# Can somebody explain time dilation to me please?

Discussion in 'Physics & Math' started by maxjojo, Mar 13, 2017.

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1. ### maxjojoRegistered Member

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Hello all, my daughter has asked me about some school work she has to do, the topic is time dilation. I have looked and youtube but did not understand it, could somebody please explain how time can slow down?

It sounds a bit strange to me.

3. ### arfa branecall me arfValued Senior Member

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5,270
You will need to understand relative motion. Then you will need to understand what a constant speed of light means in the context of relative motion.

It means, for instance, that two people walking past each other will have different past and future events at sufficiently large distances, but simultaneous for their encounter--these distant events won't be comparable for a long time of course. This is all wrapped up, as it were, in Minkowski diagrams.

5. ### The GodValued Senior Member

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3,485
Not understanding is not your fault, its kind of non intuitive.

Let me try in simple words..

1. There are two types of time dilation..one relative motion dependent and second gravitational field dependent.

2. There is a theory by Einstein called special theory of relativity, as per this theory the light speed is same in vacuum for all non accelerating observers. Non accelerating means no acceleration but constant speed.

3. Now imagine two observers are moving relative to each other, so the light speed as observed by both will be same.

4. See, ideally if you are driving a car at speed v1 and someone else is driving at v2, then there will be different relative speeds. But light if observed from anywhere either traveling observer or stationary observer the spped will be c.

5. Doing maths on this will give the concept of time dilation and length contraction.

7. ### CheezleHab SoSlI' Quch!Registered Senior Member

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I think this video explains it about as simply as possible.

8. ### maxjojoRegistered Member

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Hello again, thank you for the replies and video but I am no wiser to an answer to my question. I am not understanding how time can slow down?

Does time not pass for all at an equal rate?

My daughter went the shop last night at 8pm she returned at 8.25pm.

She was away from me for 25 minutes, I was away from her for 25 minutes.

Sorry if i am not very clear this is new to me .

9. ### exchemistValued Senior Member

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No it doesn't, when observed from outside, by something moving relative to the thing observed. But this is not an easy thing to grasp and you do need to put aside some serious time to understanding at least Special Relativity (General Relativity is a lot more complicated and harder).

The best example I can give is the cosmic rays. These hit atoms in the upper reaches of the atmosphere and give rise to subatomic particles that travel down to the surface of the Earth where they are detected. We know the natural decay rates of these, from lab measurement, we know at what altitude the cosmic rays produce them and we can measure the speed they travel. And what we find is that a lot more of them make it to the surface than they should, judging by what we see as their time of flight. So it looks, from our point of view, as if time runs slower for them.

This is exactly what should happen, according to Special Relativity. However, according to Special Relativity, what we would see if we were able to travel with these particles is not our watches running slower (we'd see them run as normal), but instead the distance between the upper atmosphere and the surface being shorter.

Either of these results in more particles surviving to reach the ground - the two are equivalent.

So time dilation and length contraction are the corollaries of one another.

But don't expect to understand this immediately: relativity is hard and you will need to read several articles or a short book before you get it. I can recommend one by B Hofmann called "Relativity and its Roots",which I found very helpful on this.

10. ### originTrump is the best argument against a democracy.Valued Senior Member

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The answer to your question is really very simple, what makes it difficult is that is does not match what we see in our every day lives. The reason that we do not experience time dilation in our every day lives is that the relative speeds between us is so small (compared to the speed of light) that the effect is very small.

I assume that your daughter is young so she is not expected to do any mathematical calculations. So the point is that when you observe someone moving, you will also observe that their clocks are moving more slowly than your clocks. If they are moving slowly it will not be noticable but it is still occuring, if they are moving at speeds very close to light then there clocks will look like they are moving in slow motion. The clock is slower because time is slower, this is not some sort of optical illusion - time itself is slower.

In your example with your daughters trip since she accelerated away and back to you and was moving for some portion of the 25 minutes, if you both had impossibly accurate clocks you would find that your clock would say more time had past than her clock would.

That is what is meant by time dilation. The reasons this more complicated - it is essentally because the speed that any information can be sent is the speed of light in a vacuum.

The reasons are probably not important just to know what time dilation. I hope this helps. I also hope that this not the begining of a thread denying relativity.

11. ### Janus58Valued Senior Member

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Up until about a century ago, this was thought to be the case, however now we know differently.
Relativity has caused us to re-think our understanding of time and space. Where before, we thought of them as two separate things, now they are considered part of a whole called space-time.
To paint a picture of the difference, I'll use an analogy.

Think of space and time like they are directions. Up until the advent of Relativity it was thought you could map out these directions like we do compass points. North-South would be time and East-west would be space.
Different points on this map would be different events separated by space and time. With this lay out, everyone would agree as to how far apart any two events where in time and space.

Relativity changed this. It turns out that the North-South/East-West mapping scheme doesn't match reality. Instead it is more like Left-Right/front-back, with each individual's own notion of these directions being the basis of the map.
With this scheme, two people, each facing in a different direction from each other would not agree on the time and space separation of two events. Events that are 3 sec(measured by his front-back direction) and 4 km part(measured by his Left-right) for one person, would be have a different time and space separation as measured by someone facing in a different direction. Some of what is the time "direction" for one of them points in the space "direction" for the other and vice-versa.

In this analogy, the different directions they are facing are the equivalent of observers having a relative velocity with respect to each other in the real world.

So when your daughter was traveling to and fro to the shop last night, not only did she measure that it took less time than you measured it as taking, but while she was moving with respect to you and the shop, she measured the distance between the shop and yourself as being shorter than what you measured it to be.

At the speed she was moving, this difference was extremely minuscule. To go back to the map analogy, you and she were almost facing in the same direction, so close, that you couldn't readily notice the difference.

This is one reason that the notion of universal time for everyone held on so long. The relative velocities we deal with in our everyday lives aren't great enough to make difference in our measurements that are noticeable without extremely accurate measurement techniques, and it has not been that long that such accurate measurements have been available to us.

12. ### rpennerFully WiredStaff Member

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People have been trying to give you a technical gloss without math which makes it impossible to estimate the size of the effect.
Historically, Newton assumed time passes for everyone the same. This was called absolute time. Historically, it usually works great, but then again historically people measure time with low precision, from near sea level on planet Earth, and from nearly the same state of motion. In 1865, the first fast phenomenon was understood well theoretically, electromagnetism. But the math of electromagnetism and the math of Newton didn't exactly line up unless there was a special state of motion which electromagnetism preferred. Experiment was not helpful in describing that special state of motion even though the experiments were well-conceived and very precise, so in 1905 Einstein advocated to update Newton's theories about space, time and motion rather than continuing trying to tie theories together in a way not compatible with experiment.

In doing so, Einstein gave us two notions of time. 1) The "coordinate time" which arises from building an imaginary Cartesian coordinate system where Newton's law of inertia (If no net force is exerted on in, a body will remain motionless or travel in a straight line with uniform speed.) applies. and 2) The "elapsed proper time" for any portion of any trajectory, which is the amount of time measured on a clock subjected to a certain motions. Then "coordinate time" is just the agreement of "proper elapsed time" for all clocks which happen to be motionless in a particular choice of Cartesian coordinate system. Since Newton's law of inertia treats zero motion and uniform linear motion as the same, the important part of choosing an imaginary Cartesian coordinate system is choosing a standard of which inertia motion is considered to be motionless.

So given a trajectory described in an imaginary Cartesian coordinate system where Newton's law of inertia applies, an inertial coordinate system, every trajectory can be described as 3 functions specifying the x, y, and z coordinates of the position of an object at a specific coordinate time t. Then the speed of the object is how much those numbers change in a given amount of elapsed coordinate time, Δt = t₁ − t₀. v = √[ (x(t₁) − x(t₀))² + (y(t₁) − y(t₀))² + (z(t₁) − z(t₀))² ]/(t₁ − t₀) = √[ (Δx)² + (Δy)² + (Δz)² ]/(Δt), where the square root comes from Pythagoras' theorem and the fact that the axes of the Cartesian coordinate system are at right angles to each other. According to Einstein (1905), the elapsed proper time for a path at constant speed v, is Δτ = √[1 − v²/c²] × Δt = √[ c² (Δt)² − (Δx)² − (Δy)² − (Δz)² ] / c, where c is the limiting speed for all things that convey energy and momentum, which just happens to be the speed of light in vacuum. So Δτ ≤ Δt. ( Δτ equals Δt only when v=0 or t₁ = t₀ which would mean Δt = 0).

So, let's say you and the shop are both "at rest" and separated by 100 km. To run her errand, your daughter then needs to travel at 600 km/hour for 10 minutes, spend 5 minutes at the shop, and travel at 600 km/hour back home (we assume that this is below the posted limit). Since the speed of light in vacuum is 1.079 252 848 800 × 10⁹ km/hour, your daughter really isn't moving that fast. Light (in a vacuum ) moves about 1.8 million times faster. So the total elapsed proper time for your daughter is:

Δτ = √[1 − v²/c²] × (600 seconds) + √[1 − 0²/c²] × (300 seconds) + √[1 − v²/c²] × (600 seconds) = 300 + √[1 − v²/c²] × 1200 = 1499.999999999814558... seconds = 1500 seconds − 0.185 nanoseconds

A normal 8-digit calculator can't even display this tiny difference from 25 minutes. That's why Newton was fooled into thinking there was an absolute time.

Einstein's 1905 theory of Special Relativity is more complicated than this, because that choice of an imaginary Cartesian coordinate system where Newton's law of inertia applies turns out to be completely arbitrary, so there is general coordinate transform to switch between describing the universe in terms of x,y,z,t of one system and x',y',z',t' of another system. That is called a Lorentz transformation. But even in these other coordinates where you and the shop are in a constant state of motion other than at rest, the same law for elapsed proper time applies to all trajectories so
√[ c² (Δt)² − (Δx)² − (Δy)² − (Δz)² ] / c = Δτ = √[ c² (Δt')² − (Δx')² − (Δy')² − (Δz')² ] / c

So the most physically relevant and special definition of time is the elapsed proper time, while the coordinate time is an invention used to help humans describe what is going on. The two definitions serve different purposes.

Later Einstein(1916) would consider gravity and position and show that they too have an influence on proper time. But that is a story for another time with much more math.

Last edited: Mar 13, 2017
13. ### maxjojoRegistered Member

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Thank you for all the lovely posts which I am finding hard to understand with all the technical jargon. I picked out this post to reply to because of the first part of the post. This user says that Newton assumed time passes for everyone the same, this is called absolute time. I would also presume the same and my reason would be because on the return of my daughter from the shop we surely spent the exact same amount of time away from each other?

Do you not agree with Newton?

14. ### Janus58Valued Senior Member

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We've gained a better model of space and time than Newton had in his time. While Newtonian physics is a very good approximation at relatively low speeds and gravity, it is still only an approximation. Relativity gives much more accurate results. It may seem to you that you and your daughter measured the same amount of time while apart, but you did not. Your ability to measure time was just not accurate enough to notice.

15. ### maxjojoRegistered Member

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My daughter did not measure the time while she was away, I was clock watching in worry and 25 minutes past by while my daughter was away. Are you trying to say that my daughter was in a different present than my present when she returned? I can not understand how it would be possible to have different times passed but she returned to me in the present. Surely you are joking and trying to confuse me because I am a women?

16. ### Janus58Valued Senior Member

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No what I'm saying is that you and your daughter would have measured a different amount of time as passing between the time she left and she returned. If both of you had identical clocks that were very very accurate, and your clock read exactly 25 mins later upon her return, her clock would have read just a bit less. She would also have been just a slightly less older than she would have been than if she had stayed home for that same 25 min as measured by you. As to your gender, I had no idea as what it was until now, and is of no consequence to my answer.

17. ### dumbest man on earthReal Eyes Realize Real LiesValued Senior Member

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Hey, maxjojo,
First off, welcome to sciforums.
You have picked a not so simple subject to hope for an oh so simple explanation!
Two key words to remember are perception and relative.
Try this Link - you may have to read through it more than once or twice - but it should help with furthering your comprehension/understanding of this non-intuitive phenomena...maybe...
At any rate, the Link : http://www.emc2-explained.info/Time-Dilation/#.WMdWqxvQelQ
Take it slow...try to learn everything in little steps!

18. ### rpennerFully WiredStaff Member

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As you say, this is school work. It is frequently encountered in high school physics, especially in college preparatory classes. Sometimes it is briefly talked about as "modern physics" which covers mostly 1895-1925, with "classical physics" covering 1592-1865, while there is no historical name given for post-1925 physics which has seen introduction of the physics of the development of the early universe, lasers, antimatter, superfluid helium, a proliferation of subatomic particles, quantum computing, nuclear fission and fusion, and observation of neutrinos, black holes, neutron stars and gravitational waves.

1) Newton guessed wrong about the nature of time.
2) There are two times that can be talked about. An imaginary shared time which is useful in agreeing when and where to meet and do things, "coordinate time" ; and a physically meaningful "proper time" which is different for different trajectories a person or clock might take. Since small differences in trajectories mean very small differences in proper time, it requires very precise clocks to measure any difference in proper time for people who are limited to surface travel. So that's why Newton didn't discover that he guessed wrong and why it is easy to synchronize your watch with the clock in town hall: you aren't moving fast enough for a clock as imprecise as a wristwatch.

The effect is small for small changes in position. A clock 4 meters above you is faster than your clock by just 13.7 seconds per billion years.
The effect is small for small changes in velocity. A freight train moving through your town with a relative speed of 32 km/hour has clocks that according to you are ticking slow by 13.9 seconds per billion years AND moving relative to you. While your clocks are ticking slow by 13.9 seconds per billion years AND moving relative to people on the train. So you are both right which 1) shows that the sharing of "coordinate time" is an illusion caused by low relative speed and low precision clocks and 2) it is not just "time dilation" but something is mixing up how we are used to measuring both time and space.

I don't know your daughter's textbook, but the whole world was in your shoes in 1905 when this idea that space and time are not what Newton assumed them to be made quite some number of professionals cross their eyes. It eventually got straightened out in 1908 when Minkowski showed behind the crazy math was a sane system of geometry of space-time (space and time taken as one thing) which respected the Invariant Interval, c² (Δt)² − (Δx)² − (Δy)² − (Δz)², the same way Euclidean geometry respects the Pythagorean distance, √[ (Δx)² + (Δy)² + (Δz)² ] between any two points. In 1916, Einstein made things harder again by showing that Minkowski's geometry was only an approximation good when gravity was too weak to care about. So 1895-1925 were some crazy years to be a physicist.

But nowadays, we have made spacecraft go at 241,350 km/h where the time dilation would cause its clocks to be slow by 0.79 seconds per year.
Nowadays, it is trivial for universities to built machines to accelerate tiny radioactive particles to 1 billion km/h where time dilation would slow their decay down to less than 40% of what it would be at relative rest to us. That's like a clock that loses 15 hours per day.

And we have engineers who keep the world's best clocks and share them through a network of Earth-orbiting satellites. Those satellite trajectories are both moving very fast with respect to us and moving very high with respect to us so both time dilation effects get tested every day by people who use those SatNav service (GPS) satellites. Those engineers have tinkered with those satellite clocks so that they don't track their own time, but time of us on the ground and worry about details about how lumpy bits of the Earth (ocean bottoms and mountain peaks) affect the paths and clocks of their satellites. So the nature of time turns out to be a business opportunity for some.

Only if those two are in about the same place and moving at about the same trajectory will their personal "proper time" agree at the precision of our most precise clocks. Some clocks are so precise, if you move them 30 cm up they can measure the height by the slowing of their ticking.

Precision is important. You say "25" minutes and a physicist wonders if you mean "25 plus or minus 0.5 minutes" or "25 plus or minus 2.5 minutes". But even if your daughter went to the moon and back, she cannot have lost even 3 seconds to time dilation. For human distances and the speeds humans travel the surface of the Earth with, these are small effects noticed only by precise clocks.

The nearest star to the Sun is over 100 million times further away than the moon. So if your daughter left home at 1 billion km/hour to go to that star and return, you would be waiting over 9 years and 60 days for her to return home. But according to any clock you sent with her, she would return home with less than 3 years and 164 days elapsed.

I'm not just a user, I'm also the staff member given oversight on the physical science sub-forums.
In science, people don't have authority, observations do. Newtonian theory about time, space, gravity and momentum have all been found to be only approximations of the true behavior of observable phenomena. So after 300 years of being the pinnacle of physics, the 20th century saw many things that Newton never did and could not describe.
The idea of "the present" is related to the idea of absolute time. For only if there is absolute time can all people, everywhere, agree what "now" means.

Switching views to the two times of relativity, "coordinate time" defined a "now", but "coordinate time" is imaginary and arbitrary and two different coordinate systems may define different "nows" so long as they don't agree on what "not moving" means. The only part of "now" to have any physical meaning is "here and now" — if two things happen in the same spot at the same time, everyone agrees on that. The fancy phrase for "now" used by physicists is called "simultaneity" — the condition of happing at the same value of coordinate time. The fact that this will not be agreed upon for different definitions of what "not moving" means, is called "relativity of simultaneity" and it marks the death of Newton's absolute time in physics.

Phenomena in physics are continuous, so your daughter always has a position in your coordinate system for any time in your coordinate system. When she returned to your home she met you in one place in space (location) and one place in time (when) so she joined you in the "here and now." Before she joined you in the "here and now" she always had a place in your coordinate system in a place "now but not here." But the changing meaning of "past", "present", "future" and "now" can be abused by human language, so physicists would rather assign them numerical labels.

t = 12:00, x(daughter, t) = x(home)
t = 12:10, x(daughter, t) = x(store)
t = 12:15, x(daughter, t) = x(store)
t = 12:25, x(daughter, t) = x(home)

This is utility of the (imaginary) Cartesian coordinate system.

No one is joking. This is the way we understand space and time since 1905.

Last edited: Mar 14, 2017
19. ### exchemistValued Senior Member

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Are you interested in learning, or are you wasting people's time here? Several people are going to quite some trouble to help you.

Janus's fairly simple point is that under everyday conditions we do not notice the effect, as it is far too small and can be neglected. But if you are, like him, an astronomer, it does show up. And if you read this link about GPS, you may get some idea of how time dilation has practical relevance to us all these days, though we may not realise it: http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

20. ### maxjojoRegistered Member

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I am getting even more confused with some of these posts, I am not too sure some of the posters know what they are talking about.

According to relativity my daughters clock runs slower than my clock while she goes the shop. I personally I cannot understand how that works because if her clock was slower than mine and time was running slower for her, then how can she return to me in my present because according to relativity she would behind me in time if it is running slower for her?

21. ### originTrump is the best argument against a democracy.Valued Senior Member

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I would just let your daughter read the posts here or read wiki on time dilation. I recommend that you do not try to help on this subject.

22. ### rpennerFully WiredStaff Member

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Technically correct, since according to special relativity the time elapsed on your daughter's clock while in a state of inertial motion is Δτ = √[ c² (Δt)² − (Δx)² − (Δy)² − (Δz)² ] / c which is less than Δt whenever any of Δx, Δy or Δz are not zero. The only way Δτ = Δt happens is when you daughter is not moving in a coordinate system that respects your notion of what it means to be motionless. But as the numeric examples have made clear since post #9, is that this is only a fraction of a nanosecond difference between Δτ and Δt unless your daughter is using an imaginary vehicle to travel at unrealistic speeds for a visit to the shop.

Just because your daughter's clock is not ticking the same time your clock keeps doesn't remove her from "the present" since "the present" is an artificial construct of coordinate time. Think of space-time four-dimensionally. Then "the present" is the 3-dimensional slice of those four-dimensional points which just happen to have the same coordinate time as what you call "now." So it's not "the present" -- it's “the all points defined as ‘simultaneous’ to ‘now’ in a coordinate system which respects a particular choice of a definition of ‘motionless’.”

While your daughter is moving with constant non-zero velocity between home and the shop, you have a relative velocity between you two. Either of you is correct to imagine a coordinate system which respects your motion as the inertial standard definition of "at rest" so either of you is correct to say your clock is in agreement with an imaginary coordinate time and there other's clock is the clock that is running slow and moving. As long as your daughter moves inertially (with constant velocity) time dilation is a symmetrical phenomenon.

The reason why your daughter's clock is physically behind yours (by a tiny fraction of a second) is that it is impossible for her to travel from home to the shop and then back again while remaining in the same state of motion. So while you at home can describe the universe with no more than one coordinate system, your daughter needs one while headed to the shop, one while at the shop, and one while headed home. When she changes coordinate systems, points distant from her change their relationship with her revised definition of simultaneity and the details of the bookkeeping mean your constant inertial motion gives you the most elapsed proper time even though at no point was your clock considered to be ticking faster than your daughters.

That's why it is simpler to just work with just one inertial coordinate system at a time and calculate your daughter's proper time from her trajectory.

Assuming the distance to the shop is L.

A(t=12:00, x=0), B(t=12:10, x=L), C(t=12:15, x=L), D(t=12:25, x=0)
AB(Δt=600 seconds, Δx = +L), BC(Δt=300 seconds, Δx = 0), CD(Δt=600 seconds, Δx = -L)
AB(Δτ = √[1 - (L/( 600 s × c ))²] × 600 s), BC(Δτ = √[1 - (0/( 300 s × c ))²] × 300 s), CD(Δτ = √[1 - (-L/( 600 s × c ))²] × 600 s)

Totals: Δt= 1500 s = 25 minutes, Δτ = 300 s + √[1 - (L/( 600 s × c ))²] × 1200 s = something a little less than 25 minutes.

600 s × c = 179,875,474.8 kilometers exactly, which is over 450 times the distance to the moon. The shop is going to be much closer than that in real life.

Say the distance to the shop was L = 1798.75 km, then to reach the shop your daughter has to travel at L/600 s = 1byy which is quite speedy for humans, but still below orbital speed. But by design this speed is 10,000 times slower than c. So √[1 - (L/( 600 s × c ))²] = √[1 - (1/10000)²] ≈ 0.999999995 = 1 - 1/200,000,000
which means Δt - Δτ ≈ 1200 s /200,000,000 = 6 µs -- a blink lasts 10,000 times longer than that difference.

So technically correct, but only measurable with the most precise of clocks.

But in science, we call those communicable, precise frameworks which are able to describe the behavior of all phenomena within a certain domain "scientific theories." And they are what correctly generalize the behavior of nature in situations where our intuition is not reliably-trained by human-scale experiences. Dealing with the gap between scientific descriptions of the behavior of proper time and human intuitions about time is a big part of "modern physics" as the scientific theory is the only one reliable at speeds faster than 0.1 c. Likewise, the physics of the atom makes no sense if you try to limit yourself to Newton's physics.

Last edited: Mar 14, 2017
23. ### maxjojoRegistered Member

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41
Typical male with a huge ego, implying I am stupid and will not understand the subject...