What's wrong with this so-called paradox?

[Delta1212]

Has nothing to do with your inability to understand the previous posts, nor is it related in any fashion with this thread. The fact that you insist, amply demonstrates that. Nevertheless, I will explain to you. Clock A shows time "0" when clock B shows T. An event happens at location A causing another event to happen at B after time "t". Clock A shows time t when clock B shows T+t, DESPITE the fact that event A caused event B. You can just as easy have the reverse, clock B showing less elapsed time than clock A, DESPITE event A , again, causing event B. You can also have the two clocks showing the same exact time. You can stop trolling on this totally unrelated subject now.

Are you claiming this as a hypothetical abstract that you can write the math to describe if you assume a faster than light frame, or something that actually happens for speeds lower than c?

[xyzt]

Are you claiming this as a hypothetical abstract that you can write the math to describe if you assume a faster than light frame, or something that actually happens for speeds lower than c?

"Faster than light frame"? LOL.

[Mordred]

For two events A and B separated by a distance [math]dx[/math] in space and a interval [math]dt[/math] in time, one can have:

 

[math]\frac{dx}{dt}>\frac{c^2}{v}[/math]

 

[math]\frac{dx}{dt}=\frac{c^2}{v}[/math]

 

[math]\frac{dx}{dt}<\frac{c^2}{v}[/math]

 

where [math]v[/math] is the relative speed of frame S' wrt. S. The key point is that

[math]\frac{dx}{dt}[/math] is NOT a speed and it is certainly not the speed at which the influence of event A propagates to event B. It is simply the ratio of spatial to the temporal separation. As such, it can have any value (see above) and it can certainly be larger than c.

I believe I know what your talking about but want to check.

 

Seems your describing spacelike, time like and light like seperation. Am I correct?

 

 

[latex]s^2= \begin{cases} >0 & timelike\\ =0 & lightlike\\ <0 & spacelike \end {cases}[/latex]

 

[latex]S\rightarrow S^{\prime}[/latex]

 

[latex]S^2=c^2 t^2-\vec{r}^{2}[/latex]

 

 

[latex](ct,\vec{r})\equiv(ct,x,y,z)[/latex]

 

 

[latex]\vec{r}=x^2+y^2+z^2[/latex]

Edited March 29, 2015 by Mordred

[Delta1212]

"Faster than light frame"? LOL.

Yeah, that's why I'm confused.

[md65536]

Has nothing to do with your inability to understand the previous posts, nor is it related in any fashion with this thread. The fact that you insist, amply demonstrates that. Nevertheless, I will explain to you. Clock A shows time "0" when clock B shows T. An event happens at location A causing another event to happen at B after time "t". Clock A shows time t when clock B shows T+t, DESPITE the fact that event A caused event B. You can just as easy have the reverse, clock B showing less elapsed time than clock A, DESPITE event A , again, causing event B. You can also have the two clocks showing the same exact time. You can stop trolling on this totally unrelated subject now.

Thanks! Would it be fair to point to this example in the future as demonstrative of your level of understanding of the equations you transcribe?

 

You have event A happening at time 0 and event B happening at time t, according to A's clock. Time t is after time 0.

You have event A happening at time T and B happening at time T+t, according to B's clock. Time T+t is after time T.

Nowhere is demonstrated B preceding A.

 

Events don't have single clocks, so I would have called the events and the clocks by different names. A and B are different clocks, I wouldn't have used the same variable t. Letting B happen at time T+tau allows for all of the different situations you described. Certainly, t can be less than, greater than, or equal to tau. However neither t nor tau is negative. By any of these clocks, event B occurs after event A.

[xyzt]

Thanks! Would it be fair to point to this example in the future as demonstrative of your level of understanding of the equations you transcribe?

 

Like I said, you need to stop trolling. The fact that you don't get it after so many explanations is not fixable.

 

 

You have event A happening at time 0 and event B happening at time t, according to A's clock. Time t is after time 0.

You have event A happening at time T and B happening at time T+t, according to B's clock. Time T+t is after time T.

Nowhere is demonstrated B preceding A.

 

You seem not to comprehend that the larger the t, the earlier the event. I gave you three equally possible cases, you need to try comprehending all three of them. There are two more, do you think you could read them?

 

 

 

Events don't have single clocks, so I would have called the events and the clocks by different names. A and B are different clocks, I wouldn't have used the same variable t.

 

An event is a pair (x.y,z,t). I cannot fix all your basic misunderstandings.

I believe I know what your talking about but want to check.

 

Seems your describing spacelike, time like and light like seperation. Am I correct?

 

 

[latex]s^2= \begin{cases} >0 & timelike\\ =0 & lightlike\\ <0 & spacelike \end {cases}[/latex]

 

[latex]S\rightarrow S^{\prime}[/latex]

 

[latex]S^2=c^2 t^2-\vec{r}^{2}[/latex]

 

 

[latex](ct,\vec{r})\equiv(ct,x,y,z)[/latex]

 

 

[latex]\vec{r}=x^2+y^2+z^2[/latex]

I made two points:

 

1. In general, Lorentz transforms do not preserve the order of events.

2. In particular, even for causally linked events the order is not preserved absent the clock synchronization.

Edited March 29, 2015 by xyzt

[imatfaal]

!

Moderator Note

 

xyzt

 

Lose the accusations of trolling every time someone has the temerity to disagree with you. Do not respond to this moderation.

 

everyone

 

In Internet slang, a troll (/ˈtroʊl/, /ˈtrɒl/) is a person who sows discord on the Internet by starting arguments or upsetting people, by posting inflammatory,[ extraneous, or off-topic messages in an online community (such as a newsgroup, forum, chat room, or blog) with the deliberate intent of provoking readers into an emotional response or of otherwise disrupting normal on-topic discussion.

 

http://en.wikipedia.org/wiki/Troll_%28Internet%29

 

For everyone's guidance - merely holding unusual point of view and arguing it consistently is not trolling (it might be soap-boxing if there is a refusal to acknowledge board counter-arguments). However, labelling another member as a troll is an ad hominem as it seeks to devalue the opponent's argument by negatively characterising them.

 

As ever - please do not respond to this moderation within the thread.

 

[Mordred]

I made two points:

 

1. In general, Lorentz transforms do not preserve the order of events.

2. In particular, even for causally linked events the order is not preserved absent the clock synchronization.

Gotcha, understand what you were getting at thanks

[LaurieAG]

So for objects separated by L and at a speed of c, it matters whether dt is larger or smaller than L/c.

 

I'm missing where this is different than what was claimed.

 

If v = c, dx/dt = (c^2)/v = c so is it lightlike?

 

Also, if the observer was far enough away so it could observe all 3 events without moving, what would be the minimum distance to that point.

[md65536]

You seem not to comprehend that the larger the t, the earlier the event. I gave you three equally possible cases, you need to try comprehending all three of them. There are two more, do you think you could read them?

[...]

2. In particular, even for causally linked events the order is not preserved absent the clock synchronization.

Sorry for vexing you, but thank you for being respectful and willing to help and learn from others, who are still learning too. I do not understand this yet, but I do not want to be one of those who gives up trying to learn about relativity just because someone on a forum tells them they won't get it.

 

Unfortunately every other source I've read says that SR does not change the order of causally connected events. The maths do not allow it without speeds exceeding c. I am having trouble making sense of your counter claim.

 

Your two other cases in full are:

You can just as easy have the reverse, clock B showing less elapsed time than clock A, DESPITE event A , again, causing event B. You can also have the two clocks showing the same exact time.

I do not yet understand how less elapsed time reverses the order of cause A and effect B. The elapsed time is still positive. You say this is an explanation, but it is not clear enough to me. This does not show that event B (which is caused by event A) precedes event A, as you claim it does.

 

I appreciate any help in understanding this.

 

 

An event is a pair (x.y,z,t). I cannot fix all your basic misunderstandings.

It is also (x',y',z',t'), etc. An event doesn't occur in only one frame. But I empathize with you.

[xyzt]

I do not yet understand how less elapsed time reverses the order of cause A and effect B. The elapsed time is still positive.

 

No, it isn't. Other members (like Mordred) understood, I do not see any point in attempting to educate you only to be "rewarded" by your impertinence.

 

 

 

An event doesn't occur in only one frame.

 

I did not claim that, I was just correcting a different misunderstanding of yours.

 

 

 

But I empathize with you.

Excellent, thank you. I appreciate that.

Edited March 30, 2015 by xyzt

[Mordred]

 

If v = c, dx/dt = (c^2)/v = c so is it lightlike?

 

Also, if the observer was far enough away so it could observe all 3 events without moving, what would be the minimum distance to that point.

Yes to the first, it's also called null like. Not sure how to answer your second question

[md65536]

Are you claiming this as a hypothetical abstract that you can write the math to describe if you assume a faster than light frame, or something that actually happens for speeds lower than c?

I think it's more likely a mixup between frames, but I can't be sure because the explanation makes no sense to me and no concrete example was given.

 

 

I can come up with an example using the Andromeda paradox.

Suppose somewhere in Andromeda a cat knocks a glass off a table (event A) causing it to shatter on the floor (event B).

 

On Earth, an observer O- walking towards Andromeda has that event A and B already happened last week, while an observer O+ walking away has that they will happen next week. (This is just Andromeda paradox, according to standard simultaneity).

 

An observer P can walk toward Andromeda, and turn around and walk away, and the coordinate time that elapses on Andromeda according to P is negative. P can walk alongside O- and say that effect B has already happened, and then alongside O+ and say that effect A has not happened yet.

 

This is the closest I can imagine that the explanations of an effect preceding a cause are describing.

 

 

 

And it's all true, but it's a trick. The problem is that events were selectively transformed from one frame to the other, and event B in the O+ frame was compared to event A in O- frame. Of course all sorts of impossible things can be derived from mixing frames. Yet, at no point can P say that B precedes A. As P accelerates, both events A and B must be transformed to compare them. While alongside O-, P agrees that event B happened last week, but so did event A, earlier. While alongside O+, P agrees that event A happens next week, but so will event B, later.

 

CasualKilla's statement that is in contention, "If event A causes event B, then event A occurs before or simultaneously with event B in any reference frame," is still true, for any given frame even in the example.

 

 

I know it's not fair to set up an argument for the opposition and then knock it down, but in absence of a better example from them it is the best I can figure.

 

One could describe a space-like interval between A and B where the order actually is reversed, or something close to light-like that requires calculation to make sense of it, but if A and B are time-like separated, their order won't be reversed by choosing a different reference frame.

Edited April 1, 2015 by md65536

[LaurieAG]

Yes to the first, it's also called null like. Not sure how to answer your second question

 

The second question is because an observer right beside the track would suffer from whiplash if the experiment was observed in real time. Either that or they would require a close to 180 degrees view to capture all the different events as they occurred.

[Robittybob1]

 

The second question is because an observer right beside the track would suffer from whiplash if the experiment was observed in real time. Either that or they would require a close to 180 degrees view to capture all the different events as they occurred.

It is a thought experiment not a exercise in reality!

[LaurieAG]

It is a thought experiment not a exercise in reality!

 

I prefer thought experiments that could be tested as opposed to ones that cannot, especially if the difference is minor.

[imatfaal]

 

I prefer thought experiments that could be tested as opposed to ones that cannot, especially if the difference is minor.

 

 

Agree - it often helps one spot the non-physical moment that screws up your thought-experiment; ie good practice ensures that the gendanken is a replacement for an experiment that we could do barring techonological barriers rather than an experiment that breaches physical law in its very conception

Edited April 8, 2015 by imatfaal
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