Why Protons Can't Travel Faster Than This Speed
The special theory of relativity tells us that nothing can cross the speed of light. Sadly for protons the limit is slightly lower than the speed of light.
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I'll petiton my local council to raise the speed limit. You can thank me now.
I'll sign but I think we'll need some good good luck 😅
First I thought you made a typo and this video would be about why massless particles must travel at c. I had never heard about this GZK limit. Thanks for this new info!
"Why can't protons travel faster than this speed?" "You... you meant photons, right?" "DID I STUTTER?"
@@General12th There is no such thing as a photon - Ken Wheeler
At 0:40, the principle of relativity is WRONG! When you have two objects where the one is moving relative to the other, it is not that each of them is stationary in it's own frame of reference and it is the other that is moving. In fact there is an absolute frame of reference where each object has an absolute velocity, it is the COMMON CENTER OF MASS of the two objects! The common center of mass is the stationary - absolute frame of reference! Therefore every object has an absolute velocity with respect to the center of mass of the universe! Do not believe anything the called "professors" tell you, the purpose of all this is on the one hand financial benefit that they have from all this fairy tales such as the theories of relativity, quantum mechanics etc. On the other hand is that they are trying, even if the most of them don't understand, to make the people as stupid as possible, so they can take full advantage in mankind! That is, they want people like dogs to not resist anything! After all, it is not accidentally that most of those who "lead" humanity are jews. Bankers, politicians,, actors, scientists (Bohr, Noether,, Feynman, Susskind, Newton, Einstein and many others) all of them aim to dominate humanity!
@@johnnym6700 oh god, the king of word salad
same here! had no idea there exist other universal speed limits below c
It's very rare that I come across a video talking about something I have literally never heard of before by any of the thousands of physics videos I've watched over the years. Excellent!
Same.
Legit question, if you’re watching physics videos for years then maybe it makes sense to go study physics at uni? These videos are nice, but they don’t really capture the picture of how a lot of things are derived
@@tgr5588 If I would study any subject where I watch hundreds of videos about for years, i would have like 8 majors. People sometimes just like to learn things. (or have ADHD like me)
@@tgr5588 Why do you suppose that watching thousands of physics videos implies no formation in physics? The GZK limit is not well known to physicists in general, it's a very niche phenomenon. I'm pretty sure most post-docs in physics don't know about it.
Why does this not have 1M views yet.
What a fun and interesting dip into relativistic particle physics! Great job making the video so accessible… we predict rapid channel growth heading your way!
Hi, thank you very much for such words I hope you're right :) I wish you all the best on your KZhead yourney guys :)
Imagine being a proton traveling at 0.99..9998c and watching photons travelling past you at c :)
I want to but i can't because I'm using all my concentration to maintain my speed of 0.999c (yeah ONLY 3 9s. I'm 1 of the "slow" kids)
😁😁😁
The Naughty frames of reference.
Not only that, but those protons would "see" light going a 1c FASTER than them. Lots of people visualizing this think light might seem very slow for them. But they don't. And its one of the "craziest" things about our universe.
It’s still weird that even from the ultra fast flying proton frame light would move with c.
First timer here. Really appreciate that the topic is not "dumbed down" like so many other sci-sites. Showing the math makes all the difference! Suscribed...thank you.
Seconded
Thank you for building up such a topic with a historic reference frame. It makes the topic so much better to understand and to enjoy. Also, switching between you talking and animations was well balanced, adding to the lecture. I'd like more of this!
I have studied this effect in the uni a few years ago but totally forgot about it. Thank you for refreshing my memory hahaha. Nice video :)
The CMB shows us that we are moving relative to some frame, because we see a clear dipole, and also a quadrupole moment in the observed temperature. The postulate of relativity does not hold for our local, real universe because we are not in an absolute vacuum. If you try to travel close to "c" relative to your starting frame, the CMB will increase in energy to the point where it will eventually turn you into plasma.
true :) CMB slightly breaks the principle of relativity.
New sub here. I love the pace, gives me enough time to actually understand what's being said before you move on.
It isn't a limit like the speed of light. It just explaining why we don't detect any protons going faster than that. If a high-energy cosmic ray doesn't interact with a photon from the cosmic microwave background, it would continue traveling through space without losing energy through pair production. This could allow it to maintain its high energy and potentially travel long distances across the universe.
Ohhhh, subscribed! Walking through the math is incredibly useful. "There's a frame of reference where the CMB is stationary" is a concept I've never considered, thanks for blowing my mind like that
The mis-teaching of relativity has obscured that fact, sadly. A related concept is the "comoving coordinates".
Great video, everything was well-explained with just the right amount of detail. Subscribed.
Thanks for the sub!
Wonderful vid, excellent visualizations, you rock!!
I love the accent! Rodiation! And Aye-ons! Just subscribed!
I've not heard this explanation yet. Thanks! very interesting.
A very interesting effect, and a surprisingly simple one. Thanks for the video, I actually learned something new today.
This is one of those things that is staring you right in the face the whole time and is so simple, but it just never dawned on you ( at least that's how it is in my own point of view 🤣). Very informative and simplistic video!
Thank you for this new video ❤
Greatly enjoy your content
Excellent content! Please keep it up.
12:15 relativity is crazy Mr. Proton is going of for the weekend trip and Mrs. Proton staying at home has to wait 25 million years for him :(
I enjoyed this video very much. I found you to be very well spoken and engaging. I hope you have great success with your channel and your Ph.D. studies. Thank you. InscrutableJohn
Thanks :)
My first idea was "it'll decay into multiple particles". It seems like my toughts were not that wrong, but I also learned quite a few new things.
This is the first time in a long time I learned something new about physics. I haven't been seeking out more knowledge how I used to and this makes me nostalgic.
That was very interesting. I'd never heard of Δ resonances before. Thank you.
Very interesting subject - and well presented! Still, you offered enough to get my mouth watery, but not enough to develop a satisfactory understanding. I'd like to hear a little more detail about the interaction between the proton and the microwave background.
I was thinking to write a short pdf script to every video with a bit more math so that viewers interested more into the topic could download and read but I didn't manage to find time yet.
Very nice video, both a lot of detail and easy explanations. Relativity declares that no rest frame has special rules of physics. But it's been mis-taught as "there is no universal rest frame," when for many purposes the CMB fits the bill. This also answers my anxiety-inducing thought experiment of "what's stopping near-light speed objects from coming from deep space and just absolutely annihilating us?" This at least puts a rough upper bound to what's possible.
Good video though the number slightly wrong in the beginning, i.e incorrectly rounded, rather truncated, see it more accurate at 10:01 then there also 21 nines then ending in 866.
I don't know what's more entertaining, the content or his accent. I like how he pronounces stuff.
:D there are divided opinions on my accent so thank you :)
@lukasrafajpps it is very strong, the accent, but that is your appeal, to me.
Amazing video, amazing explanation, amazing storytelling (and amazing accent hahaha). +1 sub
thank you :)
Yes, it's because of the new Welsh speed limit.
So interesting, thank you.
Thank you for this interesting information.
Cool. Thanks for sharing.
Very interesting. Thank you for giving me a new obsession. Now I need to watch this every night for months. And the dreams too are going to be great. 😊😊😊
It is somewhat counter intuitive to consider that going very fast could mean coming to rest for anything. But that's how it is for everything that has a constant speed.
I didn't understand most of this (I only have high school physics), but I do enjoy trying to understand this speed of light limitation. So far this is the best video to explain the why of this limit. I will be watching this again and again until I 'get it'. Thanks! Subcribed.
Hi, it is nice to hear you are interested in physics :) The fact that there is a fundamental speed limit (the speed of light) is just observed fact and nobody knows why the speed limit is exactly the number it is. It is just the way the nature is and we have no clue why. This video is talking about the fact that protons have even lower speed limit than the speed of light.
@@lukasrafajpps Indeed. But, it is also intuitive to accept that particles with mass cannot infinitesimally approach the speed of light, as it would practically equal the speed of light then, therefore occupying all of the available energy in the Universe. The explanation as to what that limit really determines, may then be quite revealing to a non-physicist.
It is encouraging to notice that people without a university or college background in natural sciences are interested in such topics at all. Please keep this attitude up and remain interested! I hope this enthusiasm will irradiate towards others and induce some spark of enthusiasm as well. There is so much noise in this present-day world that distracts our attention away from what is really defining our world and our knowledge, that videos like this are a relief in that sense.
great video thanks!
What a fascinating combination of effects.
Nice one. Thank you.
Thankyou for this vid... before watching I had naively assumed that this upper speed limit might be due to the increase in relativistic mass pushing the proton mass up so high it would become a blackhole but now I see that I'm probably orders of magnitude off when this would (could?) happen. Thanks again.
Fascinating!
Excellent presentation on this curious subject. One comment: 50 J is below the low end of bullet energies (~150 J) and much lower than standard ones (>1000 J). Not recommending a 50 J bullet to anyone, but, still. Cheers!
It's in the airgun range. In many countries you need a licence for air guns over 7 Joules.
It's in the .22LR energy range.
@@praveenb9048 -countries- *tyrannies
@@DrDeuteron soo.. you find it tyrannical, when the police has the monopoly for weapons, causing much less gun violence in that country?
example: Japan.
Insane! Thx
Cool info. Thx much.
Fascinating. I don't recall learning any of this story during my physics degree in the mid 1990s.
you explain this lovely, i hope to hear more from you in the future. Collab with Anton Petrov perhaps?
Thank you, this is an awesome video. From simple examples to real numbers in maths. 4:09 Aliens! (it's never aliens) 8:30 "photon on it's own..." proton, it happens. 10:44 Cool, I've never heard of that unit of measure!
awesome ~💫
Great video as always! I was very surprised that the limit had to do with the CMBR interaction. My first guess was that there would be a speed limit for protons when their total energy was large enough to create a black hole. As far as the limit you present, I don't think it's universal. In principle, couldn't one build a large Faraday shield which would prevent the proton from interacting with the CMBR? I'm guessing the calculation of the kinetic energy of a proton needed to collapse into a black hole is not too difficult.
Did a quick research on how far is 25.7M ly, and aparently there's plenty of galaxies within that range, Andromeda is about 10 times closer than that. So it's possible that those OMG particles were formed quite close to us.
The mystery is how something nearby could produce protons at such high energies without also being very easy to find by other means.
For a foreigner your English is really good. Understood every word.
it's mid
thanks :)
My first thought on seeing the title was that it might be something like the Schwarzchild limit; as a massive particle starts traveling faster and faster it starts gaining kinetic energy, which, after a shift of reference frame, acts like higher mass. Given the physical size of the proton, if it ever had sufficient mass-energy from its motion, it should appear to generate an event horizon, since its mass-equivalent would be in a space small enough to generate a gravitational horizon (similar to how a black hole does). Needless to say, I learned something new today. :)
Correct me if I'm wrong, but I don't believe you can generate a black hole from the energy associated with motion. That feels like it violates some consistency law, since in its own frame of reference there is no horizon. Energy only acts like mass when it's confined; if you have a low-mass particle and make it go fast, it still acts low-mass (except for a handful of equations where you can keep the Newtonian form by pretending the kinetic energy contributes to the mass, but that's not hugely enlightening IMO).
no, no, and super no. 1) the mass doesn't change 2) the energy does 3) that's doesn't matter b/c gravity couples to energy 4) but energy isn't relativistically invariant, neither is the part of curvature proportional to it 5) so there must be something else, there is: energy flux & momentum change --and that cancels everything. It's just a proton.
No, absolutely not. The curvature of the gravitational field is invariant. Besides, you can test out your own theory: There you are, now define a reference frame in which you're moving arbitrarily close to the speed of light and see if you become a black hole.
The responses to this comment are correct, though they seem a _little_ brusque.
Great video! I assumed you would talk about the cmb photons eventually turning into black holes due to the blueshift relative to the photon. I am not a particle physicist, so ill just ask if this is possible too??
Not a physicist either but I don't think so, you can't have something be a black hole in one frame and not be a black hole in another frame
This can't happen it would broke the principle of relativity although iteresting to think about it.
I'm not sure the "photons turn into black holes at the Planck energy" argument is really about turning photons into black holes, rather an illustration of the theoretical gap between particle physics and gravitation. We know the models break down at these distance/energy scales, we just don't know how to fix it yet. But no, these blueshifts aren't enough to reach the Planck energy. The blueshifted photon energy here is ~10^8 eV, whereas the Planck energy is ~10^28 eV - we're a bit short.
No, not possible for a photon to become a black hole.
@@lukasrafajppsDialect said that internal pressure of earth accelerates every part of earth outwards and spacetime falls inwards to rescue all parts of earth and this is real cause of gravity and he also said that all other scitubers are giving wrong explanation of gravity by saying time dilation is cause of gravity.Please make a reply video on it and tell true cause of gravity ,dialect disproved that time dilation is cause of gravity but his explanation is also wrong because gravity cause internal pressure of earth and internal pressure of earth doesn't cause gravity.
Continue.... Your channel is very good... Soon you will be famous U. tuber
It occurred to me recently that such highly energetic protons might be produced in the evaporation of primordial black holes. The Hawking radiation generated by a black hole becomes increasingly energetic as it becomes smaller. A black hole on the verge of vanishing completely should emit particles close to the order of magnitude of the Planck energy, which is well beyond the GZK limit. At least, if the math in regards to such evaporating black holes is correct.
Will this number change as the CMB cools? What you're saying seems to imply this. Or am I misunderstanding?
that was superb!👍👍
Thanks a lot!
Excellent. Never heard of this before, but you explained it so well, even my average brain got a decent understanding.
Thanks for the kind words and the support. Much appreciated :)
Thanks!
I thank you for the support :)
Amazing video about something I never heard of, and didn't even think was possible due to Galilean relativity. My next questions are: is the reference frame of the cmbr set as the same as Earth, or is it set by taking an average energy of the cmbr and coming up with a new reference frame which would put the 'rest' energy of the cosmic microwave at that average value. If the cmbr refence frame is different to Earth's (given the movement of galaxies and solar systems seems sensible to do), what is the solar systems' average speed relative to this cmbr reference frame?
The cmb reference frame is the one where the cmb is isotropic(the same in all directions). Earth is not in that reference frame. The cmb is slightly blueshifted in one direction and redshifted in the other. The relative velocity of 368km/s
@@narfwhals7843 thank you 👍
Keep it up, rooting for you. On a critical note tho, this script felt like it was run through ChatGPT, choppy, random subject jumps, awkward transitions and broken pace. Hope you find your own flow and faze out trying to imitate a style, without even the self confidence of pulling it off.
Interesting... "Tall poppies" protons got energetically cut down in size, more or less spontaneouusly. Thanks for that bit!
You mentioned heavier nuclei. Is there some reason they don't think it was, say, iron or bigger? If it was anti-matter would that change the readings?
Heavy nuclei would have a lower speed limit, due to photodisintegration from blue shifted photons.
At 10:01 you used c for value of beta which is not required as it is just a dimensionless ratio.
luckily c=1.
Yes true, sometimes I lose focus on these things. Thanks for correcting.
I have no understanding of physics but the subject fascinates me. The proton has a mass so it should be subjected to the laws of special relativity. I thought these laws predict that if - as particle with mass - you travel at speeds closer and closer to c your mass will become larger and larger and you will also start to deform in some specific way depending on the direction you're travling in. At c your mass would reach infinity. Is this correct? Or are there other laws/rules playing a role in this type of process?
Very interesting, I did not know about this at all, and excellent explanation. It does raise a question, though. Wouldn't the proton interact with sunlight much more than with the CMBR, as the energy of photons from the sun have much higher energies, and are more abundant?
photons from the sun only dominate close to the sun. Compared to the millions of light years i guess it doesn't matter... edit: here on earth the density of sun photons is ~10^7 per cm^3, which is a factor of 2*10^4 more than CMB. At 0.002ly from the sun the numbers are similar.
It would, but if it takes 25 light years to interact with a CMB photon, I'm guessing there's a very low chance of ever interacting with a Sun photon.
@@kapsi 25 Million lightyears if i read it correctly, so even less of a chance
@@deinauge7894 The density of the Sun photons is higher close to the solar system, as you said, but their energy is also higher. As the video states, when the proton reaches a certain speed, the energy of a CMBR photon becomes large enough to generate pions, that's why the proton cannot go faster. How I interpret that, is that it is not so much about the number of photons it encounters, but what the energy of those photons is. It needs to be over a certain threshold. The Sun's photons already have that threshold energy at a much lower speed of the proton. The energy of a blue Sun photon is 2.8eV, that of a CMBR photon only 6.6*10^-4 eV, that is more than 4000 times smaller If I look at the relativistic Doppler function, then the speed at which a certain energy is reached is dependent on the square of the original frequency/energy. The speed of the proton at which the Sun's photons would start to generate pions would therefore be around 16*10^6 lower than for CMBR photons, at a speed of 1 - 4*10^-15 already, instead of the 1 - 2*10^-22 in the video. That is just a back-of-the-sleeve calculation of a non-physicist. I would love to see a real calculation from a real physicist.
Hi, the density of photons matter because it gives us probability of interaction. It takes 25M ly for proton to interact with CMB. The number density of photons from the sun is only higher close to the Sun but that distance is negligible compared to the 25M ly. Certainly in the age of the universe it happened that a proton of cosmic ray interacted with a photon from the Sun or other star though.
New concept for me. The CMB sets a standard frame of reference. That changes a lot.
Anything can be a standard reference frame, a particular flight from NY to London for example, is just that the CMB makes for a very convenient frame.
*A* standard frame of reference, not *the* standard, since that doesn't exist under special relativity. But the CMB is nice and universal, so it's pretty convenient.
The random, abrupt digital zooming is a distraction. I suppose it probably serves a purpose or maybe it is like podcaster's Super Giant earphones that are obligatory. It's just what is done to seem professional or something.
Does this mean that there should be excess protons at the lower energies? If so, is that detectable as a proof/signature?
"lower energies" 😅 yeah. And there should be a curve of energies related to distance from the source and time traveled. The CMB didn't used to be microwaves the whole time. At one point it would have been visible. That means less speed required to reach the same effect and thus the limit would have been lower at that time. So very very old protons that have been traveling longer should also be much lower in energy.
i see it in a different way entirely. to move something this way, something else has to move that way... to accelerate anything... something else has to be accelerated against. the ideal being when you can push an equal mass backwards at twice the forward speed... even if you have no mass, you have to push against it the other way at twice the speed! (huh?) theres a sweet spot, a maximum..."center of the curve"... then as you go faster, you have to push against more of something the other way even harder to go faster again... more work for less yield... diminishing returns... assymptotes... you can never truly ever come to a full stop, theres no such thing... nothing is stationary... and you cant reach "terminal velocity"... i hear people talk of "the speed of light", but what exactly is the speed of STATIONARY? in relation to what?
To put it simply using a very rudemtary metaphor , the intrinsic lag of the proton is barriered by the intrinsic frame rate of open space .
Infinity is an unbreakable barrier that you can only approach but never pass. If I could always accelerate at any rate and in any direction, I still would not be able to move faster than my shadow. No matter how far someone walks, they can never make it all the way to the rainbow.
Wow, mindblown! 😊
Particle physics on youtube? I hit the subscription button at (near) the speed of light!
We'll probably never get there, but in theory if humanity kept building more and more powerful particle accelerators we'd run into this problem eventually. But, presumably, at much higher energies than the GZK limit, since even at this point the protons only interact on average once every 25 million years, which matters in cosmology when they're travelling right across the universe, but not when they're going round a city-sized circle.
If you had accelerator you could probably shield off this CMB and cool it down near 0K which would eliminate the problem.
This guy is awesome! Really good at explaining in a way I can understand. I have my Masters in Physics and I wish they taught physics like this when I was in school. We just did a lot of math.
Wow, thanks!
@@lukasrafajpps Dialect said that internal pressure of earth accelerates every part of earth outwards and spacetime falls inwards to rescue all parts of earth and this is real cause of gravity and he also said that all other scitubers are giving wrong explanation of gravity by saying time dilation is cause of gravity.Please make a reply video on it and tell true cause of gravity ,dialect disproved that time dilation is cause of gravity but his explanation is also wrong because gravity cause internal pressure of earth and internal pressure of earth doesn't cause gravity.
At that speed the proton starts experienceing drag from the CMB but it could have started at much higher energy and despite getting slowed down every 25my still be faster than the limit.
There are not near sources that *we know of* astrophysics and cosmology are in constant state of flux with many new important discoveries every year. Besides the GZK limit only applies to protons, and there were experiments that indicated that a fraction are heavier nuclei. Those would be decelerated so much by CMB photons. So there is a little not settled controversy if those events above GZK limit are protons (and this is not the only controversy as most detectors used can not distinguish between protons and heavy nuclei: they measured energy not mass, besides those events are rare but frequent enough to doubt all are measurement errors: about 20 events last time I counted, but rare enough to make it difficult to measure their masses (if someone tryed that I am not sure).
*LIKE* Now, does this limit have implications for a proposed Large-LHC (100 km ring)? Or for that matter an ultra-large-LHC built in Outer Space, that I've heard some discussions of recently?
This limit is far beyond what humans could ever reach. The LHC operates at 7 TeV per proton which is 7*10^12. It is 7 orders of magnitude lower than the GZK limit. The 100km rigng is expected to reach 50 TeV which is still 6 orders of magnitude below. But, if we ever had such technology to build collider large enough we could cool it to the temperatures near absolute zero and therefore this effect would not be problem.
@@lukasrafajpps Thanks for the knowledgeable answer. While the verification of the Higgs particle was fantastic it was a bit disappointing that other theorized solutions such as Supersymmetry were not seen at the energy levels generated by the LHC; now they want to request more Euros to build the 100 km ring. These numbers give me something to use a reference.
Am I understanding correctly that basically protons traveling through space meet resistance from the CMB which creates a speed limit of sorts?
If so many particles in the universe are traveing at near-light speeds (especially very low mass neutrinos), what is their effect on the total mass of the universe? And can they be considered as the "missing mass" in the dark matter problem?
I imagine we could make protons go even faster than that in very powerful particle accelerators, since they would be insulated from the cmb?
I've thought about the issue of blue-shifted CMB as a hazard to moving through space near light speed. So, this is where protons start to interact. I would guess atoms will disintegrate at a lower speed than this GZK limit. On the bright side, at some speed before your ship disintegrates, you'd have plenty of light to see by!
not to mention that after certain speed the CMB would become a ionizating radiation but I would have to calculate what doses of radiation would a man get at certain velocity :)
But you could create a faraday cage in space to shield an area from the cmb radiation and then cool it to near absolule zero in order to have a space where you can accelerate the protons arbitrarily close to the speed of light
Imagine minding your own business, wondering where do all the pions come from and why they suddenly stopped after a while.
Was the "shrinking" of proton at relativistic speed counted at calculation of proton-photon interaction? Or it doesn't matter?
Relativistic shortening only happens in the direction of movement, so the cross section stays the same. The proton is shorter but just as wide, as when at rest.
shrinking only happens in the direction of travel (lets say z coord), so from proton point of reference, photon has same size (in x and y coord) its just squashed in z direction
Yes. But doesn`t sigma proportional to 1/V?
I had similar idea after I watched video about grain of sand hitting Earth at 0.99c, I was thinking instead of sand grain, just a single neutron, traveling at 0.9(100 time the 9)c, then I found online calculator, but when entering more than 60 9s it would say that speed has to be smaller than speed of light, but at speed of 0.9(60 9s)c a neutron has kinetic energy of 10^24 joules, or 6.24*10^42 eV.
luckily such particles can't exist :)
@@lukasrafajpps perhaps they don't exist, but how energetic was the first proton, or first neutron created after the Big Bang?
Protons need light to show the way. If protons are faster than light, then it's dark
Oh the implications! The GZK 'limit' was slower in the past, and will be higher in the future. Heavier particles, those in which the Up & Down quarks are replaced by Top & Bottom quarks could move considerably faster. They'd still bleed energy, but it would be a smaller fraction of the parent particle's mass. On the other hand, a Carnot Cycle engine that makes use of the temperature differential of the radiation impacting the front of the craft and expels its waste heat out the back into the Doppler cooled wake could be developed. It would be expensive to accelerate, but once the speed exceeds a certain value where the engine's thermal efficiency based on the temperature difference is attained, any additional acceleration is free.
Heavier particles are all unstable. The heat engine won't be able to accelerate the craft because radiation impacting the front of the craft slows it down more than what any energy heat engine can provide (conservation of energy).
@@denysvlasenko1865 Unstable, yes. But at that speed, the time dilation would extend their lifetime considerably. As for the Carnot engine... We'd make use of the Fitzgerald contraction. By rotating the engine, we compress the gas in the direction of motion, then expand it after rotating 90 degrees. This way the power stroke is longer than the compression stroke! 🤑😂😉
Something new? Awesome!
Great explanation of a very esoteric topic 👍
The time dilation equation of STR does not include the equation for length (x=ct) since the equation to be solved for t' is: (ct')^2 = (ct)^2 + (vt')^2 which cannot be generated from ct' = ct + vt' in first order. Speed is irrelevant. Einstein is wrong. The equation misleading "time dilation" equation suggests the force relation in first order (from a second order equation) f' = ct'= ct(G), but Beta = v/c = mv/mc (valid for any m). The correct analysis is that space (x = vt) is not included in the equation to be solved for the "time dilation" equation. (ct')^2 = (ct)^2 + (vt')^2 (solve it for t' for yourselve(s) to understand) and note that this equation cannot be generated from the "space" equation for length in first order (ct') = (ct) + (vt') (draw it on a piece of paper). Hint: If space doesn't exist, the twins don't go anywhere; one of them (the imaginary one) just gets fat in his/her imagination (t'). Which is why Hawking hints that time must be imaginary, but never says why. "Yesterday upon the stair I saw a man who wasn't there He wasn't there again today Oh, how I with he'd go away" - Ogden Nash See my post at "From MM Experiment to STR" at physicsdiscussionforum "dot" org That is, Fermat's Last Theorem is valid for the case n=2 for all positive real numbers c^2 a^2 + b^2 since in second order (I repeat, sigh. ad infinitum, ad nauseam) c= a + b c^2 = [a^2 + b^2] + [2ab] (Binomial Expansion, proved by Newton) [a^2 + b^2] (why) figure it out and you will be enlightened....😎
"Fermat's Last Theorem is valid for the case n=2 for all positive real numbers" What are you smoking? Fermat's Last Theorem is for positive INTEGERS. Consider visiting psychiatrist. You make trivial logic errors. This is not normal.
If the number of particles per area per time decreases as the third power of energy, as claimed in the video, then the 10^16 eV protons must be less numerous that the 10^9 eV protons by a factor of (10^16/10^9)^3 = (10^7)^3 = 10^21. Since the number of the 10^9 eV protons passing per area per time is 10,000 = 10^4, the corresponding number of 10^16 eV protons must be 10^4/10^21 = 10^(-16). There are roughly 3x10^7 seconds in one year, so the number of the 10^16 eV proton per m^2 per year must be 3x10^7x10^(-16) = 3x10^(-9) while the video claims that it is 3. Can you please explain this?
Hi, keeping in mind I don't know sh... about all this. I was wondering, about the electron/positron pair part, 10 to the 6, divided by 2, 10 to the 3. Up to there I'm good. My question is, why does the first numbers (511) times 2 doesn't match the value for the proton (938)? I thought it was a conservation of energy thing, so where did it come from? The collision? Thanks!
to create electron or positron you need 511 keV of energy so to create electron-positron pair you need a photon of 1022 keV. I am not sure why you think it should match 938 MeV?
Great video, but please explain a "barn"? Maybe I misunderstood the word.
It is a unit used in particle physics and its definition is literaly 10^-28 m^2. If you will you can think about it as a thickness of the particle, the more thick the more likely the interaction is gonna happen.
Amazing video 🙂 - undergrad phys student
wish you all best to your study :)
10:51 "The average distance a proton travels per one interaction is ~25.7 million years"? Was 'distance' supposed to be duration? A few sentences earlier it does specifically state the question 'how long' it takes, but then it turns over to 'distance' at the end and all calculations are in metric distances/surface areas, so it might also be that you meant 'Light years' instead of 'years'. (The on-screen answer also says lightyears) I'm not 100% confident if "years" is wrong here, it may be an interchangeable term (even if one-way) in some specific situations such as this one...
Distance and time are interchangeable. 25.7 million years is a pretty specific distance in terms of light speed. So in this case, a half life in time also corresponds to a half-life in distance.
@@Unmannedair Thanks for elaborating on that.
distance and duration are the same thing in particle physics, since hbar = c = 1. That means it's also inverse energy (hbar x c = 197 MeV fm). That also means energy is frequency is mass (at rest), momentum is inverse distance...and if light: energy is momentum, frequency is wavenumber, and for some ppl k_B = 1, so energy is temperature (e.g., if some says "I'm a physicist!" and you say, "what's room temp in eV?", they either say 1/40, or they're a liar. Newtons G=1 means they're black-hole theorists. Regarding hbar x c, all nuclear physicists know that above number, while high energy experimentalist might say 0.2 GeV fm, and theorist would say "1". An atomic/quantum optics physicist should say 0.2 eV nm, but probably not since they work in the inverse cm. IR ppl use that too, and microns. Below that, passive microwave ppl prefer GHz, and radar ppl dip into MHz. I skipped the THz and < kHz crowd since I've never worked with them. edit: I skipped Dr Becky and the observational ppl, for whom red-shift, Z, is distance...but I can't forgive anyone who uses parsecs, which is no less geocentric, and more cultural tied to humans, than light-years.
Hi, yes I meant to say light years and I noticed the mistake when editing but since the protons are traveling really close to the speed of light then the proton travels basically 25.7M ly in 25.7M years so I didn't consider it to be a significant mistake to redo the whole part or distort the video in any way trying to correct the mistake.
Yoh, you got fancy background lights now