear how scientists work these things out. I think a greater number of laypeople have the ability to understand those things than is estimated, and I'm very thankful that communicators like you are here to regale us with that enlightenment. If you have the time and inclination, I'd love to know how astronomers came to conclude that the origin of our known universe was a big bang, as opposed to some other phenomenon that could have led to what we observe. If I may allow myself a compliment, your content is absolutely crystal, and you have incredible video presence, being very engaging and (let's not deny it) incredibly lovely. Meant with the most innocent of intent.

  • @ronaldbucchino1086
    @ronaldbucchino10863 жыл бұрын

    Clear explanation -- and -- you have a lovely singing voice. Thank You

  • @LA-MJ
    @LA-MJ4 жыл бұрын

    GPS is passive. No pings are sent by our devices.

  • @e1123581321345589144

    @e1123581321345589144

    4 жыл бұрын

    How it works is that the satellites constantly broadcast their id and time, and given the known orbital characteristics the SW on the reviving device is capable of calculating it's location based on those parameters. note: due to it's highly acurate clocks GPS is used by a lot of institutions for time keeping as well.

  • @jursamaj

    @jursamaj

    3 жыл бұрын

    I came looking for this comment. I'm amazed how few people seem to have caught that mistake. @@e1123581321345589144 Interestingly, LORAN, the predecessor of GPS was also used for time. For the same reason: it's a highly accurate clock system.

  • @Set_Get

    @Set_Get

    3 жыл бұрын

    No, not by our devices, but apparently, each GPS satellite gets frequently updated/fed (their correct position, correct time,...) from the station located in northern US.

  • @glutinousmaximus
    @glutinousmaximus4 жыл бұрын

    ... Perhaps the title might be a little more accurate with "How does Mercury _fail to disprove_ General Relativity". (You know what I mean :0) Another good presentation Dr Becky! Thanks.

  • @rbettsx

    @rbettsx

    4 жыл бұрын

    This is not mere pedantry. It's at the heart of the scientific method. It always shocks me when even quite prominent scientists refer to 'proof' of theories. Einstein's theory is no more proved than Newton's, or Copernicus'. Guilty scientists should be made to sit in a corner and and read their Popper.

  • @RealLifeKyurem

    @RealLifeKyurem

    4 жыл бұрын

    Rob42077 Hahaha, then you should stop using GPSs then or any positioning or realtime mapping systems for that matter (Google maps, Waze, etc.)

  • @kingatheist7231
    @kingatheist72312 жыл бұрын

    I really enjoy your videos Dr. Becky. I enjoy the science, but I particularly enjoy your passion for it and how you convey that to your audience. I personally find your videos quite relaxing, and I think are probably great for getting people interested in astrophysics, that otherwise wouldn't have been. (edit) also gotta love the Harry Potter references in a lot of videos, as I'm one of those obsessive Harry Potter fans that gets excited at every cutaway lol

  • @soumyadeepganguly3637
    @soumyadeepganguly36372 жыл бұрын

    Really enjoyed the explanation mam! recently discovered your channel, have already fallen in love!!!!🥰

  • @paulthompson9668
    @paulthompson96684 жыл бұрын

    11:22 When x *equals* infinity, then anything divided by x *equals* zero. When x *tends to* infinity, then anything divided by x *tends to* zero.

  • @jameswood5357

    @jameswood5357

    4 жыл бұрын

    You can't divide by infinity idiot, y/(infinity) is undefined, not 0.

  • @302Diane

    @302Diane

    4 жыл бұрын

    Also, infinity isn't a number. You can't add it, multiply by it, or anything like that.

  • @paulthompson9668

    @paulthompson9668

    4 жыл бұрын

    @@jameswood5357 So you're a communist?

  • @paulthompson9668

    @paulthompson9668

    4 жыл бұрын

    @@302Diane At least you're respectful about your post. I was referring to infinity as a concept, which may be subjected to certain algebraic operations for example in nonstandard analysis.

  • @diondixon3349
    @diondixon33494 жыл бұрын

    You said that GPS triangulates, but it actually uses trilateration. :-)

  • @AthAthanasius

    @AthAthanasius

    4 жыл бұрын

    Indeed. For those unaware, triangulatation use angles between things, which wouldn't be known in this case. Trilateration uses the distances from each known point to your position to work out your position.

  • @tectzas

    @tectzas

    4 жыл бұрын

    @@AthAthanasius I though the difference was that triangulation uses angles to pinpoint things on a 2D plane, whereas trilateration adds a 3rd dimension being height as well. Furthermore, the former uses literal triangles with a minimum of three points and the ladder uses at least 4 points with overlapping spheres. So where the spheres overlap is where you would be located. That being said you'd actually have two points where all spheres overlap but one of them is out in space so you can assume that's not where you are lol

  • @deborahkeesee7412
    @deborahkeesee7412 Жыл бұрын

    Dr B, your videos just keep getting better, enough so that I wonder if you could offer a collection of all of them either downloadable or on a CD. I have a four-year degree in Astronomy but jumped on the software bandwagon as it was exploding right around 1970, which was more attractive because I was getting rather tired of doing nothing but math just to pass the tests, some of which I eventually *didn't* pass, so something had to give! Software is mostly logic rather than computation so that fit me much better and I made a decent career out of it. But now, finally, I can do the math for fun and that made me better at it. Your videos especially have clarified one concept after another, to the point where I can jump on an error now and then and actually get thanked by a presenter, not that I've found any blunders on your part though. Getting familiar with General Relativity and how it made the Internet possible allowed me to get across to non-experts what incredible accomplishments like GPS really are and how we just might have still been figuring it out for decades, but we got lucky. Thanks again and the best of everything to you! Jeff (using a girlfriend's email)

  • @jayaramanganapathi9385
    @jayaramanganapathi93853 жыл бұрын

    Thanks for sharing this knowledge. It provides a great perspective to GR. Had it not been for the mysterious mercury orbits, and Einstein's understanding, he would have found it difficult to prove GR at least for few years.

  • @Hal2718
    @Hal27184 жыл бұрын

    And as it turns out, Mercury is most often the closest planet to Earth... and every other planet.

  • @DrBecky

    @DrBecky

    4 жыл бұрын

    Yes! I loved that recent video by CGP Grey

  • @feynstein1004

    @feynstein1004

    4 жыл бұрын

    We're top chicken

  • @TommentSection

    @TommentSection

    4 жыл бұрын

    Not quite, actually. It is on average the closest to every other planet in the Solar System, but it is most often the closest only for the inner planets :)

  • @Hal2718

    @Hal2718

    4 жыл бұрын

    @@TommentSection No, it's true for the outer planets also. Usually, they're *vastly* farther away from each other than they are each from the sun therefore, Mercury will most often be the closest.

  • @TommentSection

    @TommentSection

    4 жыл бұрын

    @@Hal2718 But the question of which is closest at any given time is highly dependent on which objects are considered. As we go farther out, more planets get in the way so that it become increasingly rare for Mercury to ever be closest. Watch CGPGrey's follow up video on it. He shows the numbers.

  • @joeb8248
    @joeb82484 жыл бұрын

    That music clip was so loud! Please equalize the volume.

  • @BitcoinMotorist
    @BitcoinMotorist4 жыл бұрын

    This was an amazing video. I had been looking for a detailed explanation like this for a long time. Instant like 👍 and sub. Just one small request Dr. Becky, can you do the video in English as well? 😆😆😆

  • @miroslavmaklenov7022
    @miroslavmaklenov70222 жыл бұрын

    i love your videos! you make learning physics fun. When i heard your singing voice i thought wow she knows how to sing too not just physics and astronomy. multi talented

  • @JuanDomenech
    @JuanDomenech4 жыл бұрын

    that "why should I care" song really woke me up... and my neighbours 😅

  • @myothersoul1953
    @myothersoul19534 жыл бұрын

    7:40 Wait!! You're trying to tell me Spock comes from a planet the orbits closer to the sun than Mercury?

  • @myothersoul1953

    @myothersoul1953

    3 жыл бұрын

    @CipiRipi00 Oh I see, that makes sense.

  • @JulianMakes
    @JulianMakes4 жыл бұрын

    Brilliantly explained Dr Becky! Just found the channel, love it. Fully subbed up. Please submit your application to Tomorrow’s World ASAP!

  • @timblack6422
    @timblack64224 жыл бұрын

    Beautifully done, and beautiful voice!

  • @HebaruSan
    @HebaruSan4 жыл бұрын

    3:50 - I cringe every time a diagram like this shows the "perihelion" farther away than the points 90 degrees around the orbit on the semiminor axis. It's odd how rarely astronomers apparently look at actual orbits.

  • @danieljensen2626

    @danieljensen2626

    4 жыл бұрын

    Maybe this is a projection from like 45 degrees above the orbital plane instead of a true top down view. But more realistically whoever the word "perihelion" is pretty long so they scooted the sun out of the actual focus of the ellipse to make the diagram "look nicer".

  • @atanasiomugambi7975

    @atanasiomugambi7975

    4 жыл бұрын

    Just realized that mistake is made in almost all illustrations I have seen. Thanks. You are the modern einstein.

  • @mawage666

    @mawage666

    4 жыл бұрын

    It's just an exaggeration.

  • @valeriobertoncello1809

    @valeriobertoncello1809

    4 жыл бұрын

    Why wouldn't you complain about the relative sizes of Mercury and the sun then?

  • @BlueEyesWhiteTeddy

    @BlueEyesWhiteTeddy

    2 жыл бұрын

    @@valeriobertoncello1809 because if mercury is a good size then the sun is too big to properly get an orbit around it and if the sun is a good size then mercury is way too small. It cannot be done. But having the perihelion as the smallest distance from the sun can be done.

  • @themeatpopsicle
    @themeatpopsicle4 жыл бұрын

    "Stars Not Where They Seemed or Were Calculated to be, but Nobody Need Worry" is my next tattoo

  • @michatarnowski580
    @michatarnowski58011 күн бұрын

    A very good video; very informed and gap-filling. The only thing I miss here is a brief summary at the end, e.g. with a timeline: 1. Le Verrier observes Mercury's precession (A) of the perihelion and predicts Vulcan; 2. Einstein predicts the gravitational redshift (B); 3. Einstein predicts the bending of starlight (C); 4. Einstein explains Mercury's oribt (A); 5. Schwarzschild explains it more precisely (A); 6. Eddington observes the bending of starlight, making Einstein famous (C); 7. D.M. Popper observes the gravitational redshift (B); 8. General Relativity is applied to GPS. I would also love to know if this effect has been predicted or observed for other objects as well.

  • @potawatomi100
    @potawatomi1003 жыл бұрын

    Excellent video and you are a very good “explainer”. Well narrated.

  • @johngolombek61
    @johngolombek614 жыл бұрын

    ok its official Dr. Becky and Dr. Neil deGrasse Tyson my favorites for everything space and science. Cheers from cross the pond.

  • @LeutnantJoker

    @LeutnantJoker

    4 жыл бұрын

    Meh, these days Tyson loves the camera and hearing himself talking a bit too much for my taste. There's smarter scientists out there that are less in love with the camera and a bit more professional.

  • @JoeDeglman

    @JoeDeglman

    4 жыл бұрын

    Both of them are my favorite sci-fi sources. Definitely since that sci-fi great Hawking passed away.

  • @swirvinbirds1971

    @swirvinbirds1971

    4 жыл бұрын

    @@LeutnantJoker I think Tyson gets a little too much hate. The guy has a good sense of humor and does a good job of bringing science to the masses. Is he right about everything? No... But show me someone who is.

  • @gregbrockway4452

    @gregbrockway4452

    4 жыл бұрын

    John Golombek-You should check out: Isaac Arthur John Michael Godier Astrum Anton Petrov Scott Manley These are all most excellent science and astronomy KZread channels.

  • @tonyelsom6382

    @tonyelsom6382

    4 жыл бұрын

    @@gregbrockway4452 Yes, spot on..no hate against NDT, just not my cuppa..

  • @terralakins7565
    @terralakins75654 жыл бұрын

    I'm betting that the five "thumbs down" are all mathematicians. Lol. The rest of us still think you're awsome @drbecky

  • @Richardj410

    @Richardj410

    4 жыл бұрын

    I think it is flatties who don't believe that space exists.

  • @goprojoe7449

    @goprojoe7449

    4 жыл бұрын

    She simply doesn't know what she's talking about. I'm just an engineer educated in physics, and I can see that she does not have a PhD in her field.

  • @302Diane

    @302Diane

    4 жыл бұрын

    @@goprojoe7449 OK. I know I'm going to hate myself for asking, but what do you think she got wrong?

  • @harshpratapsingh310
    @harshpratapsingh3104 жыл бұрын

    Thanks for the Explanation!

  • @raulassis1
    @raulassis14 жыл бұрын

    Fascinating video. Can you do a video actually solving the GR equations for Mercury orbit?

  • @whynottalklikeapirat
    @whynottalklikeapirat4 жыл бұрын

    Who is General Relativity? Did he win wars or does it depend on the observer?

  • @simongleaden2864
    @simongleaden28644 жыл бұрын

    Scientific theories cannot be proved, but they can be confirmed. One can only disprove a theory.

  • @dpsamu2000

    @dpsamu2000

    4 жыл бұрын

    Observations not theories are confirmed by peers capable of taking the same steps an observer claimed he took to observe what he claims to observe. Theories are arguments that are convincing or not to peers capable of understanding them based on the quality of the observations supporting them. Only disproved by observation that doesn't match consequences predicted by theory.

  • @mrigankamaulichakraborty7088
    @mrigankamaulichakraborty70883 жыл бұрын

    A proper channel, very accurately described.

  • @liudas5377
    @liudas53774 жыл бұрын

    That was brilliant. Thank you for posting...

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