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What is the horizon problem? 

King's College London
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In this 3 Minute Thinking video, Dr Malcolm Fairbairn from the Department of Physics at King's College London explains the horizon problem. He takes us back to the birth of the universe to examine the Big Bang Theory and horizon problem.
3 Minute Thinking is a brand new series of bite-size videos that explore curious topics like climate change, artificial intelligence and Shakespeare. Please visit the 3 Minute Thinking webpage for more information - www.kcl.ac.uk/3Mint/Physics-Ma...
Dr Fairbairn is a part of the Theoretical Particle Physics & Cosmology research group. His research is concerned with the interaction between cosmology, particle physics and astrophysics. In particular Dr Fairbairn is interested in dark matter, dark energy, cosmological inflation and particle astrophysics. To read more about his work visit his research profile on the King's College London website: www.kcl.ac.uk/nms/depts/physic...
Learn more about studying Physics at King's College London here - www.kcl.ac.uk/nms/depts/physic...

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3 дек 2013

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Комментарии : 113   
@thomashemingson2639
@thomashemingson2639 2 года назад
So you made up a fictitious "rapid expansion" period to validate a problem with your theory. Great science.
@molrat
@molrat 28 дней назад
i think he was trying to say basically the expansion of the universe makes up for it but tried to make it sound simple by saying that idk
@drjcarrick
@drjcarrick 2 года назад
Keep coming back to this video when I need to remind myself of the horizon problem. I think I first saw it as an undergrad. This time I'm preparing for a PhD viva... Great explanation!
@plmolnwtr
@plmolnwtr 10 лет назад
Loving the effort on increasing the uni's exposure through media. Keep it up!
@sinclairal
@sinclairal 2 года назад
I like how you just say they effectively travelled faster than the speed of light like that's a easy way to solve it. lol.
@arminverger3629
@arminverger3629 10 лет назад
Well thanks, very understandable comparing to other people's explanation.
@ds_nz1134
@ds_nz1134 Год назад
I would love an explanation of what kind of thing is the Big Bang itself that without factoring in inflation is too big at the time 0 and has to have points of different temperature.
@kazuhaaa9896
@kazuhaaa9896 6 лет назад
Wow that was so easily explained. Thank you!
@mahitoshray6691
@mahitoshray6691 2 года назад
wanted to say thank you this video helped me finish my assignment on horizon problem
@Sinnbad21
@Sinnbad21 5 лет назад
I’m confused. At one point A and B were touching at the very beginning when the the universe was a tiny ball. Didn’t they have time to touch during then before being pushed away faster than the speed of light? This seems like common sense. Am I missing something?
@orchoose
@orchoose 2 года назад
yes
@astronemir
@astronemir 6 лет назад
Great explanation, thanks!
@Alfster18
@Alfster18 Год назад
Great video. Concise and covers the key points really well! I would point out that at the surface of last scattering when the universe became transparent the EM radiation is actually in the infrared region (since z = 1100). Thus, it didn't go from orange > red > IR > microwave - it went from IR > microwave.
@Rofl890
@Rofl890 7 лет назад
Do A and B really need to be touching at one point in time in order to explain this? What if they are the same temperature because they both obey the same laws of physics and the universe was created in the same way everywhere?
@lucapontiggia3123
@lucapontiggia3123 7 лет назад
That's a decent question, perhaps let me try answer it this way. If have two completely isolated systems. System A has temperature of say 100 degrees and B 1000 degrees. By system just imagine a perfectly insulating box of gas. Now these two systems have never been in contact, however if you look at each box individually they both look the same(gasses are spread out evenly, they both follow all the same laws of physics, the gasses evolved exactly the same way cause as you rightly said the universe is the same everywhere - however they are fundamentally a different temperature - A is 100 degrees and B is 1000 degrees). Now replace the two boxes with perfect conductors and let them touch. Over time the heat will conduct until both systems form an equilibrium temperature. When they are in equilibrium separate them and observe... Now, the two systems still look identical, BUT their temperatures are equal, why? Well because they were in contact and thus through laws of thermodynamics allowed heat to transfer. To come to the universe, replace the boxes with the parts of the Universe. You would expect that opposite sides might have clumps of different temperatures (or the same) but they would be clumped (large uneven blotches), if they never touched. But since they ARE even EVERYWHERE there must have been contact, just like there needed to be contact between the two boxes for the temperature to be the same. But how could there be contact if the distance were too far apart from light(information) to reach? Hence the Horizon problem. A bit long but hopefully it clarifies this point for you :)
@markhagan6675
@markhagan6675 6 лет назад
Luca Pontiggia Why are the boxes different temperatures?
@Sinnbad21
@Sinnbad21 6 лет назад
Luca Pontiggia sorry for the confusion but I can’t seem to understand why these Space A and Space B clumps would ever be different temperatures? They’ve had to have touched in the beginning during or slightly after the Big Bang. All of space was confined to one small single point and then was spread out over time. That means point A and Point B were touching at the beginning but no longer are since they went opposite directions as the universe was expanding. So why would they be different temperatures if they were once touching? Physics is the same across the universe so that makes all of this c nfusing to me. Hope that makes sense! And thanks ahead of time
@raredrop6872
@raredrop6872 5 лет назад
@@Sinnbad21 Because a uniform universe is a boring universe! If you would go with that ideology then perhaps nothing would had existed. You see, universe is locally unstable but globally stable.
@raredrop6872
@raredrop6872 5 лет назад
That is why a planet or sun cannot exist from nowhere but a whole universe can
@emmanuelblum7454
@emmanuelblum7454 4 месяца назад
Perfect explained Thank you
@gooberclown
@gooberclown 3 года назад
This explanation represents a lapse in logic. Other than that, it's perfectly lucid and understandable, like the phrase, 'the moon is made of green cheese'.
@maujo2009
@maujo2009 10 лет назад
What about the flatness problem and its relation to the horizon problem?
@iman6189
@iman6189 3 года назад
the bigger something is, the more flat it appears
@gooberclown
@gooberclown Год назад
Good question.
@gamersmash7023
@gamersmash7023 Год назад
I have a question. Why does the furthest points have the same temperature but anywhere inside of the horizons has different temperatures? What properties of the furthest points (the horizons) is different from anything inside of the furthest points that is only causing the horizons to have the same temperature but nothing inside of it?
@apuritan
@apuritan 8 лет назад
Honest question: how do you look in two directions at once? Professor said when we look back in time (and then drew an arrow) and then we look in this other direction (and drew a second line). So, how are they physically looking in these two planes?
@CurtisGproductions
@CurtisGproductions 8 лет назад
+apuritan He doesn't literally mean look at two different directions at the same time. He means, if you measure the temperature of the sky in one direction and then measure the temp in the complete opposite direction, the have the same temperature.
@shahbazsaeed4799
@shahbazsaeed4799 8 лет назад
they are not specifiaclly looking at both directions they are assuming analysing and proving.
@discodan10
@discodan10 8 лет назад
Its a guess not a solution
@timking2931
@timking2931 3 года назад
I’m confused? I thought nothing moved faster than the speed of light, Yet it’s theorized our universe did for quite some time???🤯
@Achrononmaster
@Achrononmaster 2 года назад
No, that is not theorized. Our universe is not moving in the sense you are thinking. Spacetime expansion is not a physical motion of anything, it is separation between particles. If two particles head off in opposite directions at near light speed the distance between them increases faster than light speed, this does not violate special relativity, because empty space between them is not moving. It is similar to parallax effects in a way. You can probably, with enough contrast, easily move a shadow at near light speed, the problem is getting the shadow projection far enough away that you can still see it (a laser on the Moon? That'd be visible through a telescope). You can easily get a shadow to accelerate far faster than any rocket, just by waving your hand on a sunny day. Similar effect, nothing physical is actually moving _in the shadow._ (Have you ever bumped into a shadow and had the wind knocked out of you?)
@evitagleinig6184
@evitagleinig6184 3 года назад
hi my name is Haumea im 8 years old and love Physics Sience and chemistry and i lovs the video
@99SmilyOrange
@99SmilyOrange 6 лет назад
thx for the video, i have a question: you say at the time of inflation the expansion was "effectively faster than light" how could that be? that breaks the fundamental law of physics about the velocity of light! also since the points A and B started from the same point in the beginning then it is not odd that they have the same initial conditions. I stilll dont see the problem thx Prof!
@Sinnbad21
@Sinnbad21 6 лет назад
99SmilyOrange I have the same question as your last one. They start at the same point so why would they ever be different temperatures? So confusing
@emilypaige2885
@emilypaige2885 2 года назад
Here's what Brian Greene wrote in *The Hidden Reality* : "The speed limit set by light refers solely to the motion of objects _through space_ . But galaxies [or regions of space] recede from one another not because they are traveling through space... but rather because space itself is swelling and the galaxies are being dragged along by the overall flow. And the thing is, _relativity places no limit on how fast space can swell,_ so there is no limit on how fast galaxies being pushed by the swell recede from one another. The rate of recession between any two galaxies can exceed any speed, including the speed of light. "
@theknave4415
@theknave4415 3 года назад
The age of the universe, and the speed of light, doesn't appear to match up with the observed size of the universe.
@craigcoates6247
@craigcoates6247 4 года назад
30 seconds into a 3 minute video and it gets to the point.
@jasonhutto5223
@jasonhutto5223 Год назад
If it is impossible to accelerate something to the speed of light because it would require an infinite amount of energy, how were objects A and B accelerated beyond the speed of light?
@mohammedtalibmosa7344
@mohammedtalibmosa7344 8 лет назад
That why I love physics,it give confidante meaning for living
@jasonhutto5223
@jasonhutto5223 Год назад
How did the universe expand in the first place if the sum of all mass was concentrated in one area, or point? If light and matter cannot escape a black hole, how could anything escape gravity of the mass of all things in one place?
@mattrix2007
@mattrix2007 7 лет назад
soooo, where did the fire come from ?
@Vix.Strada
@Vix.Strada 8 лет назад
Hi Malcolm.. Nice Video.. very interesting indeed.. Let me ask you one thing and what you think.. What would happen to our Universe if a new Big Bang would take place in our already existing universe.. as we know it..? please try to answer me.. this question keeps me awake night after another... My Best regards / The Thinker
@saccamadiqeu2600
@saccamadiqeu2600 8 лет назад
don't worry about it
@shahbazsaeed4799
@shahbazsaeed4799 8 лет назад
the big bang is supposed to be from nothing to something, so there is no chance to happen it while the universe is running beautifully. and if you stuck to this idea, convert it to another dimension may be some other dimension this is happening right now beyond our mind limits, imaginations and senses.
@Jay_Flippen
@Jay_Flippen 9 лет назад
However, in opposition to the point A and B separation (the solution to cosmological expansion and the big bang), their seems to be an odd sense of milky-way centrism that contributes to the homogeneity problem (in reference to the "observable universe"). Also, structures are being analyzed that are too large and fully formed for a universe age of 14-ish billion years… which was a major dependent value of the big bang. Humans do seem to try and consider everything too often in a specific singularity. I'm not trying to negate what could be called "the big bang" so much as I am negating or arguing against "the" big bang. Aside from big bang(s), there still is dark energy, supernovas, quasars, other radiation sources (i.e. solar wind), centripetal force, Lorentz transformations (and by that I mean large scale, long distance accelerations coupled with dark energy… i.e. galaxy rotation mechanisms and galaxy acceleration), and gravitational slingshot effects which go against an otherwise inevitably highly concentrated source… from the effects of gravity.
@Bia-starlight
@Bia-starlight 2 года назад
Now I don't get why it was seen as impossible. Damn.
@Samklemens
@Samklemens 5 лет назад
It's a proposed solution, no? Are you, sir, uncomfortable with uncertainty?
@CarlosRodriguez-ue8ep
@CarlosRodriguez-ue8ep 7 лет назад
soo you say is not linear is just 2 points of the same expansion....well if that soo in the middle of it.... it will be more or less strong of B and A that is my thinking to prove that you are rigth
@jfitz369
@jfitz369 7 лет назад
"Then there was a period called cosmological inflation when the universe expanded quickly, effectively faster than the speed of light, where A got zoomed out over there and B got zoomed out over there even though that appears to be impossible. And that's how we've got the solution to the horizon problem!" ... That's not a solution.
@alexluke6665
@alexluke6665 6 лет назад
Space can expand faster than the speed of light, but nothing can travel through space faster than the speed of light. We think inflation was caused by exotic, extremely high energy particles shortly after the BB, which provided a negative pressure on the Universe, causing it to expand rapidly. After a short time these particles decayed into normal particles.
@MichaelAChristian1
@MichaelAChristian1 2 года назад
@@alexluke6665 Those are claims not science.
@alexluke6665
@alexluke6665 2 года назад
@@MichaelAChristian1 Yes, they are. I have a degree in Physics with Astrophysics at University.
@MichaelAChristian1
@MichaelAChristian1 2 года назад
@@alexluke6665 That is your evidence for breaking the speed of light trillions of times? I think you proved my point. You can't fit a glass of water into a "." much less the solar system.
@alexluke6665
@alexluke6665 2 года назад
@@MichaelAChristian1 I have literally no idea what you are talking about.
@orchoose
@orchoose 2 года назад
I like the usage of minkowski diagram.
@BigNewGames
@BigNewGames 7 лет назад
My simple question is how did they determine the distance of the cosmic microwave background radiation from us?
@shuyuwang6122
@shuyuwang6122 7 лет назад
BigNewGames we can determine the time that took the radiation to reach us. The distance is the time interval times the speed of light.
@BigNewGames
@BigNewGames 7 лет назад
@Shuyu Wang; Okay, but how is the distance to the CMB determined? Time is easy to determine but great distances are only measurable by stars that go super nova, producing a relative luminosity. So if the CMB is simply a different temperature then how can the distance to it be calculated? Assuming the distance away because of the age of the universe is not an accurate means to measure.
@alexluke6665
@alexluke6665 6 лет назад
CMB is everywhere, and uniform to one part in 10^5. It doesn't just exist in patches, it's everywhere. Hence why it is 'background'.
@kosannihilata
@kosannihilata 7 лет назад
As a Christian, speaking to the other Christians, please understand that "God created" is not unequivocally the best answer to the Horizon Problem. We Christians have the same exact problem, which is called the Starlight Problem. If, as a Christian, you believe in "young earth creationism" or "literal creation theory", then how did the light from a star reach earth from millions of lightyears away, if the earth is only 6,000 years old? This is not a stumbling block, and this is not a man who is attacking your faith. It is a man explaining how to think through solving this very real problem in our limited capacity. Also, if you base your views of science on a single 3-minute video, that might be another problem altogether. Give the thought credence, and evaluate our own Starlight Problem. By Faith you are saved, but that doesnt mean you cant evaluate and be in awe of what we have around us. It doesnt mean we arent allowed to ask questions....
@mathemagics4497
@mathemagics4497 2 года назад
Let's say you make a new planet, then light from distant stars would still reach it even if the planet is just created. I think you meant, if the universe is 6000 years old, instead of the Earth. Then that's interesting.
@gooberclown
@gooberclown Год назад
Einstein said that matter cannot travel faster than light. Therefore, no solution and no cigar.
@raykay126
@raykay126 9 лет назад
Why does it matter that they have the same temperature? "because they didn't have enough time to reach each other" Yeah I know that but I am saying why cant it just be a coincidence?
@NoSignalConspiracy
@NoSignalConspiracy 8 лет назад
It can. But its super unlikely. There are endless possibilities for variation in temperature. But only 1 possibility for uniformity
@filip8985
@filip8985 4 года назад
3 minutes - 30 seconds of intro - 10 seconds of outro
@thanhhuynh8292
@thanhhuynh8292 4 года назад
Another explanation: A and B are actually physically close to each other but light is bent.... which means... there's a blackhole between them and us... hmmm.... who's with me?
@johnholme783
@johnholme783 4 года назад
Elegant solution, but what evidence is there for it?
@sionaa.5038
@sionaa.5038 4 месяца назад
I do not understand the problem. We think that the universe started almost in one point. So it would not be suprising that all sufficiently large regions of the universe had basically the same starting conditions. Then they developed according to the same laws of nature. So why wouldn't they all look very similar now?
@evitagleinig6184
@evitagleinig6184 3 года назад
the person on the photo is my mumy
@Achrononmaster
@Achrononmaster 2 года назад
omg people! Expansion of space is _not_ a motion of space, it is a motion of separation of particles. The space does not actually move. The particles never move faster than light speed, nor does the distance between them "move", the distance between them can increase faster than light speed, but it does not "move" anywhere. Separation between particles is not a particle, it is a quantity that depends on observing two separate particles, not observing anything in-between them. So nothing in-between needs to be moving at all. Same, or similar, to how you can make a shadow move as fast as you like, faster than light if you can project it far enough away and still see it. When a shadow moves nothing _in the shadow_ is moving (you cannot get knocked over by bumping into someone's shadow, except psychologically). So... the lecturer misspoke. Space never has expanded "faster than light", space does not expand. Distance between particles does expand, but that is not itself a physical particle --- not a physical mass --- separation between masses is a correlation function, not itself an object. So when someone says "expansion of space" always think of it as shorthand laziness for "separations between past event world-lines increasing." Always there must be a reference to two or more objects to measure the gap between. A relational quantity, not an absolute quantity.
@beezap8892
@beezap8892 7 лет назад
spherical horizon explained on my channel, lemme know what you think.
@kenantahir
@kenantahir 3 года назад
well that is not a problem to begin with that actually is quite obvious ... i didn't think that was even a problem
@mrgarnache3868
@mrgarnache3868 10 лет назад
The problem is it either makes the hypothsis wrong or it says that period of time science does not apply rendering it a bad hypothsis not a Science Theory .... My more sensible solution would be that rather than adding an inflation period , realise that because of the massive gravity and speed of expansion that TIME moves so much more slowly that the universe expanded much more than people realised then .... what is my proof of the inacurate calculation ? Well obviously if time runs more slowly but light moves at the same speed from the observers point of view inside the universe ,,,,, light move move further at the beginning of time because it moves the same distance but time is essentialy slower allowing for that to happen ..... So my proof is that Planck says that light in 10X-43 sec moves 1.06x10-73 Meters ,,,,, So if light moves that far in that time TODAY it would have moved MUCH further when time ran MUCH slower back then making the inflationairy problem not a problem .... Their is a calculation obviously that takes some of my theroy into account because the hubble consant would put the universe at 60 billion years not 13.7 , it's my contention that the "inflationairy period" would not be necesary if you calculate the speeding up of time as the gravatational pull , less mass, and slowing velocoty correctly , because you would have your basic expodential curve of time ..... speeding up VERY slowly in the beginning and then accelerating very quckly later an the stabalising .... the same essential outcome but using actual SCIENCE not making a period of time outside of science and calling it a scientific answer ..... which it's NOT .... it's a hypothsis at best .... one I claim to be unnecessary and absurd as well.
@BenjaminCronce
@BenjaminCronce 10 лет назад
You make a lot of assumptions that contradict current measurements and even conflict with each other. I won't say it's illogical, it just doesn't fit what we know and understand.
@mrgarnache3868
@mrgarnache3868 10 лет назад
You realize that the "inflationary period" was created because the original background radiation proved the original big bang theory false right ? ...... So they added the 2 magic forces of nature that don't exist and ALL mass moving faster than light which is impossible ....... AND it turns out the measurements were WRONG ...... and you say it doesn't fit "what we know" LOL The new measurements of the background radiation show that the radiation is NOT spread evenly as they thought when they invented the inflation nonsense , that is what we know today , rendering the whole inflation nonsense proven absurd by the newest facts we have. The inflation nonsense was a PURE fabrication , a theory made up to fit a set of measurements that were incorrect in the first place. It's an example of manufacturing complete nonsense in a desperate attempt to salvage a theory .... which as I pointed out was not even necessary as the measurements were simply wrong. So what you are left with having to decide is .... Are you going to believe in 2 forces of nature that don't exist and ALL mass in the universe moving faster than light which only came about based on a false premise that the radiation was spread evenly which has now been proved incorrect ...... OR understand that it really is just a made up bunch of nonsense that is CONTRAIRY to the latest facts and has ZERO proof of ever happening AND it contradicts all of our observations of how fast mass can move ? People like Stephen Hawking and Rodger Penrose have both admitted the inflation period is nonsense and have completely new theory's about the expansion of the universe.
@BenjaminCronce
@BenjaminCronce 10 лет назад
MrGarnache We are already observing galaxies moving faster than light way from us. This has been verified by many top-notch Universities and is considered FACT. Nothing can move through space faster than c, but space itself has no such limit and space is expanding. The fastest galaxies are moving about 2.5x c from us this very moment. Well, ignoring that the information is 30bil+ years old. "This very moment" is a bit abstract.
@mrgarnache3868
@mrgarnache3868 10 лет назад
Benjamin Cronce None of that has anything to do with weather the inflation theory is nonsense or not which is the topic.
@BenjaminCronce
@BenjaminCronce 10 лет назад
MrGarnache Did you even read what I wrote or did you have a canned response? Hyper-inflation is happening RIGHT NOW. We know it can happen because it is happening. The question is did it happen in a very specific way. That we do not know yet. Is inflation nonsense? No, because it is happening right now, so we know it to be true.
@llibressal
@llibressal 6 лет назад
If we're seeing the same thing,(red shift, background radiation, etc), in every direction then we would have to be at the exact center of the universe. ...And the chances of that not being the case is quite literally astonomical.
@alexluke6665
@alexluke6665 6 лет назад
Not true, imagine being in an expanding balloon. No matter where you are in the balloon, as it is blown up and expands every other point in the balloon moves away from your position. Imagine the Universe as this balloon and you'll see why we see everything being redshifted away from us.
@MichaelAChristian1
@MichaelAChristian1 2 года назад
@@alexluke6665 No. Wrong. You are in 3d space.
@mattb9310
@mattb9310 2 года назад
This doesn't make sense to me. Imagine a meteorite hitting the ocean, the shock-wave moves at the same speed in all directions, right? Same thing with the universe, you have uniformity because the result is more like a big wave than a big bang. There is no point A and point B. IMHO the horizon problem doesn't exist. There is no spoon!
@rossharring6996
@rossharring6996 8 лет назад
gee whiz! you got any evidence of that
@TheGreatUtopiaCat
@TheGreatUtopiaCat 7 лет назад
I love modern science!
@Carsonb55
@Carsonb55 5 лет назад
fairytale!!!!
@ian9toes
@ian9toes 9 лет назад
The real solution is found in the Bible. Isaiah 45:12 "I am the one who made the earth and created people to live on it. With my hands I STRETCHED out the heavens. All the stars are at my command."
@Ryan-PulsarProductions
@Ryan-PulsarProductions 9 лет назад
AMEN!! :) Scientists can't explain these evidences of intelligent design through creation so they make up conjectures. Scripture has been reinforced as truth through unbiased science time and time again.
@SolocovGE
@SolocovGE 9 лет назад
***** wait that wasn't a joke ?
@lucasdarianschwendlervieir3714
***** As far as I know scientists are not trying to falsify intelligent design; in the case of cosmologists, they are trying to use empirical evidence to establish facts about the early universe, and explain them using physics. Of course you can question their intention and bias, which are really human mistakes.
@rCrazyfm
@rCrazyfm 9 лет назад
***** Isn't that exactly what you are doing? You cannot explain the origin of the universe, so you simply make up a "god" that created everything.
@setnoset
@setnoset 9 лет назад
Miguel Sousa You shouldn't suppose the belief in God comes from the lack of explanation of scientific facts. Most often the belief precedes it, and is established to the person on grounds of personal experience. The problem is if it negatively interferes with scientific research. Yes sometimes we let our emotions get ahead of ourselves, we all do. But don't suppose only negative effects exist. One may on the other hand think of God as their inspiration to understand nature. To quote an extreme example, Einstein believed in an impersonal God and contrary to what is sometimes believed, he didn't work out methodically some of his great ideas; they came to him intuitively. To take another example, Francis Collins was a director of the Human Genome Project. Well you can read more on him if you want.
@MsChlogirl
@MsChlogirl 6 лет назад
Liar, Liar, pants on fire. Universe is NOT expanding
@alexluke6665
@alexluke6665 6 лет назад
Yes it is.
@jordanvanderwerf
@jordanvanderwerf 4 года назад
This sucks
@samcross7881
@samcross7881 9 лет назад
see the big bang never happened( youtube)
@jessicaleblanc9908
@jessicaleblanc9908 5 лет назад
LOL he so out-updated .. I hope this guy isn't teaching you physics
@el34glo59
@el34glo59 4 года назад
He teaches physics but you're gonna school him huh?
@TheGreatUtopiaCat
@TheGreatUtopiaCat 7 лет назад
...faster than the speed of light? Sounds like a bullshit wrapping up to some failed theory
@Rofl890
@Rofl890 7 лет назад
The expansion of space can travel faster than the speed of light, but nothing can travel through space faster than light. However I have my own problems with this theory as well. I don't agree that the problem is actually a problem.
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