Understanding Time Dilation in Einstein's Special Theory of Relativity

[windscar]

Delta T > To?

I was working on the derivation of the time dilation of Eisteins Special Theory of Relativity, when I realized that your change in time from the final equation is actually higher than the time of the observer at rest. Now I understand why the time an object traveling close to the speed of light should slow down, but if you put 1 sec for an object traveling at half of C, you end up getting 1.1547 sec. So, then as 1 sec of your time has passed it would say that 1.1547 sec has passed for the object moveing at half C. But since it has experienced more time, time would be going faster So I guess my question is, how do you us this number to show that time is actuallly going slower in the moveing frame of reference? From how I solved this equation, it looks like it should be the inverse of Einsteins equation. Which would be 0.866 sec for an object traveling half of C for 1 sec. To me this seems like it would be more right because in 1 sec of your time, the object traveling half C would only experience 0.866 of a sec. Hence, being slower. I have another problem with it too, but I think I should wait until I get this issue resolved before I move on to that. But for now I think that your time dilation would equal your normal time, times the square root of one minus it's velocity squared over speed of light squared. (instead of divided by the Lorenzt Factor)

 

[windscar]

Basically, while working it, it looks like to me the variables have just been switched. Because the only way I see that you can get the Lorenzt factor from a light triangle using pythageroms theorem would be to say the time would be contracted to the time of the adjacent side of the 90 degree angle. And then setting it up with Ct as the hypotenuse and Vt as the base. The hypotenuse would be observed as traveling a shorter Ct that would be equal to the adjacent side of the right angle. So the hypotenuse is the "longer" distance of what the observer at rest know's what he should see if light could be seen to travel at a faster speed from adding it's velocity. But an observer at rest doesn't see light traveling this longer distance, so when observeing this path of light, you would see the light traveling a shorter distance equal to what you would see light travel from you at rest (because all observers have to see light travel at the same constant speed). The amount Ct would be seen to contract into the distance Ct'. So basically, the Ct is shortned to the Ct' and Vt is used for the base.
(vt)^2 + (ct')^2 = (ct)^2 solve for t' and factor -c^2 out of (v^2 - c^2) for the lorenzt factor, t'=t * sqrt(1 - v^2/c^2)
if you switch the variables and solve for t' you get t'=t / (sqrt(1 - v^2/c^2) but you end up getting a larger amount for time because that would be takeing the distance traveled by light and then determining how much longer it would have to be to fill the length of the hypotonus of the triangle that is not observed by either object!

 

[Mentz114]

...time is actuallly going slower in the moveing frame of reference?

You've misunderstood time dilation. Clocks *appear* to be moving more slowly when observed from a moving frame. They actually are not and to a person in the frame of the clock nothing has changed.

This is called a 'kinematic' effect.

 

[windscar]

You've misunderstood time dilation. Clocks *appear* to be moving more slowly when observed from a moving frame. They actually are not and to a person in the frame of the clock nothing has changed.

This is called a 'kinematic' effect.

Atomic clocks have been flown around the world and then compared to atomic clocks that stayed on the ground. The atomic clocks actually had run slower, showing they had experienced less amount of time compared to the clocks that stayed on the ground. Relativity is an actual affect that has been proven by experiment, but I am asking why does the time dilation equation give a larger number for dialated time.

 

[MeJennifer]

Atomic clocks have been flown around the world and then compared to atomic clocks that stayed on the ground. The atomic clocks actually had run slower, showing they had experienced less amount of time compared to the clocks that stayed on the ground.

They run just as fast but they simply run a shorter time. The same with the twin experiment, the twin's clock that traveled ran just as fast but again for a shorter time.

 

[Mentz114]

OK, I was talking about inertial frames. The effect you mention happens because frames are accelerated and is certainly real.

You're interpreting the formula incorrectly.

The figure 1.154 means 1.154 of my minutes equals one of his.


http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/tdil.html

[EDIT] I'll leave you in MJ's capable care.

 

[windscar]

They run just as fast but they simply run a shorter time. The same with the twin experiment, the twin's clock that traveled ran just as fast but again for a shorter time.

Anyone traveling with a constant speed would not notice any type of time dilation on their clocks. I was simply saying that an observer at rest would have to see the time of another object with a constant velocity slow down. This is because if the object emits a beam of light perpendicular to it's direction of motion, you would predict that it has moved a distance of ct at an angle away from that object. Since the object itself see's no type of dilation it see's light travel perfectly perpendicular from itself. The distance traveled by light at an angle would have to travel a larger distance to reach the same point as if it traveled perpendicular to the object. But an observer at rest does not see it travel this longer distance and observes light traveling a distance of ct. So an observer at rest would see the distance light had traveled at an angle contracted to the distance ct. Therefore, ct' would be distance light had traveled along the angle, and t' would have to be smaller to give a distance that was actually observed from an observer at rest.

 

[MeJennifer]

I was simply saying that an observer at rest would have to see the time of another object with a constant velocity slow down.

You are mixing something up.

Not the observers, but the light signals between observers in relative motion will appear delayed (in addition of course to the regular Doppler shift).

But absolutely nothing happens to the objects or to the photons in question, as this would obviously be a violation of Einstein's first postulate.

 

[windscar]

But absolutely nothing happens to the objects or to the photons in question, as this would obviously be a violation of Einstein's first postulate.

This actually does not violate Einstein's first postulate. Einstein's theory itself claims that relative to an observer at rest; time slow's down, length in the direction of motion is contracted, and mass increase's. The whole time that on observe in constant motion does not observe any of these affect's. The reason being that, if your space is contracted, for example; Your measuring rod would be contracted along with it. SO, if you used a contracted measuring rod to measure contracted space, you would get the same measurement for your distance in the direction of motion. And both firgures assume that both observes see light travel a constant speed relative to themselves, and that is the basis for deriving the theory.

 

[MeJennifer]

You are mistaken windscar, not only do you mistake the light signals between objects for the proper values of those objects you also assert that time can slow down.

Observers traveling between two events can certainly take their own time, some will do it quickly while others will take more time, as you see in the case of the twin experiment, but time itself does not slow down of speed up. Time simply goes at one second per second, always!

 

[windscar]

And both firgures assume that both observes see light travel a constant speed relative to themselves, and that is the basis for deriving the theory.

The theory is saying that this is what needs to happen in order for both observers to see light behave in the same manner at the same time.

 

[windscar]

You are mistaken windscar, not only do you mistake the light signals between objects for the proper values of those objects you also assert that time can slow down.

Observers traveling between two events can certainly take their own time, some will do it quickly while others will take more time, as you see in the case of the twin experiment, but time itself does not slow down of speed up. Time simply goes at one second per second, always!

I am sorry but you are seriously mistaken. Everything you are saying goes against Einstiens Theory of Relativity. I recommend you study more on the subject to get a more complete understanding of it. I have studied this threory for years. I only had a problem with assuming that t' being used at the base of the light triangle of vt' and t' being used at the adjacent side of the right angle ( the distance light traveled perpendicular to the object traveling at vt). Mainly because if you used vt' in the proof then your velocity in the Lorentz factor would have to be determined from your dialated time of the object traveling at a constant speed relative to an observer at rest. And it isn't, the velocity of the object to determine the amount of time dilation is found using the time of the observer at rest. I know beleiving that an object can actually have their time slow down is hard to grasp, but it is an actual affect and anyone who writes any books on this subject say that time does in fact actually run slower.

 

[MeJennifer]

I am sorry but you are seriously mistaken.

Ok, no problem.

 

[windscar]

I only had a problem with assuming that t' being used at the base of the light triangle of vt' and t' being used at the adjacent side of the right angle ( the distance light traveled perpendicular to the object traveling at vt).

I said t' being used at the adjacent side in error, t' is used in Ct' in the hypotenuse, and this is why you get a larger number for t', because the hypotenuse is larger than the other two side's and you would need a larger number in order to "fill" it. I used the adjacent side as being the dialation, because it is the shorter side and the hypotenuse Ct would be observed contracting to a distance of exactly Ct' that is the adjacent side. But you end up getting exactly the inverse of the origanal equation, and then they would be equal if you multiplied my equation by the other object time instead of dividing it. But then wouldn't this bring up errors in comeing up with other relativistic equations that determine length contraction, and mass increase? Or even the famous E=mc^2?