Jump to content

A not so small discrepancy in Relativity of Simultaneity


Truden

Recommended Posts

Hi everyone,

As I already mentioned in my first post about the gravitation hypothesis, I'm not a physicist.
I work on logic problems.
One such logical problem I saw in the "Ladder Paradox" which explains the relativity of simultaneity.

- - - 

The relativity of simultaneity shows a not so small discrepancy when a third simultaneous even is introduced in the “Ladder Paradox” thought experiment.
Link to the Wikipedia page, treating the ladder paradox – click HERE to read.
I'm sure that all of you know the so-called paradox. 
For better understanding, I’ll use the same graphics, modified for the purpose of the problem. (The text below is copy/paste from my personal weblog)

To question the length contraction and the relativity of simultaneity I introduce a third event in the ladder paradox problem.

How?  Simply, by attaching a rod to each door, which is welded perpendicularly on the inside of the doors, in a way that the rods tips touch each other when both the doors are closed. (See the red attached arms on the graphics)
Think of this touching event as verification of the simultaneity – touching verifies simultaneity, no touching – no simultaneity.
Obviously, this event will be absent in the ladder reference frame since the doors in that frame are not closing simultaneously.
Missing event in one of the reference frames is against the law of physics.

To add a bit of an entertainment to the problem, we can put mechanical bomb trigger on the place of the touching event and blow the garage to pieces in its reference frame, while in the reference frame of the ladder it will still be flapping doors, due to the missing event and the impossibility to trigger the bomb.

Graphics:

1. left-hand side – garage reference frame with simultaneously closing doors.
The touching event is present in the third graphic from the top.
2. right-hand side – ladder reference frame with non-simultaneously closing doors.
The touching event is missing.

 

Relativity of Simultaneity - Ladder Paradox

 

[ADDITION]

Since too many opponents have been confused with the rods, arguing the technicality, not the logic, I decided to change the door system in order to accommodate their requirements.

The door system can be modified in few different ways; vertically sliding, horizontally sliding etc.
I got rid of the rods in a way to be easy to visualize the added touching event, and now it takes place on the top of the doors, few inches under the hinge, on which both doors are hanged (see the red dots). The open/close sequence remains the same of course.

Do not think of the touching event in the garage frame of reference as of event which may not occur. Think of it as of clapping hands.

What you see below is the door system without the construction holding it. Since the construction doesn’t have moving elements, it is not of our interest.

RofS_doors.jpg
Link to comment
Share on other sites

1 hour ago, J.C.MacSwell said:

You are trying to construct an event that can happen simultaneously in both reference frames at more than one location along the direction of relative travel and realize it does not work...this is just as SR would predict...not going to happen

I'm not trying to construct "an event that can happen simultaneously in both reference frames".
I'm showing that an event is missing in one of the reference frames, which is unacceptable.

Link to comment
Share on other sites

Here's the problem, in the third diagram on the left side you show the ladder just fitting inside the barn with the doors closed, however, this isn't possible.  The ends of the doors themselves can't travel faster than the speed of light. In the time the doors go from fully open to fully closed, the ladder will have moved from the  left to the right by some amount.  Thus for the ladder to fit in the barn while the door are closed and the rod ends have met, the barn must be quite a bit longer, and not just a little bit longer than the ladder.  (if you increase the length of the barn to account for the movement of the ladder while the doors close, this means you are moving the doors further apart, which in turn means it takes longer for the rods to meet, causing you make the barn longer.. )

While this doesn't mean that you can't arrange things so that the ladder fits inside with both doors closed and the ends of the rods meeting, but that the ladder id going to have a lot more extra space between the ends of the ladder and the doors.  So much so that even when you switch to the ladder frame, the ladder will fit into the barn.   Also in the ladder frame, even though the doors will start closing at different times, due to the way that velocities add in Relativity, they won't close at the same speed in the ladder frame and the ends of the rods will meet at the center at the same time.

Your apparent paradox only arises because you failed to take everything into consideration.  You assumed things would happen in a certain way without doing an actual analysis of all the parameters involved. 

Link to comment
Share on other sites

1 hour ago, Janus said:

Here's the problem, in the third diagram on the left side you show the ladder just fitting inside the barn with the doors closed, however, this isn't possible.  The ends of the doors themselves can't travel faster than the speed of light. In the time the doors go from fully open to fully closed, the ladder will have moved from the  left to the right by some amount.  Thus for the ladder to fit in the barn while the door are closed and the rod ends have met, the barn must be quite a bit longer, and not just a little bit longer than the ladder.  (if you increase the length of the barn to account for the movement of the ladder while the doors close, this means you are moving the doors further apart, which in turn means it takes longer for the rods to meet, causing you make the barn longer.. )

While this doesn't mean that you can't arrange things so that the ladder fits inside with both doors closed and the ends of the rods meeting, but that the ladder id going to have a lot more extra space between the ends of the ladder and the doors.  So much so that even when you switch to the ladder frame, the ladder will fit into the barn.   Also in the ladder frame, even though the doors will start closing at different times, due to the way that velocities add in Relativity, they won't close at the same speed in the ladder frame and the ends of the rods will meet at the center at the same time.

Your apparent paradox only arises because you failed to take everything into consideration.  You assumed things would happen in a certain way without doing an actual analysis of all the parameters involved. 

Did you read the OP until the end?

Did you see the second image of the door system?
I made it for people who already had your argument.
Would you comment on the second door system, please?
 

Link to comment
Share on other sites

2 hours ago, Truden said:

Did you read the OP until the end?

Did you see the second image of the door system?
I made it for people who already had your argument.
Would you comment on the second door system, please?
 

Still won't produce a scenario which produces a paradox.   For one thing, in the ladder frame different parts the doors will start moving at different times and different speeds.

You simply cannot produce a paradox in SR if you properly apply all the principles.

Link to comment
Share on other sites

Quote

Still won't produce a scenario which produces a paradox.   For one thing, in the ladder frame different parts the doors will start moving at different times and different speeds.

You simply cannot produce a paradox in SR if you properly apply all the principles.

1

I'm not producing a paradox :D
I'm showing that the "Ladder Paradox" is impossible, therefore the relativity of simultaneity is impossible.
It seems that you don't agree with the "Ladder Paradox" too because you're not arguing my point, but the technicality of the paradox itself.
Are you aware that this paradox explains how the relativity of simultaneity works?
If you want to argue my addition to the experiment, you should explain the missing event. The rest of the experiment does not contradict SR.

Link to comment
Share on other sites

2 hours ago, Truden said:

I'm showing that the "Ladder Paradox" is impossible, therefore the relativity of simultaneity is impossible.

Maybe if you show how you calculate thesis, position, etc of the ladder and the doors, it will be possible to point out where you have gone wrong. At the moment, it looks like you have just drawn some pictures that create a problem. Which, of course, one can do with any theory! You need to show that you are actually applying the theory ...

Link to comment
Share on other sites

4 minutes ago, uncool said:

I'm going to put my marker in for "There is no infinitely rigid rod in relativistic mechanics" as the reason this "discrepancy" fails. 

Ignore the rods, and use the second doors system.

8 minutes ago, Strange said:

Maybe if you show how you calculate thesis, position, etc of the ladder and the doors, it will be possible to point out where you have gone wrong. At the moment, it looks like you have just drawn some pictures that create a problem. Which, of course, one can do with any theory! You need to show that you are actually applying the theory ...

No need for calculations here.

The ladder paradox does not deal with calculations. It is a thought experiment accepted as an explanation of the relativity of simultaneity and length contraction.
I only add a third event to the experiment, and you should focus your arguments on that.
As long as you don't comment on the third event, your arguments are irrelevant.

Link to comment
Share on other sites

It is a thought experiment that has associated calculations. Yes, those calculations have a non-calculation explanation, but there are still calculations.

 

I don't understand your picture. What, exactly, is your "third event"? And remember, in the original ladder paradox, there are 4 relevant events: 

1) Back of ladder passes entrance of barn

2) Front of ladder passes exit of barn

3) Entrance door closes

4) Exit door opens.

Edited by uncool
Link to comment
Share on other sites

22 minutes ago, Truden said:

No need for calculations here.

Well, there are because you have drawn the ladder and building reduced in size. So you have just guessed at these, and the relative positions at different times. You have obviously guessed wrong and so someone (ideally you) needs to calculate what really happens in order to understand why your guesses are wrong.

Link to comment
Share on other sites

10 minutes ago, uncool said:

It is a thought experiment that has associated calculations. Yes, those calculations have a non-calculation explanation, but there are still calculations.

 

I don't understand your picture. What, exactly, is your "third event"? And remember, in the original ladder paradox, there are 4 relevant events: 

1) Back of ladder passes entrance of barn

2) Front of ladder passes exit of barn

3) Entrance door closes

4) Exit door opens.

Sorry if my OP is not clear enough for you, but it cannot be made clearer than that.
The first image in the OP is an altered image from the original Wikipedia article for the Ladder Paradox, which I hoped will give you the idea for the third event "touching of the rodes".
The second image is to avoid arguments on a technicality, as rigidity, fast closing doors etc. 

So, where the red dots are, the two doors touch; that is the event which is added to the original experiment.
This touching event is missing in the ladder frame of reference, which is unacceptable.
An event cannot be missing in one of the reference frames. It can occur in different space-time, but it should be present in both reference frames.

If you understand my point, you'll understand why we don't need calculations.

12 minutes ago, Strange said:

Well, there are because you have drawn the ladder and building reduced in size. So you have just guessed at these, and the relative positions at different times. You have obviously guessed wrong and so someone (ideally you) needs to calculate what really happens in order to understand why your guesses are wrong.

Sorry, that's irrelevant.
Your arguments should deal with the third event.

Link to comment
Share on other sites

18 minutes ago, Truden said:

So, where the red dots are, the two doors touch; that is the event which is added to the original experiment.

As this doesn't happen, we need to think about why. One problem with diagrams as you (and Wikiedia) have drawn them is that it looks as if the doors are shut for a significant time with the ladder between them. In reality they would have to move at near light speed (as Janus noted). Then, as uncool noted, the rods are not rigid and would be bent and compressed by the movement so they never meet. The instant the doors are fully closed they need to open again, so there is no time for the ends of the rods to reach the positions where they would meet.

The explanation is basically the same as that under the variations described on the Wikipedia page, particularly the "Shutting the ladder in the garage" version. 

Link to comment
Share on other sites

27 minutes ago, Strange said:

As this doesn't happen, we need to think about why. One problem with diagrams as you (and Wikiedia) have drawn them is that it looks as if the doors are shut for a significant time with the ladder between them. In reality they would have to move at near light speed (as Janus noted). Then, as uncool noted, the rods are not rigid and would be bent and compressed by the movement so they never meet. The instant the doors are fully closed they need to open again, so there is no time for the ends of the rods to reach the positions where they would meet.

The explanation is basically the same as that under the variations described on the Wikipedia page, particularly the "Shutting the ladder in the garage" version. 

The event does happen. That's how the experiment is constructed. When you clap your hands, you don't say that they don't clap. 
If you question the original experiment, then you are questioning the relativity of simultaneity.
My addition of the experiment does not question and does not change the existing events. It only adds one more event.

As I already said few times, use the second door system for your arguments. The original door system is to make it easy to understand the touching event in the door closing sequence.
Please note that this scenario can be replicated in thousands of different variations not only with ladder and garage. I use the existing Ladder Paradox, to make it easy for you to understand.

Edited by Truden
Link to comment
Share on other sites

Just now, Strange said:

Im afraid I can’t make any sense of those drawings. Can you explain it?

You should study the Ladder Paradox then.
Once you understand it, you'll understand the idea of the touching event, introduced by me.
And then, use the second door system for your arguments.

Link to comment
Share on other sites

 

6 minutes ago, Truden said:

You should study the Ladder Paradox then.
Once you understand it, you'll understand the idea of the touching event, introduced by me.
And then, use the second door system for your arguments.

Please you read the rules of this forum.

Two members of long standing have now asked you to explain further.

 

It seems to me that your argument is basically "If you can't understand it it's your fault, not mine for not fully explaining."

 

I do understand the ladder paradox and at least some of its variants, but I do not understand the scenario you are proposing.

Several members have told you words to the effect that  "the devil is in the detail" and that your proposal is woefully short on detail.

 

 

Link to comment
Share on other sites

22 minutes ago, studiot said:

 

Please you read the rules of this forum.

Two members of long standing have now asked you to explain further.

 

It seems to me that your argument is basically "If you can't understand it it's your fault, not mine for not fully explaining."

 

I do understand the ladder paradox and at least some of its variants, but I do not understand the scenario you are proposing.

Several members have told you words to the effect that  "the devil is in the detail" and that your proposal is woefully short on detail.

 

 

 

Please accept my apologies. I didn't mean to offend anybody.
The point is that I cannot explain it better than it is explained in the Wikipedia.
But let's try.

The question is; is it possible a longer than a garage ladder to fit between the simultaneously closed doors of the garage?
SR answers YES, because of the length contraction.
The answer is argued; it should not fit, because from the ladder FoR (frame of reference) the garage is even smaller.
SR answers that it is possible due to the relativity of simultaneity; the doors of the garage do not close simultaneously in the ladder FoR.

How that happens is shown in the right-hand image with the garage/ladder.
Now, as you can see on the right-hand image (the ladder FoR) there is no touching event because the doors do not close simultaneously. 
However, it is against the laws of physics, because an event cannot be missing from one of the reference frames.
Hence the discrepancy in the relativity of simultaneity and length contraction.

Hope that now it's more clear.

Edited by Truden
Link to comment
Share on other sites

18 minutes ago, Truden said:

The point is that I cannot explain it better than it is explained in the Wikipedia.

But you are asking us to focus on your "second door system". You need to explain your diagrams for that (instead of assuming people don't understand the basic problem).

The top diagram seems to be some sort of isometric projection with doors that are either open or closed but only seem to cover the top half of the opening. The bottom diagram shows some lines. I don't know which are supposed to be the doors, from which direction is is seen or which way they move. Even some simple annotations would help.

But while you think about that:

1. Special relativity is internally consistent so, even if it were wrong, it is impossible for there to be a paradox of the sort you propose. (This is a mathematical proof so has nothing to do with evidence, tests, correctness, etc)

2. As a result, your conclusion that there is a paradox is mistaken. We all need to work together to understand where the error is in your thought experiment.

3. You cannot disprove a scientific theory with a thought experiment (if that is what you are trying to do).

4. Any communication between the doors at each end to test if they are both closed at the same time can only take place at the speed of light or less. That is why the rods will not meet in either frame of reference. The same sort of argument must apply to your second system. But as none of us (it seems) have understood it, it is hard to say more than that.

 

Link to comment
Share on other sites

OK, lets clear this one too.
Here are the doors:

RofS_doors1.jpg

The top image shows only the closed doors without the holding construction. (The holding construction is not of our interest.)
The profile of the doors is painted black from outside and gray from inside.
They are hanged on a single hinge rode, which you see in the middle between them.
The red point is where the touching event occurs. 

The bottom image shows the doors (didn't draw the whole length) in open position with the red dots showing where the touching event will happen when the doors are closed.

I'm not going to comment whether the SR is "internally consistent" and whether an experiment cannot disprove a theory.
I'm interested in how a theory can explain a missing event in one of the reference frames.

Edited by Truden
Link to comment
Share on other sites

So your doors open like a Delorean? Fair enough. (If a little impractical :))

And instead of rods with the rod contact points at the ends, you have trapezoidal panels which swing with the doors? This doesn't really change anything. 

So, it is still exactly the same explanation as above. The panels will be compressed/deformed by the acceleration of the opening and closing and will never meet in either frame of reference.

28 minutes ago, Truden said:

I'm interested in how a theory can explain a missing event in one of the reference frames

As that can't happen the theory doesn't have to explain it. What needs to be explained is where the error is in your scenarios. I am fairly sure it is because of rigidity. But let's see what Janus says as he always demonstrates a great insight into such problems.

Edited by Strange
Link to comment
Share on other sites

6 hours ago, Truden said:

I'm not producing a paradox :D
I'm showing that the "Ladder Paradox" is impossible, therefore the relativity of simultaneity is impossible.
It seems that you don't agree with the "Ladder Paradox" too because you're not arguing my point, but the technicality of the paradox itself.
Are you aware that this paradox explains how the relativity of simultaneity works?
If you want to argue my addition to the experiment, you should explain the missing event. The rest of the experiment does not contradict SR.

!

Moderator Note

One reason a simple explanation works for the ladder paradox is that the system is not complicated. A qualitative question is asked, so a qualitative answer suffices.

Once you add complexities, and ask what's actually going on, math is absolutely required. As Janus has pointed out, the issue is in failing to apply rigor to these new parts of the problem. You can't simply proclaim "X will happen." You need to show that relativity predicts that X will happen.

That burden is on you. 

 
Link to comment
Share on other sites

6 minutes ago, Strange said:

So your doors open like a Delorean? Fair enough. (If a little impractical :))

And instead of rods with the rod contact points at the ends, you have trapezoidal panels which swing with the doors? This doesn't really change anything. 

So, it is still exactly the same explanation as above. The panels will be compressed/deformed by the acceleration of the opening and closing and will never meet in either frame of reference.

As that can't happen the theory doesn't have to explain it. What needs to be explained is where the error is in your scenarios. I am fairly sure it is because of rigidity. But let's see what Janus says as he always demonstrates a great insight into such problems.

As I said in the OP, do not think of the event as "will not happen".
It happens as part of the experiment construct; the doors stop when they meet at that red dot point. 

3 minutes ago, swansont said:
!

Moderator Note

One reason a simple explanation works for the ladder paradox is that the system is not complicated. A qualitative question is asked, so a qualitative answer suffices.

Once you add complexities, and ask what's actually going on, math is absolutely required. As Janus has pointed out, the issue is in failing to apply rigor to these new parts of the problem. You can't simply proclaim "X will happen." You need to show that relativity predicts that X will happen.

That burden is on you. 

 

I don't see an added event as complexity which needs mathematical work.
I just modified the doors of the experiment, which introduces one more event.
The question is why the event is missing in the ladder FoR.
What math can we use here?

Link to comment
Share on other sites

Guest
This topic is now closed to further replies.
×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.