# Why AND HOW could Time Slow DOWN?

1. Sep 3, 2009

### ConfusedRiou

Ive been reading this forum two days straight and is very intrigued in Relativity. With the twin example, twin A time would be slower then Twin B. I need this explained to me in simple terms WHY? WHY? WHY? WHY? What does traveling at near light speed make time go slower. You guys and girls and discussing and this part is never explained. Why would time go slower? Id it the gravity and the mechanics of the actual clock that is slower and not time . Please any help would be appreciated

2. Sep 3, 2009

### TMFKAN64

No, it's *really* time that is slower... not just the clock!

"Why?" is always a hard question to answer... I'm afraid that the best I can come up with is "Because the speed of light in a vacuum is constant regardless of the speed that an observer of the light is moving."

So, imagine a beam of light hitting a mirror on the ceiling and bouncing back to the source. A stationary observer would measure the speed of light as c = 2 * h / t, where h is the height of the room and t is the roundtrip time of the light. An observer moving along the floor with speed v (who thinks *he* is stationary!) would see a light source and mirror moving *backwards* with speed v, and the light moving *diagonally* from the source, hitting the mirror, returning to the source (which has moved a distance vt', where I'm using primes to denote the moving observer's measurments). The moving observer sees the length of the diagonal path as sqrt(h'^2 + (vt'/2)^2), so this observer measures the speed of light as c = 2 * sqrt(h'^2 + (vt'/2)^2) / t'. But we have said that these values of c must be equal. We must also have h = h'. (If they are different, which is smaller? Both observers think the other observer is moving with speed v.) Therefore we conclude that t and t' must be different!

If you use a little algebra here, you can actually derive the relationship between the two.

3. Sep 3, 2009

### ConfusedRiou

So in basic understanding you saying the distance that i percieve that it takes it longer then what actually occured and that means what?

Im not nearly advanced as you or anyone of for that matter i cant wrap my brain around this.
For example if my twin was to leave the earth at 12.00pm and i just stood there and we had very huge clocks attached to us ..what is the exact moment that he started to live a shorter time? What exactly does him flying at near light speed causes our times to be off. If it takes him 20 light years to get to a planet and back to earth, then on earth he would be back in 20 years. While hes in a spaceship hes flying to the planet at near light speed which would take him 10 years to get there and 10 years to get back how in the world would our times be different. We are agreeing on the same thing

4. Sep 3, 2009

### JesseM

The additional confusing part is that there is no objective sense in which one clock is ticking slower at any given moment, it's only over the course of the entire trip that we can say one clock has elapsed less time. This is related to the fact that there's no objective definition of speed in relativity, you can only talk about speed relative to a particular frame of reference. For example, in the frame where the Earth twin is at rest the whole time, the traveling twin is traveling at relativistic speed during journey out and the journey back after the turnaround, so the traveling twin's clock is running slower during both phases. But you can look at things from the perspective of another frame where the Earth is moving at relativistic speed and the traveling twin is actually at rest during the journey out, and in this frame the Earth twin is aging slower during the journey out, so the Earth twin is younger at the moment of the turnaround in this frame unlike in the Earth's frame (see the relativity of simultaneity). But then after the turnaround the traveling twin is moving even faster than the Earth to catch up with it according to this frame's view of things, so the traveling twin's clock is aging slower during the second phase in this frame, and if you do the calculations you find that when the two twins meet, this frame predicts exactly the same thing about how much the traveling twin's clock is behind the Earth twin's when they compare readings next to each other (different frames always agree about localized events like this, even though they can disagree about which of two widely-separated clocks is ahead due to the relativity of simultaneity).

5. Sep 3, 2009

### ConfusedRiou

Ok let me get this right and i appreciate all help and direction by the way. So your telling me that there isnt one point where you can pinpoint where the twin is actually getting older then the other one? HOW HOW HOW? There has to be a point it just doesnt happen. And what is the cause of traveling at light speed. I hear others say all the time that traveling at light speed causes you acquire more time.I have a few questions that you can answer for me

1. What would make time run slower. I can keep hearing Earth twin would think traveling twin clock was running slower? Why? they would be running exactly the same.What force , what energy .

2.So if traveling twin in space think earth is moving at at relativistic speeds and earth twin otherwise why would the traveling twin the absolute time that is behind. Im hearing is having to do with accerlation but what does starting and stopping have to do with anything?

6. Sep 3, 2009

### TMFKAN64

In my example, the distance that the light travels looks longer to a moving observer. But the speed of light is constant to any observer, so this means that time must be moving slower for the moving observer compared to the stationary one, otherwise the moving observer would say the light is moving faster. Does this make sense?

When an observer is moving, two things happen: time goes slower, and distances in the direction of motion shrink. (You can work this out with a similar example, except instead of having the light hit the ceiling and reflect, have it hit a wall.) This happens *whenever* an observer is moving at *any* speed... it's just too small an effect to see when you are driving on the highway!

The important thing is that time and distance measurements always depend on the observer. In other words... time is relative! :-)

7. Sep 3, 2009

### ConfusedRiou

OK OK i think i might have it. Is it the gravity that makes time go slower? The inertia from the acceleration of velocity.if this is true what comparison does gravtity have with time?

8. Sep 3, 2009

### matheinste

In special relativity acceleration has no direct affect on clock rates. Gravity has an effect but gravity is not treated in special relativity. Time dilation, the slowing down of a clock in SR, always relative to another clock, is the result of relative inertial, that is, non-accelerated, motion. It happens at all velocities but is only of any significance at relative velocities of a sizeable proportion of the speed of light, that is, relativistic speeds. The differential ageing in the twin paradox usually onlly adds confusion at an earlier stage of learning SR, but the effect is due to the travelling and stay at home twins following different spacetime paths, the travelling twin's path being non-inertia.

Matheinste.

9. Sep 3, 2009

### JesseM

No, nothing to do with gravity. I think it's best to think in terms of a spacetime diagram with time on one axis and space on another, so you can see each twin's worldline as a path through spacetime. Here's one from the twin paradox page, with time as the vertical axis and space as the horizontal one, drawn from the perspective of the frame where the Earth twin (Terence) is at rest so his position in space doesn't change over time in this frame:

You can see that the length of the two paths is different--if these were ordinary paths in space, and you drove along each one with an odometer running, then even if the two cars had the same odometer reading when they departed from the point at the bottom of the diagram, they would have different odometer readings when they reunited at the top. In ordinary space, if a car travels in a straight line between two points with a separation $$\Delta x$$ along the horizontal x-axis, and separation $$\Delta y$$ along the vertical y-axis, then the distance traveled between the points (the amount the odometer reading will increase) is just given by the pythagorean theorem, it's $$\sqrt{\Delta x^2 + \Delta y^2}$$. In relativity clocks measure time elapsed along paths through spacetime in much the same way that odometers measure distance elapsed along paths through space, but the formula is slightly different--if a clock travels along a straight path between two points in spacetime (like Terence's path above, or like Stella's path between the 'start event' and the beginning of the 'turnaround'), and the two points in spacetime have a spacial separation of $$\Delta x$$ and a time separation of $$\Delta t$$, then the amount the clock will increase is given by $$\sqrt{\Delta t^2 - (1/c^2)*\Delta x^2}$$ (if you use a system of units where c=1, like light-years for distance and years for time, then this can just be written as $$\sqrt{\Delta t^2 - \Delta x^2}$$, which looks almost like the Pythagorean formula except for the minus sign). Because this formula is a little different than the Pythagorean formula, it actually works out that a straight-line path between two points in spacetime (like Terence's between the start event and the return event) will always correspond to a greater amount of clock time elapsed than a non-straight path between the same two points (like Stella's path), unlike with spatial paths where a straight-line path between two points in space always has a shorter distance than a non-straight path between the same points (because in Euclidean geometry a straight line is the shortest distance between points).

But aside from that difference, it's closely analogous. The reason the traveling twin ages less has to do with the overall shape of the paths, you can't pinpoint the moment where the Earth twin ages more, just like with spatial paths you can't pinpoint a particular section of the bent path that the extra distance is accumulated on the odometer. And just as different frames can disagree on which twin is aging more during a particular phase of the trip like the outbound leg, it's also true that different Cartesian coordinate systems in 2D space could disagree on which car had accumulated a greater odometer reading at a particular height along the y-axis. For example, suppose in the above diagram we have the y-axis oriented vertically and the x-axis oriented horizontally--in this case, if we pick the y-coordinate of the turnaround, Stella's car will have accumulated a greater odometer reading at that y-coordinate than Terence's car. But now suppose we orient the y-axis so it's parallel to the outbound leg of Stella's trip (which is equivalent to keeping the y-axis vertical and rotating the diagram so that the outbound leg of Stella's trip is vertical while Terence's is at an angle)--in this case, at the y-coordinate of the turnaround, it will be Terence who's accumulated a greater odometer reading than Stella. So until the two cars reunite at a common location, there is no objective frame-independent truth about which has accumulated a greater odometer reading at a given y-coordinate, just like in relativity there is no objective frame-independent truth about which clock has accumulated a greater amount of time at a given t-coordinate.

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10. Sep 3, 2009

### Al68

A clock runs at different relative rates in different reference frames. A single clock doesn't speed up or slow down in any absolute sense, its rate is just frame dependent, analogous to the way relative velocity is frame dependent.

If you notice a utility pole moving at 30 mph relative to your (moving) car, then after you hit your brakes the utility pole is moving at 10 mph relative to your car, you might ask what caused the utility pole to slow down. The answer is that the pole didn't slow down in an absolute sense, only in a relative sense. The relative speed of the pole is frame dependent.

It's the same for clocks in relativity, a clock's rate depends on reference frame. In the twins paradox, earth's clock runs slower relative to the ship's clock because, just like any clock, its rate is different relative to different reference frames. Same for the ship's clock. Neither clock changes its rate of operation in any absolute sense. Each clock just keeps proper time in its own rest frame.

In other words, time doesn't "slow down" in a different reference frame, it always was slower in that reference frame.

11. Sep 3, 2009

### ZapperZ

Staff Emeritus
You have a problem in understanding the basic principles of Special Relativity. I would suggest you try to tackle that FIRST before attempting to incorporate gravity and acceleration.

What you're asking is almost impossible to "teach" on a forum like this. The BEST approach for you to do (besides actually taking a class like most students), is to go through an elementary introduction to SR and see if you can work through that. If after doing that, you have specific areas that you don't understand, that it would be easier for everyone to try and handle that, rather than what is being done right now where you are jumping in right in the very middle of the story. So of COURSE it doesn't make any sense. This is not how most of us study and understand SR.

I would strongly suggest you go through this text:

http://www.oberlin.edu/physics/dstyer/Einstein/SRBook.pdf [Broken]

Zz.

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12. Sep 3, 2009

### I_am_learning

Why why why why why why do a football flies off if I hit it?
Because you provide it energy (/momentum/ whatever you say).
Why why why why why why do a football flies off if it gets energy (/momentum/ whatever you say)?
because atoms are .... bla bla bla?
Why Why why why do atoms behave in such way?

............. Because this is what we observe. This is what is said to be experimentally verrified. This is what we are supposed to believe at the present.

What i meant to show is that to every theory, there must be some experimental framework. All theories are just a mean to equationize what we observe