Is My Time Dilation Equation Correct?

[svijay1991]

hi friends
i am really confused with time dilation ...
Time is quantity which is defined by us, and it will be always constant
then how einstein said the time will dilate when we travel at the speed of light..

thank u...

 

[Naty1]

Just search these forums for dozens and dozens of discussions.

You can start here and see my explanation:

https://www.physicsforums.com/showthread.php?t=564179

 

[phinds]

here's a simple one with graphics:

http://www.phinds.com/time%20dilation/

 

[ghwellsjr]

Or you could just read what Einstein said in his 1905 paper introducing Special Relativity. Just do a Google search on Einstein 1905 paper.

 

[bobc2]

hi friends
i am really confused with time dilation ...
Time is quantity which is defined by us, and it will be always constant
then how einstein said the time will dilate when we travel at the speed of light..

thank u...

Hi, svijay1991. Sometimes it could help to think about time dilation from a geometric point of view. Here is a space-time diagram showing the two different coordinate systems (red and blue) describing two different 3-D worlds that two observers live in as they move in opposite directions (with respect to the black rest system). The thing that happens in special relativity theory is that (from the view point of the black rest system) any observer in constant velocity motion will live in a space in which the X4 coordinate (time axis) and X1 coordinate are slanted such that a 45-degree line (represents a photon of light) always bisects the angle between X4 and X1. I have labled the X1 physical space that each observer is living in. Notice that the red and blue guys are living in two different 3-D worlds. Each 3-D space is a cross-section of the 4-dimensional universe.

Two points in time, t1, and t2 are identified for the red and the blue worlds. They represent the clock times showing in each world at those labled events in space-time. The red t1 clock time is the same as the blue t1 time; red and blue t2 times are also the same.

Thus, it is clear that when blue is in his world at his clock time, t2, blue's world literally includes red in his simultaneous space with red's clock reading time t1. And you can see that when red is at his t2 time, his simultaneous space includes blue with blue's clock time of t1.

The hyperbolic curves in my space-time diagram may be a little puzzling, so here are a couple of additional space-time diagram sketches along with a development of the algebra associated with the hyperbolic curves in the diagrams.

 

[svijay1991]

thank u all for ur reply
now i have two doubts
1. regarding example in this link http://www.phinds.com/time%20dilation/
here the path of the light seen by the person in planet may not be same as in the diagram because while traveling nearly at a speed of light, the light won't reach the mirror rather it will reach the surface nearer to mirror in some manner.. since light is not particle like ball which will come to our hand when we through it up while we travel (by following parabolic path)

2. Consider there are only two bodies A and B be exist in universe and one of which is moving in a uniform speed nearer to light speed. but as per relativity an observer in A will feel he is moving with respect to B and at the same time an observer in B also will feel he is moving with respect to A.. In this case whose time will be diluted ? so can we say time is not diluted ?

 

[ghwellsjr]

thank u all for ur reply
now i have two doubts
1. regarding example in this link http://www.phinds.com/time%20dilation/
here the path of the light seen by the person in planet may not be same as in the diagram because while traveling nearly at a speed of light, the light won't reach the mirror rather it will reach the surface nearer to mirror in some manner.. since light is not particle like ball which will come to our hand when we through it up while we travel (by following parabolic path)

As long as the spaceship has been moving at a constant speed, then the light will reach the mirror (because it is aimed at the mirror).

2. Consider there are only two bodies A and B be exist in universe and one of which is moving in a uniform speed nearer to light speed. but as per relativity an observer in A will feel he is moving with respect to B and at the same time an observer in B also will feel he is moving with respect to A.. In this case whose time will be diluted ? so can we say time is not diluted ?

Time dilation occurs for anybody or clock that is moving in any frame you choose. If you choose a frame in which A is stationary, then B is moving and B is the one experiencing time dilation. If you choose a frame in which B is stationary, then A is moving and A is the one experiencing time dilation. If you choose a frame in which both A and B are moving, then they both experience time dilation. The faster a body moves in a given frame, the more time dilation it experiences. Time dilation, like speed, is relative to a chosen frame. But there is no frame in which A and B are both stationary so you can never get rid of the time dilation.

 

[timmdeeg]

If you choose a frame in which A is stationary, then B is moving and B is the one experiencing time dilation.

If B moves relativ to A, then B's time is dilated in A's frame, according to Lorentz transformation. B experiences his wristwatch time (proper time). The same vice versa.

 

[ghwellsjr]

If you choose a frame in which A is stationary, then B is moving and B is the one experiencing time dilation.

If B moves relativ to A, then B's time is dilated in A's frame, according to Lorentz transformation. B experiences his wristwatch time (proper time). The same vice versa.

Isn't that what I just said?

 

[svijay1991]

As long as the spaceship has been moving at a constant speed, then the light will reach the mirror (because it is aimed at the mirror).

Consider the distance between the source and mirror =1 lakh km
And the spaceship moves at a speed of 2 lakh km/s
In this case the time taken by the body to reach the mirror will be 1/3 sec
And with in this time the spaceship will pass the distance of 2/3 lakh km so the light will fell on the place at a distance 2/3 lakh km from the mirror.

where i went wrong?

 

[bobc2]

Isn't that what I just said?

No, that is not what you said. Here is what you said:

Originally Posted by ghwellsjr:
If you choose a frame in which A is stationary, then B is moving and B is the one experiencing time dilation.

B does not experience time dilation. It's just like timmjeeg said, A observes B's time to be dilated from the point of view of his (A's) frame.

 

[svijay1991]

@bobc2
consider how the observer in A and B feel
(i.e)An observer in A will feel that B is moving away from him
simillary the observer in B also will feel A is moving away from him
so here we cannot predic who is moving and who is stationary since rest and motion are not absolute.
so can we say time will not diluted at all, and it will be always constant...

 

[phinds]

@bobc2
consider how the observer in A and B feel
(i.e)An observer in A will feel that B is moving away from him
simillary the observer in B also will feel A is moving away from him
so here we cannot predic who is moving and who is stationary since rest and motion are not absolute.
so can we say time will not diluted at all, and it will be always constant...

NO, we definitely cannot say that. Reread post #7.

 

[svijay1991]

then where i went wrong
what is wrong in my statements

 

[svijay1991]

here's a simple one with graphics:

http://www.phinds.com/time%20dilation/

Consider the distance between the source and mirror =1 lakh km
And the spaceship moves at a speed of 2 lakh km/s
In this case the time taken by the body to reach the mirror will be 1/3 sec
And with in this time the spaceship will pass the distance of 2/3 lakh km so the light will fell on the place at a distance 2/3 lakh km from the mirror.

where i went wrong?

 

[Snip3r]

Consider the distance between the source and mirror =1 lakh km
And the spaceship moves at a speed of 2 lakh km/s
In this case the time taken by the body to reach the mirror will be 1/3 sec
And with in this time the spaceship will pass the distance of 2/3 lakh km so the light will fell on the place at a distance 2/3 lakh km from the mirror.
where i went wrong?

no it will hit the mirror. what you said was the idea behind MMX experiment however it failed

 

[svijay1991]

no it will hit the mirror. what you said was the idea behind MMX experiment however it failed

how it will hit the mirror.
where i was wrong

 

[phinds]

then where i went wrong
what is wrong in my statements

you said

so can we say time will not diluted at all, and it will be always constant...


AGAIN, I say to you REREAD POST #7

 

[ghwellsjr]

Isn't that what I just said?

No, that is not what you said. Here is what you said:

Originally Posted by ghwellsjr:
If you choose a frame in which A is stationary, then B is moving and B is the one experiencing time dilation.

B does not experience time dilation. It's just like timmjeeg said, A observes B's time to be dilated from the point of view of his (A's) frame.

I have to admit, it took me a while to figure out that you object to my use of the word "experience" and you and timmdeeg are right, nobody ever experiences time dilation because when B's time is dilated, his wristwatch's time is also dilated and so he cannot tell that time for him is dilated so it is not an "experience" for him.

Time dilation is a function of motion. Nobody "experiences" motion either. But motion is defined in Special Relativity according to an arbitrarily chosen Frame of Reference, not necessarily according to an observer. It doesn't matter whether A observes B or even if there is an A. As long as B is moving according to a Frame of Reference, then B's time is dilated, whether or not he can perceive either his motion or his time dilation.

 

[ghwellsjr]

here's a simple one with graphics:

http://www.phinds.com/time%20dilation/

Consider the distance between the source and mirror =1 lakh km
And the spaceship moves at a speed of 2 lakh km/s
In this case the time taken by the body to reach the mirror will be 1/3 sec
And with in this time the spaceship will pass the distance of 2/3 lakh km so the light will fell on the place at a distance 2/3 lakh km from the mirror.

where i went wrong?

Maybe you went wrong in understanding what phinds's diagram is depicting. In the top part, where you see only D1, the light is bouncing up and down between the two stationary mirrors. I think you understand that part. But in the bottom part, where you see the pair of 2D1 paths for the light along the "V" shape, the two mirrors are shown at the bottom of the V and at the top right hand leg of the V, but in actuality, the two mirrors are always one above the other, just like in the top part of the diagram. But the mirrors are in motion, just like the packet of light is, constantly moving to the right.

So the way you should interpret the drawing is to start by thinking about the upper mirror being located at the top of the left hand leg of the V with the light packet just bouncing off of it and proceeding downward. The lower mirror is directly below the upper mirror. Both mirrors are moving to the right with the light packet somewhere in between them. The diagram shows the location of the lower mirror at the time when the light packet hits it but you should also think of the upper mirror as being directly above it because both mirrors are traveling at the same speed to the right. After the light packet bounces off the bottom mirror, it start traveling upwards. Finally, when both mirrors are off to the right, the diagram shows where the upper mirror is when the light packet reaches it but the bottom mirror also is directly below it.

Does that help you understand what is happening?

 

[nitsuj]

I have to admit, it took me a while to figure out that you object to my use of the word "experience" and you and timmdeeg are right, nobody ever experiences time dilation because when B's time is dilated, his wristwatch's time is also dilated and so he cannot tell that time for him is dilated so it is not an "experience" for him.

Time dilation is a function of motion. Nobody "experiences" motion either. But motion is defined in Special Relativity according to an arbitrarily chosen Frame of Reference, not necessarily according to an observer. It doesn't matter whether A observes B or even if there is an A. As long as B is moving according to a Frame of Reference, then B's time is dilated, whether or not he can perceive either his motion or his time dilation.

Nice retort!

 

[svijay1991]

The speed of the spaceship is such that the path of the photon seen by the guy on the planet is 4D1

from here http://www.phinds.com/time%20dilation/

How can u say that the path of the light seen by the guy on the planet would be in V shape
Again i repeat if we through any object upward while we travel it will definitely come to our hand because the object will follow the parabolic path.

moreover the guy inside the spaceship also would not find the light hitting the mirror.
because as the time passes the spaceship will be in different place but the light will always travel in straight line.

 

[phinds]

from here http://www.phinds.com/time%20dilation/

How can u say that the path of the light seen by the guy on the planet would be in V shape

Uh ... because it WOULD be? The light is in the frame of reference of the ship.

Again i repeat if we through any object upward while we travel it will definitely come to our hand because the object will follow the parabolic path.

Yes, but that's because you are talking about something that travels REALLY REALLY REALLY slowly compared to light AND that is being affected by gravity so as to follow a non-linear velocity.

moreover the guy inside the spaceship also would not find the light hitting the mirror.
because as the time passes the spaceship will be in different place but the light will always travel in straight line.

Nonsense. The light is in the frame of reference of the space ship.


EDIT: Look, you clearly don't "get" this stuff. It's been explained to you several times now. If you really want to learn what's going on, you need to stop thinking that the explanations are wrong and start trying to understand why they are correct.

 

[zonde]

moreover the guy inside the spaceship also would not find the light hitting the mirror.
because as the time passes the spaceship will be in different place but the light will always travel in straight line.

Ah, but you have wrong idea about the setup. You think that light source is laser but actually light source is spherical so that it emits light in all directions. Certainly some light will reflect from mirror in such a way that it returns back to light source. And we are considering only that light.

Or alternatively you can indeed think that light source is laser but it is adjusted until beam hits the spot that we want.

 

[Snip3r]

Uh ... because it WOULD be?

beautiful :)

Ah, but you have wrong idea about the setup. You think that light source is laser but actually light source is spherical so that it emits light in all directions. Certainly some light will reflect from mirror in such a way that it returns back to light source. And we are considering only that light.

Or alternatively you can indeed think that light source is laser but it is adjusted until beam hits the spot that we want.

this is misleading. no matter whatever the light source is, it will behave as if you are at rest when in constant velocity

 

[zonde]

this is misleading. no matter whatever the light source is, it will behave as if you are at rest when in constant velocity

Do you mean that light source behaves the same way no matter if it is moving or not?
Then you are wrong, light source behaves differently when it is at rest and when it is moving.

But according to relativity similar light sources behave the same way in their own rest frames.

 

[svijay1991]

EDIT: Look, you clearly don't "get" this stuff. It's been explained to you several times now. If you really want to learn what's going on, you need to stop thinking that the explanations are wrong and start trying to understand why they are correct.

Thank u phinds
i am going to think it in different aspect as u mentioned.
but still i am confused
thanks for ur answers

 

[phinds]

Ah, but you have wrong idea about the setup. You think that light source is laser but actually light source is spherical ...

nonsense --- it's a laser

 

[Snip3r]

But according to relativity similar light sources behave the same way in their own rest frames.

i meant this. but i don't understand why do you think a laser won't work

 

[Snip3r]

Thank u phinds
i am going to think it in different aspect as u mentioned.
but still i am confused
thanks for ur answers

try this. get on to the top of a tall building and flash a light downwards. According to you the light ray must be deviated and should not hit the target (because Earth is moving around sun, 30 Km/s which is moving around the galaxy, 220 Km/s which is in turn moving at a very high speed from other galaxies) but it will.