Time Dilation

[chinglu]

Moderator note: chinglu has been banned from sciforums for 3 days for trolling.
------------
When you get back, chinlgu, you will need to address at least one of the following points:

1. Do you agree that if a frame records a proper time interval between two events, then any other frame will record a longer time interval between the same pair of events? Yes or no?

2. Go through any or all of posts #117, #118, #165 or #177 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in those posts.

3. Go through Pete's post #332 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in that post.

4. Address post #334, which currently remains unexamined by you.

5. Go through post #333 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in that post.

See you in three days time, chinglu. Let's hope we start getting some honesty from you then.

Well, I sm not sure how to respond.

Can you please explain how your statement

$$\Delta t' = -k/v, \Delta t = -k/\gamma v$$

is different from the OP?

Thanks

 

[Pete]

Well, I sm not sure how to respond.

Start here:

you will need to address at least one of the following points:

Pick a point. Address it.

 

[chinglu]

James R:
You have yet to address this.

Well, I sm not sure how to respond.

Can you please explain how your statement

$$\Delta t' = -k/v, \Delta t = -k/\gamma v$$

is different from the OP?

Thanks

 

[James R]

chinglu:

Please don't tell lies, or you'll be banned again.

You need to address at least one of the following points:

1. Do you agree that if a frame records a proper time interval between two events, then any other frame will record a longer time interval between the same pair of events? Yes or no?

2. Go through any or all of posts #117, #118, #165 or #177 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in those posts.

3. Go through Pete's post #332 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in that post.

4. Address post #334, which currently remains unexamined by you.

5. Go through post #333 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in that post.

 

[chinglu]

chinglu:

Please don't tell lies, or you'll be banned again.

You need to address at least one of the following points:

1. Do you agree that if a frame records a proper time interval between two events, then any other frame will record a longer time interval between the same pair of events? Yes or no?

2. Go through any or all of posts #117, #118, #165 or #177 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in those posts.

3. Go through Pete's post #332 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in that post.

4. Address post #334, which currently remains unexamined by you.

5. Go through post #333 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in that post.

OK, this is your post.
http://www.sciforums.com/showpost.php?p=2710813&postcount=343

Now, I asked you how this is different from the OP and this is the 3rd time. you would consider yourself a troll for not answering this.

Why do you refuse?

We have no need to go through all these posts of yours.

We both agree
http://www.sciforums.com/showpost.php?p=2710813&postcount=343

is correct.

Now, it is on you to indicate why this is different from the OP.

That is where we are.

 

[Pete]

James R:
You have yet to address this.

Done many times, chinglu. Try points 2, 3, 4, or 5. Or start with point 1 for the step by step guide:

1. Do you agree that if a frame records a proper time interval between two events, then any other frame will record a longer time interval between the same pair of events? Yes or no?

2. Go through any or all of posts #117, #118, #165 or #177 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in those posts.

3. Go through Pete's post #332 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in that post.

4. Address post #334, which currently remains unexamined by you.

5. Go through post #333 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in that post.

You know, this question was fully answered by rpenner way back in [post=2663273]post 5[/post]. The rest of the thread has been trying to help you catch up.

Applying the Lorentz transform from S to S' for Q, we see that
$$\begin{pmatrix} t'_Q \\ x'_Q \end{pmatrix} = \begin{pmatrix} \frac{1}{\sqrt{1- \frac{v^2}{c^2}}} & \frac{-v}{c^2 \sqrt{1- \frac{v^2}{c^2}}} \\ \frac{-v}{\sqrt{1- \frac{v^2}{c^2}}} & \frac{1}{\sqrt{1- \frac{v^2}{c^2}}} \end{pmatrix} \begin{pmatrix} t_Q \\ x_Q \end{pmatrix} = \begin{pmatrix} \frac{1}{\sqrt{1- \frac{v^2}{c^2}}} \frac{\frac{5}{6} \, \textrm{light-seconds}}{v} \sqrt{1 - \frac{v^2}{c^2}} \\ \frac{-v}{\sqrt{1- \frac{v^2}{c^2}}} \frac{\frac{5}{6} \, \textrm{light-seconds}}{v} \sqrt{1 - \frac{v^2}{c^2}} \end{pmatrix} =\begin{pmatrix} \frac{\frac{5}{6} \, \textrm{light-seconds}}{v} \\ - \frac{5}{6} \, \textrm{light-seconds} \end{pmatrix}$$

The poster then asserts that a clock on world-line A, which is moving at speed v according to S, is not time-dilated.

It is wrong for a number of reasons. Just because at event O (which is on world-line B, and not on world-line A) $$t_O = t'_O = 0$$ does not imply that on world-line A (the world-line of the moving clock) that $$t = t'$$. Specifically, on world-line A, t=0 and t'=0 specify two different events.

 

[chinglu]

Done many times, chinglu. Try points 2, 3, 4, or 5. Or start with point 1 for the step by step guide:


You know, this question was fully answered by rpenner way back in [post=2663273]post 5[/post]. The rest of the thread has been trying to help you catch up.

The post of James R does not disagree with the OP.

 

[chinglu]

Here is the OP
t' = ( t - 0 )γ = tγ.

Here is James R
$$\Delta t' = -k/v, \Delta t = -k/\gamma v$$
Since $$\Delta t' = -k/v, $$ , then
$$\Delta t' = -\Delta t\gamma$$

So James R banned me because he agreed with my OP because I am right.

That seems scientific.

 

[James R]

We have no need to go through all these posts of yours.

chinglu:

I have bolded part of my previous post as an aid to your understanding.

You need to address at least one of the following points:

1. Do you agree that if a frame records a proper time interval between two events, then any other frame will record a longer time interval between the same pair of events? Yes or no?

2. Go through any or all of posts #117, #118, #165 or #177 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in those posts.

3. Go through Pete's post #332 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in that post.

4. Address post #334, which currently remains unexamined by you.

5. Go through post #333 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in that post.

So James R banned me because he agreed with my OP because I am right.

The reason for your ban appears in post #339, above. You were banned for 3 days for trolling.

Now you have three options:

1. Address at least one of the above points.
2. Cease posting in this thread.
3. Continue your evasive trolling and be banned again.

Your choice.

 

[chinglu]

You have to be f'ing with me. You cannot be this stupid.

Here is your post

http://www.sciforums.com/showpost.php?p=2695990&postcount=333

Note it is 333 as you demanded.

I agree with all of your lines so there is no point in going line by line since you finally understood it.

In that post you claimed

$$\Delta t' = -k/v, \Delta t = -k/\gamma v$$

When we reduce this we have

$$\Delta t' = \Delta t \gamma$$

If this math is false, please explain.

The OP said exactly this.

So, in summary, your post #333 is absolutely correct. The only problem is it agrees with my OP.

 

[James R]

chinglu:

Here is your post

http://www.sciforums.com/showpost.php?p=2695990&postcount=333

Note it is 333 as you demanded.

I agree with all of your lines so there is no point in going line by line since you finally understood it.

Let us be clear then. You now agree that everything I wrote in post #333 is correct? Yes or no?

Let us be doubly clear. Here is a quote from my post #333:

Special relativity says that stationary clocks measure the proper time, so the proper time in this case is measured in the unprimed frame. Special relativity also states that the proper time should be shorter than the time in any other frame. This is true for this particular pair of events.

So, once again we conclude that there is no problem for special relativity here - only problems with chinglu's understanding of special relativity.

You now agree with this statement? Correct? Yes or no?

So, in summary, your post #333 is absolutely correct. The only problem is it agrees with my OP.

Your opening post claimed that there was a problem with special relativity.

Now you admit there is no problem after all.

Is that correct? Yes or no?

 

[chinglu]

chinglu:



Let us be clear then. You now agree that everything I wrote in post #333 is correct? Yes or no?

Let us be doubly clear. Here is a quote from my post #333:



You now agree with this statement? Correct? Yes or no?



Your opening post claimed that there was a problem with special relativity.

Now you admit there is no problem after all.

Is that correct? Yes or no?

No, I was talking about the math not your opinions.

I could care less about your opinions.

Your opinions did not match the mathematics.

I note you have refused to address my post where your math agreed with my OP 100% from #333.

Can you explain that. You march around here as an intellect, I am surprised you ran from this. I would consider myself a coward to run away from a math argument, especially one I proposed.

So, we have your math after my education agreeing with the OP.

If this is false say it.

$$\Delta t' = -k/v, \Delta t = -k/\gamma v$$

When we reduce this we have

$$\Delta t' = \Delta t \gamma$$

This is exactly the OP.

 

[James R]

chinglu:

No, I was talking about the math not your opinions.

Then you need to do this:

5. Go through post #333 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in that post.

You claimed you had done this, and yet it seems you have not.

Your opinions did not match the mathematics.

5. Go through post #333 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in that post.

In other words, you need to show exactly where my "opinions" do not "match the mathematics".

I note you have refused to address my post where your math agreed with my OP 100% from #333.

I addressed exactly that point in post #333. You said you went through it and that it was correct. Now you're saying it's wrong again. SO:

5. Go through post #333 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in that post.

You march around here as an intellect, I am surprised you ran from this.

You have not yet managed to address even ONE of the following points:

1. Do you agree that if a frame records a proper time interval between two events, then any other frame will record a longer time interval between the same pair of events? Yes or no?

2. Go through any or all of posts #117, #118, #165 or #177 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in those posts.

3. Go through Pete's post #332 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in that post.

4. Address post #334, which currently remains unexamined by you.

5. Go through post #333 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in that post.

I would consider myself a coward to run away from a math argument, especially one I proposed.

Then address at least one of the above points, or consider yourself a coward.

 

[chinglu]

chinglu:



Then you need to do this:

5. Go through post #333 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in that post.

You claimed you had done this, and yet it seems you have not.



5. Go through post #333 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in that post.

In other words, you need to show exactly where my "opinions" do not "match the mathematics".



I addressed exactly that point in post #333. You said you went through it and that it was correct. Now you're saying it's wrong again. SO:

5. Go through post #333 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in that post.



You have not yet managed to address even ONE of the following points:

1. Do you agree that if a frame records a proper time interval between two events, then any other frame will record a longer time interval between the same pair of events? Yes or no?

2. Go through any or all of posts #117, #118, #165 or #177 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in those posts.

3. Go through Pete's post #332 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in that post.

4. Address post #334, which currently remains unexamined by you.

5. Go through post #333 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in that post.



Then address at least one of the above points, or consider yourself a coward.

Janes R, let us try to be more than flatworms.

I have already conceded to you in #333. I understood your superior intellect.

So, you are the champion of the universe.
Now, your math is the following.
$$\Delta t' = -k/v, \Delta t = -k/\gamma v$$

When we reduce this we have

$$\Delta t' = \Delta t \gamma$$

This is exactly my OP.
Now, are you going to claim you are wrong?

This is on you.

 

[James R]

JI have already conceded to you in #333. I understood your superior intellect.

Let us be clear then. You now agree that everything I wrote in post #333 is correct? Yes or no?

 

[chinglu]

Let us be clear then. You now agree that everything I wrote in post #333 is correct? Yes or no?

I agree with the math that lead to your equations

$$\Delta t' = -k/v, \Delta t = -k/\gamma v$$

When we reduce this we have

$$\Delta t' = \Delta t \gamma$$

What the hell do you want. This is your stuff. Are your going to run as a coward from your own math?

Oh, by the way, you finally got it right and agreed with the OP.

 

[James R]

**** Moderator note: chinglu has been banned from sciforums for 7 days for trolling.

 

[James R]

There is no dispute over the mathematics in question.

What remains at issue is this: chinglu claims that the fact that $$\Delta t'$$ is longer than $$\Delta t$$ for his chosen events is some sort of problem for the special theory of relativity, because (as far as I can tell) chinglu asserts that the primed frame for these events is the "moving" frame.

chinglu is wrong on that point. In this instance, the unprimed frame is "moving", in the sense explained in post #333 above. Therefore, the unprimed frame records the proper time and the proper time is shorter than the time in the other frame, as predicted by the theory of relativity.

On chinglu's return, he will address at least one of the following points, or be banned again for further trolling on this topic.

1. Do you agree that if a frame records a proper time interval between two events, then any other frame will record a longer time interval between the same pair of events? Yes or no?

2. Go through any or all of posts #117, #118, #165 or #177 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in those posts.

3. Go through Pete's post #332 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in that post.

4. Address post #334, which currently remains unexamined by you.

5. Go through post #333 line-by-line, saying clearly whether you agree or disagree with each step and explaining clearly any errors you can find in that post.

 

[Pete]

chinglu, the disputed line in your original post is this:

So, moving clock coming toward rest origin beat not time dilated.

Is this wrong?

Yes, it's wrong.

 

[rpenner]

Going back to Posts 1 and 5, I finally got around to drawing pictures in HTML5/JavaScript. For concreteness in the images, I have chosen the relativistic speed v = 0.5 c, so that the visual effects of relativity are obvious.

In a 1+1 space time, let us have two inertial frames S, with unprimed coordinates x and t, and S', with primed coordinates x' and t'.

S is dark red. S' is dark green. Each tick represents one light-second on the horizontal axis and one second on the vertical axis.

Let A be the time-like world-line containing all events in this spacetime such that $$x' = - \frac{5}{6} \, \textrm{light-seconds}$$.

The time-like world-line A is the light green line.

Assuming that the frames S and S' agree on event O as being the origin of their respective space and time coordinate systems, we call this standard configuration such that event O has the following coordinates:
$$x_O = 0, \, t_O = 0, \, x'_O = 0, \, t'_O = 0$$

The event O has been labeled in both the S (red) and S' (green) frames, but the points fall on top of each other since they are just two names for the same event.

Let B be the time-like world-line containing all events in this spacetime such that $$x = 0$$.

The time-like world-line B is the light-red line which corresponds with the time axis of the S coordinate system.

Obviously, unless the frame S and S' are not in relative motion, world-lines A and B share only one event in common. Following convention (established below) we call this event Q.
Let us call the motion of S' relative to S as v, so now we may compute the coordinates of Q in both frames:
$$x_Q = 0, \, t_Q = \frac{\frac{5}{6} \, \textrm{light-seconds}}{v} \sqrt{1 - \frac{v^2}{c^2}}, \, x'_Q = - \frac{5}{6} \, \textrm{light-seconds}, \, t'_Q = \frac{\frac{5}{6} \, \textrm{light-seconds}}{v}$$
Applying the Lorentz transform from S to S' for Q, we see that
$$\begin{pmatrix} t'_Q \\ x'_Q \end{pmatrix} = \begin{pmatrix} \frac{1}{\sqrt{1- \frac{v^2}{c^2}}} & \frac{-v}{c^2 \sqrt{1- \frac{v^2}{c^2}}} \\ \frac{-v}{\sqrt{1- \frac{v^2}{c^2}}} & \frac{1}{\sqrt{1- \frac{v^2}{c^2}}} \end{pmatrix} \begin{pmatrix} t_Q \\ x_Q \end{pmatrix} = \begin{pmatrix} \frac{1}{\sqrt{1- \frac{v^2}{c^2}}} \frac{\frac{5}{6} \, \textrm{light-seconds}}{v} \sqrt{1 - \frac{v^2}{c^2}} \\ \frac{-v}{\sqrt{1- \frac{v^2}{c^2}}} \frac{\frac{5}{6} \, \textrm{light-seconds}}{v} \sqrt{1 - \frac{v^2}{c^2}} \end{pmatrix} =\begin{pmatrix} \frac{\frac{5}{6} \, \textrm{light-seconds}}{v} \\ - \frac{5}{6} \, \textrm{light-seconds} \end{pmatrix}$$

The event Q has also been labeled in both the S (red) and S' (green) coordinate systems and again the points fall on top of each other.

The poster then asserts that a clock on world-line A, which is moving at speed v according to S, is not time-dilated.

So, moving clock coming toward rest origin beat not time dilated.

Is this wrong?

It is wrong for a number of reasons. Just because at event O (which is on world-line B, and not on world-line A) $$t_O = t'_O = 0$$ does not imply that on world-line A (the world-line of the moving clock) that $$t = t'$$. Specifically, on world-line A, t=0 and t'=0 specify two different events.

To see this parameterize the events on A with the parameter a (with units of length):
$$x_{A_a} = \frac{a}{\sqrt{1-\frac{v^2}{c^2}}}, \,
t_{A_a} = \frac{(\frac{5}{6} \, \textrm{light-seconds})(\frac{c^2-v^2}{v c^2}) + \frac{a}{v}}{\sqrt{1-\frac{v^2}{c^2}}}, \,
x'_{A_a} = - \frac{5}{6} \, \textrm{light-seconds}, \,
t'_{A_a} = \frac{(\frac{5}{6} \, \textrm{light-seconds}) + a}{v}$$

So if you wanted to answer a question about time dilation of a clock moving (according to S) on world-line A and ending at event Q, you need to choose a starting event P on A. (Once again, O is not on A.)

$$P_{t'=0} \, = \, P_{a = - \frac{5}{6} \, \textrm{light-seconds}} $$ with coordinates:
$$x = \frac{- \frac{5}{6} \, \textrm{light-seconds}}{\sqrt{1-\frac{v^2}{c^2}}}, \,
t = \frac{(\frac{5}{6} \, \textrm{light-seconds})(\frac{-v}{c^2})}{\sqrt{1-\frac{v^2}{c^2}}}, \,
x' = - \frac{5}{6} \, \textrm{light-seconds}, \,
t' = 0$$

But $$P_{t=0} \, = \, P_{a = - (1 - \frac{v^2}{c^2}) (\frac{5}{6} \, \textrm{light-seconds} )} $$ has different coordinates:

$$x = - \sqrt{1 - \frac{v^2}{c^2}} (\frac{5}{6} \, \textrm{light-seconds} ) , \,
t = 0, \,
x' = - \frac{5}{6} \, \textrm{light-seconds}, \,
t' = \frac{v (\frac{5}{6} \, \textrm{light-seconds})}{c^2}$$

So because $$P_{t'=0} \neq P_{t=0}$$ you have to be extra careful when talking about time dilation as a clock moves from P to Q, since
$$t_Q - t_P$$ depends on the choice of P.

The event P has also been labeled in both the S (red) and S' (green) coordinate systems and again the points fall on top of each other. Here P is shorthand for $$P_{t'=0}$$ but this matter little if you are not confused.

And using the Lorentz transforms, we can go from one coordinate system to the other, and then back again.


sr_post5_unprimed by PhysForum Photos, on Flickr


sr_post5_primed by PhysForum Photos, on Flickr

Since S' is the frame where P->Q represents no change of spatial location, Δt' (measured between P and Q in the S' frame) is the proper time and is shorter than Δt (measured between P and Q in the S frame) in the frame where P->Q represents something moving with speed v=0.5c.

Thus the time between events of an object seen as moving (P->Q in S or O->Q in S') is longer than the proper time in a frame where the object is not moving (P->Q in S' or O->Q in S, respectively).

This is the exact meaning of the time dilation expressed by the common phrase "moving clocks tick slowly."