# Length contraction and time dilation equivelant?

1. Apr 30, 2010

### teodorakis

Hi, i asked this before but i think i found a clearer way to define my quesiton. As i asked in the title, does length contradicts as a result of time dilation? Or time dilation and length contraction are equal?
When we deal with formulas generally we use the vertical clock and derive time dilation formula than we use this time dilaiton formula in horizontal clock and derive the length contraction formula. So can we say length contraction is the result of time dilation, length in the direction of motion must contradict for consistency of the time dilaiton formulas, or can we equally say as a result of length contraction, time must be dilated?

2. Apr 30, 2010

### Staff: Mentor

I would say that both length contraction and time dilation are consequences of the Poincare symmetry.

3. Apr 30, 2010

### teodorakis

could you explain more?

4. Apr 30, 2010

### Staff: Mentor

You are asking if one is the result of the other, I don't think so. I think both are a result of the same thing, an underlying symmetry to the laws of nature called Poincare symmetry. Symmetries seem to be some of the most fundamental things in physics.

5. May 1, 2010

### phyti

We know for a fact that Poincare did not design the universe, so how do we know his symmetry was used?

6. May 1, 2010

### Staff: Mentor

There is a sticky at the top of the forum that lists the experimental evidence.

7. May 2, 2010

### abluphoton

both length contraction and time dilation are the manipulations made to preserve the speed of light for any observer. whichever is needed to do the job is employed. [ i talk so because im not such a big fan of this theory :) ]
well, if we look at the lorentz transformation matrix, we can see how time and space of one observer gets reinterpreted, to another observer, in terms of one another. that mixing happens, that is why time fit to be addressed as another dimension. well, in a particular case of relative motion. the speed of light can be conserved using both time and space. i mean a combination o them. they need not always be the same.

correct me if im wrong.

8. May 2, 2010

### matheinste

We don't have a choice as to which one is "used". While not exactly equivalent they are in a sense complementary and both occur together as a logical consequence oif the theory.

Matheinste.

9. May 2, 2010

### teodorakis

when deriving mathematically we use x=ct and x=c't' equate them and do some math and the lorentz eq pop up. So we say that according to another observer that is in motion realtive to some other observer, both time and distance change, without a priority to each other. What do say about this?

10. May 6, 2010

### abluphoton

well, yea we dont have a choice with that.

also it is x=ct and x'=ct' which is used to relate readings o relative observers.

11. May 6, 2010

### stevmg

According to AP French in "Special Relativity" the mesons that reach earth without much decay are a consequence of either time dilation (the moving frame of the meson) or the length contraction of the Earth frame. Either one applies and will calculate to the same result. Sounds like each principle is a corollary of the other.

12. May 6, 2010

### teodorakis

Oh god i just finish my thesis without sleeping till morning(do nothing till deadline and write the whole thesis in one week, that's how i roll, i am exhausted anyway, when i checkout my e-mail i saw a reply and couldn't help myself but to check out pf. So if i bored you enough with my delicant special life and academic career, i want to say that when we derive time dilation in some kind of light clock we use the principle of relativity and say that it must be delayed in any other type of clock according to the principle of relativity, or we wold have a detector of understanding that we are in motion(by comparing the clocks in our reference frame and using the mismathc between clocks) anyway i want to ask we know the time dilation in any other clock by our derivaiton in another one, but can we derive the time dilation alone in any clock?

13. May 7, 2010

### Staff: Mentor

Yes, provided that you use the relativistic equations that describe the functioning of the clock. The light clock is used because the relativistic equations are easy to explain and use.

14. May 7, 2010

### teodorakis

so you say that we can derive the time dilation in any oter clock by just only applying the constantness of light and the other relativity principles?

so can you prove me the time dilation with just these assumptions ,in horizontal light clock ?

15. May 7, 2010

### Staff: Mentor

No, that's not what I said at all. I said that if you use the relativistic law governing the operation of any clock then you will find that it dilates.

For example, an atomic clock is based on the hyperfine transition of Cesium. The relativistic law governing the hyperfine transition is QED. If you apply QED to a moving Cesium atom you will find that the it dilates as expected.

16. May 9, 2010

### Passionflower

In fact there are no differences in any of the laws of physics for a "steady" or "moving" object. I write those between quotes because something is always moving in relation to something else.

So what you really are trying to say is that when an observer is comparing his own clock with a moving clock he will observe that his own clock runs faster than the moving clock and vice versa. And this is only correct under special relativity conditions (spacetime is assumed flat).

17. May 9, 2010

### LukeD

Length contraction and time dilation are 2 things that happen, but one does not cause the other. You need both formulas together to get special relativity (and with just those 2 formulas, you can derive everything)

You cannot observe one without the other because they both happen whenever something is moving. There is no way to say, hold the time dilation constant and increase the length contraction.

18. May 10, 2010

### Staff: Mentor

You misunderstood my point. You are correct that there are no differences between the laws of physics for a steady or moving object, but there are differences between the relativistic laws and their low-speed approximations. That is why I specifically mentioned QED, which is a relativistic formulation of quantum mechanics, rather than earlier versions which were only low-speed approximations.

19. Dec 29, 2010

### teodorakis

i want to ask this in some new perception, i want to say that we find time dilation formula by vertical clocks and use this time formula for any other type of clock because if the other type of clocks(any type including vertical) should dilate the same rate as we found, because if any difference occurs one can understand that he/she is moving and that's inconsistent with the principle of relativity. And to complete the big picture we need one more formula about length contraction which we get by using the time formula in horizontal clocks.
Finally every condition about relativity is provided by these two transformations.
Do i get it right?

20. Dec 29, 2010

### Staff: Mentor

Essentially, yes, but I would call them two features of one transformation, the Lorentz transform. There is one remaining important feature: the relativity of simultaneity. You can easily derive that from the time dilation and length contraction and the postulates.