Time Dilation - Sixty Symbols
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- čas přidán 6. 03. 2011
- The twins paradox, muons and special relativity are among the issues in this video about the symbol gamma, which can represent the Lorentz factor.
With Mike Merrifield
More symbols discussed at www.sixtysymbols.com/ - Věda a technologie
I just had the displeasure of passing through a particularly exasperating part of the internet. Listening to a physics professor talk about physics is just so wonderfully soothing.
+TheMagicRat933 Do you remember which part of the internet it was?
I guess that was this part with a very heavy concentration of stupidity, where, in accordance with the General Theory of Intelligence, your mind bends when you pass close to it.
TheMagicRat933 describe this supposed devilry you stumbled upon...
SergeofBIBEK gusari certain
Man that was the single best explanation of the twins paradox Ive ever heard, and Ive been doing physics for a fair while now.
I have to say that I'm amazed about how easy it was for the professor to explain such a complicated subject... he must have done it a lot of times!
I just want to say how much I appreciate how much time and effort you put into these videos without having a serious monetary incentive. Gives me hope that there are still a lot of people out there that see the real value of knowledge and choose to share it.
I always love the way this professor explains things on sixtysymbols. He makes whatever the subject easy to understand.
Thank you so much for explaining the Twins Paradox, I've never quite understand it when my teacher taught me in class, nor did I understand the wikipedia page that explains. Now I finally do, your videos are inspirational as always, I enjoyed viewing them. Thank you.
Absolutely incredible as usual....these videos will never get old
Finally someone explained that in the twin paradox it's not the difference in speed that matters, but the acceleration. Thank you. :-)
Finally someone who explained the twins paradox properly.
You guys make it so much easier to understand. Keep the videos coming!
Lol, first time watching this video again in a few years, and the first thing that excites me is at 1 minute when I realize gamma is a unit-less quantity
well of course it is unit-less... It's a factor... right?
I am very glad the paradox was explained, it was bothering me for a while. Deciding which reference frame to look at. Simple in hindsight
the formula for Time dilation is
Δt` = Δt/sqrt(1-v^2/c^2)
from this formula you can also derive the lorentz contraction of bodies as speeds get closer to c.
Mind asplode.
Awesome video. I've been just going through and clicking on all of the Sixty Symbols videos. I'm no physicist, and in fact...never even took a physics class in High School. But this stuff is all very interesting to me, and I've thoroughly enjoyed every second of these 'lessons' so far. This is now, by far and away, my favorite.
Cheers,
-Adam
Baltimore, USA.
thank you so much for resolving the twin paradox and not leaving it as a cliff hanger !!
I "liked" this video before I even started watching it. Just from the title I knew it would be great!! You guys rock.
Good and complete explanation of the twin paradox. (When I hear people explaining the paradox the story usually stops after the first twin returns and they have different ages.)
you sir just BLEW MY MIND!!!!! i love these vids please keep them coming!
@figaro99999 This video was supposed to be about that... we have another video which goes into the difference between special and general relativity!
After watching your relativity videos, I can honestly say that finally, I can almost say that I almost grasp the concept....almost.
great vid. nice explanation of the twins paradox too, i think its the best ive heard!
fucking killed it. Sorry for being so blunt. this vid is the product of a smart proff, and a smart editor. Didn't stop talking once, and every second drenched with information.. so cool.
4:03 - 5:24 Great explanation about the "transition" from special to general relativity.
Simply LOVE these ones!
The definition of a "reference frame" is a specific velocity. When the rocket accelerates, its velocity changes, and therefore its reference frame changes.
omg thats so awesome, i learned a ton. i remember learning about this in physics but it never made any sense until now
Damn, finally I've got the answer to the twin paradox. I read and read, yet those text never explained this clear. Thank you professor. Thank you SixtySymbols team.
@Doriide I love these things too. And it would be awesome to see them more often, but only do as much as you can to keep the quality as high as you have it!
Glad to know what the formula is. It's going into my notes for a sci-fi book I've been planning.
Love the dramatic zoom-in at 2:11
With regards to the Muons, within their reference frame we would be the ones that time is lengthened for, but this is resolved through length contraction, i.e. the distance to the earth would be contracted due to the very high velocity of the earth relative to the muon, allowing it to cross the distance in it's incredibly short lifespan.
@miezpiez
I think the point here is to remember, a circular movement involves acceleration as well. I can't give you a direct answer, but I think this is central to the issue.
@koktelici No, the relative motion between the earth and the satellite are cancelled out by the fact the satellites are higher from the earth, and thus time runs faster. And it's the gravitational time dilation that wins so the clocks have to be adjusted for that. The relative motion only reduces the amount.
NICE!!! Totally refreshed me!! Please please pretty please make one more for General Relativity!! :D
@miezpiez The start conditions of the experiment need the twins to be in the same reference frame. We cannot say that one twin travelling at near-c is the start point of the experiment, since we're finding out what happens if one twin undergoes serious acceleration *relative to the other*. It doesn't matter how sharp the turn-around angle is.
@boswell255 Yep had the same idea.
I think in this way the Signal speed becomes Infinitly.
But do remember that any material has a spring effect, you push on one side, the rod compresses a bit and stretches out again, so the lag depens on the lenght and material.
The Lorentz transform will not allow you to separate time from length. Muons are virtual particles. During motion the particle cycle or frame is contracted while the wave frame remains constant. This is explained by the four vector equation. In motion the muon exists for a longer time. The frames exist on a time scale of no more than 1.3 x 10^-21.
@miezpiez One would need a constant acceleration to fly in a circle because velocity is a vector quantity(meaning it has direction.) This is why you can feel sharp turns in the same way you can feel acceleration forward while driving and etc..
If you listen to what he says at the end of the video about the twin paradox, something has to accelerate to attain light-speed, which messes up special-relativity. Only the object that has accelerated to near-light-speed feels the greater effect of time dilation. This kind of answers your other question too.
This all becomes very clear with a diagram (see the one with the red and green lines in the wikipedia article to special relativity). x = spacial dimension. events that happen at the same time for A are placed on this line. x' = similar but for B. If something (B) moves relative to A its ct is at a degree to the ct of A. In that case B's x (x') is at the same degree to A's x. 45° = c. Now you can do special rel. calculations with a ruler. :)
@boswell255
No. As the vibration would only travel the speed of sound (The compression of the material is in the category of sound and vibrations) hence it would be slower.
@IamBread18 Hello.
koktelici`s comment is correct. There is a discrepancy due to relative velocity, and another due to gravity.
@miezpiez If your direction is changing, so is your velocity, and so your acceleration has to increase / decrease aswell.
@malani292 You are the best!!! I can't say I have understood 100% clearly, but something that I thought was impossible now makes more sense!
The diagram of lorentz contraction was really helpful to get the gist of it!
I think I can now accept something that I have learned before :)
E^2 = m^2c^4 + p^2c^2
and actually there's a separate formula for time dilation in general relativity if i'm not mistaken, the mass-equivalency principle wouldn't really help much with dilation, all it proves is that faster particles must gain more mass/energy in order to accelerate, and that massive particles can't reach light speed since it would take infinite energy/mass, it also explains how photons can have energy, but not mass.
@culwin well thats like saying," if you go in the x direction, then you have to go in the y and z directions too". Space time is the same concept as the three dimensions of space.
@LeconsdAnalyse There is, but the relative velocity is cancelled out by the gravity. Say, normal = 0, faster time = +ve, slower time = -ve, The motion brings the time brings it to say, -5, but the gravity counters this and brings it to +1 (not exact or to scale, but the point is gravity wins). It's the gravity that causes the damage.
@TodKF Use the time dilation formula, t=γτ where γ = 1 / √(1-v²/c²).
Example: Your 1st question. v=0.9c ⇒ γ=2.2941573387056037392 ⇒ τ = t/γ = 0.4359 hour ≈ 26 min 9 sec.
@Tinteskou I don't there are any out-takes on this one... Professor Merrifield nailed it in one semi-concise take!
@miezpiez acceleration is a vector quantity. so if u change direction, u change the acceleration.
@boswell255 The rod is so long and as a result, so very flexible, that any input at one end would first partially compress the rod over the vast distances involved. This compression would then travel along the rod at the speed of sound in the metal. This is much slower than the speed of light in a vacuum.
It is not sensible to mix physical entities with an analysis of relative effects.
@posro1988 Yep, that's correct, assuming that "accelerating" (any change in direction or speed) is specifically referring to speeding up, then the one that accelerated is the one that will go slower. So it works out.
As far as I know, this is the only way to time travel, according to the laws of physics.
Time runs slower near gravitating bodies, but this is a general relativistic effect due to the curvature of spacetime, a little different from the basic time dilation of special relativity (which assumes a flat spacetime).
even so, the value of the acceleration does not change, but it's direction counts. it always points to the middle. acceleration is a vector.
Inward Spherical waves multiplying time dilation at right-angles relative to surrounding masses compressing the wave-amplitude at maximum compression points at wave crest and troughs equally balanced by opposite eXpansion at interchanging points the Plancks constant is multiplied by a larger amount and time will contract running more slowly within that ref-frame because its has the greatest energy or mass the shorter the wave lengths and the time period oscillating in harmonic motion.
Since all things is relative, to know what the temporal condition(s) is when
computing the Euclidean geometry & Cartesian coordinate calculation(s)
include the following ((x - a)² + (y - b)² = r²) factor
The time dilation rate ▬ The sum of time that is passing in location x
The time dilation ratio ▬ The sum of time that is passing in location x - y
If 3 days at point a = 19 years at b, your rate is 2.592 • 10⁵ for location x
& your ratio is 2.592 • 10⁵ ∓ 5.99184 • 10⁷ seconds for location x - y
@goldentitan21 That would only work if space is curved enough to close on itself. In such a universe, we would observe that the expansion is slowing down. Instead, we measured that the expansion is actually accelerating, so space is not curved enough and the twin on the spaceship would just travel in the same direction until the Big Rip takes place.
@ViraIVideos That speed still needs to be 2 or 3 orders of magnitude larger in order to percieve this change. We're talking 90% the speed of light to get a time dilation factor of 2 in comparison with a stationary object. Even 5 million miles per hour isn't enough to drastically affect the results I think.
@MindLessWiz With the Doppler effect, there is either a red or a blue shift of light depending on whether the emitter is moving away from or towards the observer. However, this effect is not what I am referring to. I refer to the "Transverse" Doppler shift due purely to the time dilation of the emitter's frame caused by its relative motion. This can only be independantly observed at the instant the emitter and observer pass each other. No one has ever sat on a muon to observe this shift.
Did not understand a word of it, but that was awesome.
NO.
Recall that `tau` (proper time) is the indefinite integral of √(1 - v²/c²) dt.
So if v=0 then tau=t, and if 0
Centripetal Force ▬ Moving, or directed inward to a center, or axis
Centrifugal Force ▬ Moving, or directed outward from a center, or axis
I did go aboard many carnival rides & the "Merry Go Round" is only one of them, also according to physics, physical law(s) & analytical logic I felt centrifugal force (e.g. as the body accelerates in a nonlinear direction centrifugal force creates a linear direction)
It's the same force felt by a body in a magnetic field accelerating in a circular direction
The more you think about it, the harder it is to understand.
you think about it the wrong way then
Niels Bohr said, "If you aren't confused by quantum physics, then you haven't really understood it."
Boom. Told.
dustichux867 Are you talking about quantum mechanics or special relativity?
Special relativity
@miezpiez Except to move in a circle you have to experience acceleration. Remember, acceleration is also involved when you're changing direction of motion, not just when you're changing speed. The only way you could travel in a circle without accelerating is if you're traveling through curved space; but then you're in the domain of general relativity
@miezpiez When you fly in a circle, you keep accelerating "towards the middle" to stay on the circular path. If you don't accelerate, you would go straight. So he'd be accelerating all the time.
I agree with most of what you're saying, I just need to add this little correction: if an object is moving at a constant speed and time inside that object is slowed down, the length of that object is decreased.
@miezpiez
the tangential acceleration may be the same in that case, but there will still be a centripetal acceleration!
@CaptainObviouzz A chance in direction is also considered acceleration
thanks; clear explanation. Just a suggestion - make the brief intervals between parts of the talk, a bit longer - say 5 secs. This gives a few moments to absorb what's just been said - and something on which the mind can hang the next segment!
wow that muon fact was awesome!
@miezpiez I guess it would be basically the same, because flying a curve (circle) means continuous acceleration.
@miezpiez if you go round in a circle you are actually constantly accelerating towards the centre of the circle... not sure but i think this means that it would have the same effect as the video.
@Ashcombeguy He's obviously talking theoretically. There are no rod 30 light years long. But what would happen is the atoms will compress, then expand again, kind of like a spring.
@saliverdis To go anywhere in space and come back to Earth, you need to:
1) accelerate toward your destination, for half of the distance or less
2) decelerate so that your velocity is zero when you reach your destination
3) accelerate toward Earth again, for half of the distance or less
4) decelerate so that your velocity is zero when you reach Earth.
When each acceleration or deceleration takes place, the symmetry is broken. Acceleration can be measured on the spaceship, but not on Earth.
@5r22 any change of direction IS acceleration. So any path other than a straight line has acceleration.
@miezpiez To make a circle, you have to change direction, ie accelerate, otherwise you would go straight. I think in this case, general relativity applies.
also, as a follow up to the Energy formula, the m in the formula is always for rest mass , relativistic mass is obtained from the full formula that also featured momentum.
people often forget about E^2=m^2c^4+p^2c^2, but they should know it because it applies to moving objects, wich is what relativity mostly deals with , E=mc^2 is only useful for calculating intrinsic energy , it's useful for nuclear bombs i guess
@Tallguyification That can be resolved with General Relativity, like he said. I imagine in this case, assuming they followed the same trajectory through spacetime, they would measure the same time relative to one another.
Prof Merrifield - the great explainer
@engelteir They've actually done it with clocks and in fact the clocks go out of sync and the one that isn't moving shows a larger time as having passed whilst the one moving shows a shorter time. This is why they need to constantly readjust the clocks of satellites because their orbit spped but more signifcantly, their distance from the earth, means their clocks are slower.
time dilation is interesting stuff. They've had a few really cool documentaries on the discovery channel back when documentaries where a thing. if I understand it correctly, time dilation slows down your clock enough to make long journeys possible in single-generation timescales. but I might be wrong on that.
@miezpiez although it doesn't seem like it circular motion is a state of constant acceleration .. because the velocity is constantly changing so .. that is still acceleration unfortunately
gps positioning systems correct for the time dilation present in the orbiting satellites.
Yes it does, as gravity can bend light (also space), this difference in speed has to be compensated through time dilation.
Thanks for uploading.
Even if the value of the speed is constant, the direction is not. There's angular acceleration.
When you do the U turn you will feel the centrifugal force, therefore, you will know that your reference frame is moving. If you CAN determine that your frame is moving, you are not in an inertial frame, so you can't say it's the same if you were moving or if you were stationary and the other twin was moving. It's not equivalent because in the second case you wouldn't feel the force and he will!
@PBDPBD Earth may seem accelerating but the brother on spaceship is the only one who feels the acceleration of his journey.
@TankEsquire so basically the one that does the accelerating is experiencing the "slower time"
I also once calculated in my head while trying to fall asleep, the approximate time dilation there would be if a space ship travelled to Proxima Centauri at a certain speed. AKA I found out how much time would pass on Earth and how much time would pass by for the crew on the space ship.
To change direction you must apply a force. Or in other words acceleration.
Yes. Yes, it does. Two things moving relative to each other will see the passage of time move at different rates.
If you move from A to B in 1 second you have velocity B-A in point B. When your reference frame is with a velocity C, then each movement from A to B results in an acceleration in B. Since we measure time as an effect of acceleration vs velocity (gravity, earth orbit), the amount of time goes faster on earth because there is more gravity = more acceleration = more time. Your clock is build on earth, remember?
@miezpiez If you go in a circle you are still accelerating, towards the center, so you would still undergo acceleration
I remember a very cool young adult book that dealt with this brilliantly. "Singularity" by William Sleator. Two Twins who find a shack in the back of an inherited house. Time moves faster in the shack than it does earth. Ergo, it moves slower than the earth.
all things moving constantly - special relativity theory or light theory checks in but if there is a change of velocity or time then the laws of physics checks in.
@miezpiez As soon as he said that I imagined the same scenario. It would be nice if he could answer.
I would imagine that there have to be some forces involved to make the trajectory, therefore resolving the paradox.
The twin on the space ship is the one who will feel the acceleration, ergo he is the one accelerating. (When you accelerate in a car, you feel "pushed back". You know what I mean.)
What you see isn't really the main thing here, the forces acting upon these characters are.
@passwordresetisbroke I wanted to keep the comment short, so I left out the effects of the general relativity. (shouldn't have done that).
So, there are 2 effects:
- clocks go 7µs/day slower (special relativity)
- clocks go 45µs/day faster (general relativity)
the result: clocks go 38µs/day faster.
It seems to me that we are talking about how the devices we use to measure time are effected. I can understand that. But, just because an atomic clock is effected by its velocity and relation to a nearby large source of gravity doesn't mean that time is effected. Also, we hear them talk about perspectives. Perspectives are very subjective.
@yonoid818 yes, but they would be off by nanoseconds. even planetary orbit speeds are almost negligible compared to the speed of light.