Time Dilation - Sixty Symbols
Вставка
- Опубліковано 21 січ 2025
- 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.sixtysymbol...
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.
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
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!
Man that was the single best explanation of the twins paradox Ive ever heard, and Ive been doing physics for a fair while now.
The definition of a "reference frame" is a specific velocity. When the rocket accelerates, its velocity changes, and therefore its reference frame changes.
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.
Finally someone explained that in the twin paradox it's not the difference in speed that matters, but the acceleration. Thank you. :-)
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.
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.
@figaro99999 This video was supposed to be about that... we have another video which goes into the difference between special and general relativity!
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?
There would still be a centripetal acceleration in order for you to travel in the circle wouldn't there?
earth is also rotating the sun and the solar system is spiraling relative to the galaxy , so that is important . Then my question would be if the one on a rocket goes in a strait line that intercepts with earth in a thousand years, so the rocket is in stable reference frame as the earth moves... ? Also, C is defined by time or distance primarily?
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.
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
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
@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.
Finally someone who explained the twins paradox properly.
I'm sort of confused, aren't I traveling close to the speed of light relative to SOMETHING? Am I currently under the effects of time dilatation?
@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.
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.
@miezpiez If your direction is changing, so is your velocity, and so your acceleration has to increase / decrease aswell.
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.)
@miezpiez acceleration is a vector quantity. so if u change direction, u change the acceleration.
I "liked" this video before I even started watching it. Just from the title I knew it would be great!! You guys rock.
@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.
What if i am travelling with a constant speed in a circle ? What if the twin travels from the Earth and back not in a line but has a circle ?
You would be accelerating because acceleration is dependent on velocity not speed and because you’re direction is constantly changing you are accelerating
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
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.
@5r22 any change of direction IS acceleration. So any path other than a straight line has acceleration.
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.
@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.
@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.
@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..
@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.
@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.
Prof Merrifield - the great explainer
@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
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).
@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.
@Tinteskou I don't there are any out-takes on this one... Professor Merrifield nailed it in one semi-concise take!
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
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.
@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.
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.
After watching your relativity videos, I can honestly say that finally, I can almost say that I almost grasp the concept....almost.
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 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.
Absolutely incredible as usual....these videos will never get old
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. :)
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 You cannot do a big circle without accelerating, though. There must be some force pushing you around (or pulling, in the case of gravity)
@miezpiez
the tangential acceleration may be the same in that case, but there will still be a centripetal acceleration!
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.
How would the planets gravity affect the twin who stayed at home?
What do you know about time & time dilation (e.g. temporal field)?
@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.
@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.
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.
gps positioning systems correct for the time dilation present in the orbiting satellites.
@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.
You could go around in a circle at constant *speed* but that would not equal constant velocity. You would be constantly accelerating (towards the center of the circle).
@miezpiez I guess it would be basically the same, because flying a curve (circle) means continuous acceleration.
thank you so much for resolving the twin paradox and not leaving it as a cliff hanger !!
But from the travelling twin's perspective didn't Earth also accelerate and decelerate? What am I missing?
The paradox is that in special relativity there is no absolute frame of reference and everything is relative. Meaning both twins could equally correctly say that they are staying still while the other is moving at the speed of light,
You guys make it so much easier to understand. Keep the videos coming!
@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
Regarding the twin paradox, I am not happy with the standard explanation using acceleration, turning around and using two reference frames.
For a start, the time dilation was REAL for the clocks used by Hafele & Keating.
Time dilation is caused by the speed of the object that accelerates from "rest".
It accumulates during the execution of this relative speed at a constant rate.
It does so for motion in any direction.
The outbound frame and inbound frame for the twin are the same frame.
(TBC)
@boswell255 Technically no. This is because the person at the other end will still be able to see the rod as they move it back and forth; this would mean the person at the other end would also have to be able to see it as it goes back and forth. You're not actually sending a message, as the rod you can see is 30 light years away from the other person. The rod they see is still moving but does not contain the same message you are sending. It's confusing, but i think i might be right?
@mortenlu I don't think so, I think the highest factor by which it can slow down is around 7, so the most you'd live (from a stationary (relative to you) observer's frame of reference) would be under 1,000 years.
To those muons moving to the earth, in their frame of reference, there are not moving, so for them, they would have decayed before reaching the earth, while to us, they have not.
And in LHC, two beams of hadron moving in the speed 10m/s below light in the opposite diretion. From the reference frame of one of them, the other beam is travelling faster than the speed of light,but if special relativity is true, what speed of the later beam would the former beam observe?
@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.
But what do you mean by speed?
The speed of each of the twins relative to the other is the same. So, why would one of them be aging in a different way than the other.
If earth's gravity is the reason of the difference, then i would be able to understand this paradox. Otherwise it wouldn't make any sense.
Thank you for your comment anyway :)
So, what if one of the twins flew off on a trajectory that is a big circle, earth being somewhere on its' circumference? Assuming he would start at (near) lightspeed and arrive back at (near) lightspeed and having done no acceleration-turn around-deceleration, what would be the result then?
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!
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.
But how is it possible that theres no absolute reference frame to measure velocity, so velocity is relative, but change in velocity per change in time is not relative, acceleration?
Let v=c-ε, where ε>0 is as small as you like. Then, γ = 1 / √(1-v²/c²) = 1 / √(1-(c-ε)²/c²) = 1 /√(2ε/c)·√(1- ε/2c) (after some rearranging). Therefore, using the Taylor expansion of 1/√(1 - x²), we get: γ=√(c/2ε){1+(ε/4c)+O(ε²)}~√(c/2ε) (ε→0+). Hence, t=γτ ~ √(c/2ε)τ (ε→0+).
what is it that causes time dilation? is it just that it takes force carrying particles longer to reach their destination if it's moving away from them?
Basically.
hows that? like gravity carrying particles? at what speed do they travel?
The Euclidean/usual metric is motivated by the Pythagorean theorem.
What is the motivation for the metric used in SR ?
@miezpiez Wouldn't he have to decelarate to stop, making the effects of relativity "stop working"? Just a thought.
@miezpiez when you are traveling in a circle you are constantly accelerating towards the center
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?
If two particle moves in opposite direction, whose time will be slower than whom? how is that sorted out?
The twin on the ship is moving relative to space itself. Space and time are connected, so it's actually the twin on the rocket's movement through space that causes the time dilation.
@miezpiez
Im thinking the same, when you speed away some of your motion through time is diverted into motion through space. The speed of the object through time slows down when it diverts some of its motion through time into motion through space. What this means is the objects progress through time slows down and time elapses more slowly for the object and the occupant than it does for you and things not moving through space(all your energy is through time). So wouldn't you get the same result?
@miezpiez Circular motion itself is accelerated. In order to follow a circular trajectory, a force called the centripetal force has to act on the moving object (e.g. in planetary motion, gravitational forces act as centripetal forces - though, of course, planets don't move on perfect circles). And when an object is subjected to a net force, it isn't at rest, and thus its motion is accelerated. Hope I got that right, else correct me...
Everytime the twin paradox is explained it doesn't work because the twin has to turn around, but that's because it is being assumed that space is flat. Why not assume that space is curved so that the twin that leaves just loops back around to the Earth? How does the curvature of space change how we should think about the twin paradox?
I guess that to spacetime to be curved that way, you need a gravitational field?
Not exactly. He means the shape of overall space, not the curvature of any given patch of spacetime due to the presence of energy. Depending on the spatial curvature in relativity(I think) space could be shaped as a hyperbolic plane or a hypersphere, as well as simply flat.
@IamBread18 Hello.
koktelici`s comment is correct. There is a discrepancy due to relative velocity, and another due to gravity.
so their relative clocks would slow down.... but if they had an actual clock... shouldnt it still show the same time?
An what is about the other extreme? Shouldn't time run like 'infinite fast" if you dont' move and not be near a gravitational object? I know that I myself am a "gravitational object". But what i I am a Neutrino or so? Thanks for Answers!
4:03 - 5:24 Great explanation about the "transition" from special to general relativity.
@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.
What if the spaceship go pass the earth at a constant velocity which is near to the speed of light relative to the earth and at a trajectory very near to the earth, and inside it is an atomic clock. There would also be another identical atomic clock on earth. Both the clocks would start ticking when they pass through each other, and the spaceship would send out Radio signal to tell what time is its atomic clock indicates. Then what would the time difference be?
Love the dramatic zoom-in at 2:11
@CaptainObviouzz A chance in direction is also considered acceleration
@miezpiez
In order to have a curved path, the twin will have to accelerate. Even if he stays moving at a constant speed, he won't have zero acceleration since direction is changing (since acceleration is a vector and not a scaler quantity.) I'm curious what the result would be for a trip with zero acceleration though. My guess is that the twin that went on the trip would be younger. Not completely sure though.
I'm asking for generousity since I still don't understand and a bit sceptical,
I wonder which one would arrive faster, light that came from 10m away from you, or the light from you that travels from you to a mirror 5m away? Can anyone generously show me an experiment like this?
@miezpiez Even in a circular movement you have acceleration, so i assume it would be the same