# Could i make this clear

1. Apr 2, 2008

### Denton

That special relativity is only due to the concequence that nothing can travel faster than c.

Such that time dilation is only due to the fact that we cannot measure the 'proper' time due to there being absolutely no way to convey information faster than the speed of light, and so every person would see their clocks, their life as being exactly the same, and just the outside world looking in would have the delay. Same can be said about length contraction, as the matter is almost (and i only say almost, dont kill me) catching up to the light, we see a compression rather than an actual compression.

Even though the answer must surely be "Of course, thats special relativity", it seems to me that special relativity is given almost supernatural characteristics that seem to defy our world, of twins aging rapidly etc when it is actually merly an illusion.

2. Apr 2, 2008

### JesseM

This is a common misconception, but you're wrong--time dilation and length contraction aren't about what you see, in fact depending on whether it's moving towards you or away from you, a moving clock will appear to be ticking faster or slower than the time dilation formula predicts because of the Doppler effect, and a moving object will actually appear to have an unchanged length due to the Penrose-Terrell effect discussed on this thread. But you can figure out the times events "really happened" in your frame, as opposed to the time you saw them, either by factoring out the light delay (so if in 2005 I see an event 5 light years away in my frame, I'll say it 'really happened' in 2000 in my frame), or by having a network of local synchronized clocks at different locations and looking at what the reading was on a clock right next to the event as it happened. See my post #2 on this thread for a little more on these methods.

Whatever method you use to get rid of the issue of image delays, you will find that time dilation is a real effect, not an optical illusion. For example, suppose that according to time and distance measurements in my frame, in 2020 I see a traveler 20 light years away aged 30, and then in 2022 I see the same traveler 12 light years away, now aged 36. If I factor out image delays, I'll calculate that the traveler was 20 light years away and 30 years old in 2020 - 20 = 2000, and the traveler was 12 light years away and 36 years old in 2022 - 12 = 2010. So although he visually appeared to age 6 years in just 2 years from 2020 to 2022, I'll say he "really" aged 6 years in the 10 years from 2000 to 2010. Since he moved closer by 8 light years in those 10 years, he must have been traveling at 0.8c, which gives a time dilation factor of $$\sqrt{1 - 0.8^2}$$ = 0.6, so this matches the observation that he aged 6 years in the 10 years of my frame's time between 2000 and 2010.

3. Apr 2, 2008

### Denton

What is the mechanism by which this occurs? i.e. why does speed change time?

4. Apr 4, 2008

### michael879

Your wrong. The postulate of SR is that light travels at c in all reference frames. From that all of SR can be derived, including the fact that nothing can travel faster than c.

Assuming the postulate is true, it is very straightforward to prove time dilation and length contraction. Since experimental evidence and maxwell's equations suggest the postulate IS true, time dilation and length contraction (as supernatural as they may seem) exist in the literal sense (i.e. after taking into account the time it takes light to reach you from an event).

5. Apr 4, 2008

### michael879

I don't think anyone has a great answer for this.. Like I said, SR is just a straightforward proof of some weird phenomena working off a single postulate. Theres nothing explanatory in it.

However there is one explanation you might like and that is the concept of 4-velocities (velocity through 4 dimensional space-time). Everything in the universe has a constant 4-speed of c. Light's velocity is completely spatial with no time component while an object at rest is completely timelike with no spatial component.

With this explanation (that everything moves at a constant 4-speed c), it becomes more clear how time dilation "works". As an object's velocity spatial components increase, the time component must decrease because the 4-speed is constant. Therefore as an object approaches c in some reference frame, its speed through time approaches 0.

6. Apr 4, 2008

### Schrodinger's Dog

To be correct it's actually the change in speed or acceleration that causes time dilation in respect to the frames of reference IIRC. No two frames of reference when added can equal more than c, no matter what there respective speeds, because of time dilation and length contraction.

To get an idea why the theory was postulated it might be worth looking at the history of physics, particularly the Michelson-Morley experiment, which suggested an ether was responsible for the peculiarities of time, a sort of dragging effect caused by the luminiferous aether. This was disproven by special relativity and the preceding experiments, that lead Einstein and Lorentz to postulate, that Ether was not an explanation for the experimental observations where no drag effect was observed. This is explained above and in the previous post.

If you could know why the Universe behaves the way it does, you could create a theory from first principals, but at the moment all the theories do is show that the model is experimentally correct. Beyond that it is difficult to know exactly why the universe has a limiting upper speed of c, it just does, and the theory and its maths is self consistent.

If you think about the bending of space by gravity in general relativity this also explains why gravity has an effect on time. The proof? If you place a clock in space and a clock on Earth they go out of synch. Not just because of the relative speeds (or accelerations) that will not account for it alone, but by the gravitational warping of space and therefore time by the Earth's gravitational well. More proof? During an eclipse the light from the sun is bent by the gravity of the moon, which precisely reflects the maths in Einstein's equations. The shortest distance between two points is a straight line, but bends in space-time mean that the light is not travelling on a straight path. Gravitational lensing is also an adequate piece of evidence for the theory.

Last edited: Apr 4, 2008
7. Apr 4, 2008

### JesseM

In any given frame, the time dilation of a clock as measured in that frame is solely a function of its speed, not its acceleration (if the clock is moving at speed v, then it is slowed down by a factor of $$\sqrt{1 - v^2/c^2}$$. What you may be thinking of is the fact that if two clocks depart from each other and then reunite, and one clock moved at constant speed between the two meetings while the second one accelerated to turn around, it will always be the one that accelerated that has elapsed a smaller time. But you can actually show this by using the normal speed-based time dilation formula in any given frame; in any inertial frame, if a clock has a varying speed v(t), and you want to know how much time it elapses between two of the frame's own time coordinates $$t_0$$ and $$t_1$$, then you just do the integral $$\int_{t_0}^{t_1} \sqrt{1 - v(t)^2/c^2} \, dt$$ and this gives you the answer. Different frames will define the times of the two meetings of a pair of clocks differently, and they'll also define the speed as a function of time v(t) for the clocks differently because they are each using their own coordinates, but when they evaluate this integral they'll all get the same answer for how much time elapses on each clock between the two meetings, and they'll all find that the clock with a changing v(t) (the one that accelerated) elapsed less time than the clock with the constant v(t) (the one that was moving inertially).

8. Apr 4, 2008

### Schrodinger's Dog

I was informed that it was the acceleration that was responsible for the time dilation. Maybe I was misinformed.

EDIT: Just as AAMOI is there anyway you could prove experimentally that time was dilated only because of the relative speeds, and acceleration was never involved? Not that I'm saying you're wrong it just occurred to me.

Last edited: Apr 4, 2008
9. Apr 4, 2008

### JesseM

You actually need two postulates to derive SR--the first one says all the laws of physics work the same in every inertial frame, so for example, if one frame observes that an clock moving at speed v in that frame has its rate of ticking slowed down by a factor of $$\sqrt{1 - v^2/c^2}$$ in that frame, the same must be true of a clock moving at speed v in any other inertial frame. Then the second postulate says that in every inertial frame the speed of light is always c.

10. Apr 4, 2008

### DaveC426913

It is a mistake to look at movement through space and movement through time as separate things and then ask why one affects the other; look at movement through the single continuum: space-time.

It is an analagous mistake to ask, when traveliing in a boat on a lake, why your headway north is changed by your decision to turn westward. You can't head west without limiting your movement northward (since you cannot exceed the top speed of your boat). Turn far enough West and you will make zero northward headway.

11. Apr 4, 2008

### JesseM

It really depends on whether you're talking about coordinate-dependent time dilation--the rate a clock is ticking at any given moment, which is different in different frames--or coordinate-independent facts about which of two clocks ticks more over an extended period of time, where both clocks start and end at the same location so they can compare readings locally (all frames will make the same predictions about what they each read at both meetings).

12. Apr 4, 2008

### Schrodinger's Dog

Yeah I realise the maths in the equations has no distance involvement explicitly. The maths is actually easy enough for anyone to see that. Of course if you were to do a real world experiment you would have to take all factors into account. But the maths can ignore the vectors involved. Unfortunately QM can't.

13. Apr 4, 2008

### michael879

you could reduce this down to one postulate (although not the one I originally posted):
The laws of physics are the same in all inertial frames.
Since Maxwell's laws are laws of physics that implies that the speed of light is c in all inertial frames.