On The Non Relativity Of Simultaneity

In summary, the conversation discusses the concept of simultaneity and its relation to the theory of relativity. The speaker shares their paper on the non-relativity of simultaneity and their belief that simultaneity is absolute, not relative. They also mention their approach to overthrowing the theory of special relativity and invite discussion on their ideas. However, another participant points out that their argument relies on assumptions beyond just special relativity. The conversation ends with a disagreement on the use of algebra to prove the concept of simultaneity.
  • #1
TheAtheistKing
Hello everyone, I am new to this forum.

In oct 2000 I submitted a paper to the European journal of physics on the non relativity of simultaneity. Essentially, the paper didn't deal with the theory of relativity, so much as it did with the issue of simultaneity.
The paper was not published, however since that time I have expanded on my original paper, and focused more on the incorrectness of the relativity of simultaneity. I would like to discuss my work here, as I am preparing to resubmit the paper to the Journal. I would like to have some general reaction to the material that is going to be submitted to them.

The original paper didn't focus on time dilation, but rather it focused upon length contraction. There is a simple way to understand why length isn't relative, and the answer has to do with simultaneity.
The definition of an inertial reference frame is a frame in which Newton's laws are valid. Now, suppose that F1 is an inertial refefence frame, and F2 is moving at a constant speed relative to F1. It will follow that F2 is also an inertial reference frame.
Now consider a ruler R1 at rest in some inertial reference frame F1. There are no forces acting upon this ruler, because we have stipulated that it is at rest in this frame i.e. v=0. Now, suppose that another ruler R2 has an identical length to R1, if the rulers are at rest with each other. Thus, the ends of the rulers can be made to 'coincide' as illustrated below:

R1: A......B
R2: A`......B`

Now, suppose that the same two rulers are now in uniform relative motion to each other, so that each is still in an inertial reference frame. They are now in relative motion, and the relative speed is v.

Assumption 1: The Lorentz Fitzgerald length contraction formula is true.

Consider things now from the point of view of ruler 1 at rest and ruler two moving from right to left as illustrated below. Ruler 2 is length contracted as shown below:

Initial state
R1: A......B
R2:______________A`...B`

Inermediate state
R1: A......B
R2: _________A`...B`

Final state
R1: A......B
R2: A`...B`
As you can see, the order of states is very clear. B coincides with B` BEFORE A coincides with A`.

Now consider things from the point of view of ruler 2 at rest and ruler 1 moving from left to right as illustrated below. In this frame ruler one is length contracted, and the order of states is shown below:

Initial state

R1:A...B
R2:______A`......B`

Intermediate state
R1:______A...B
R2:______A`......B`

Final state
R1:_________________A...B
R2:______A`......B`

As you can see, A coincides with A` before B coincides with B`.

Thus, if assumption 1 is true, then there are different states of the universe X,Y, such that X before Y AND Y before X. This should be regarded as impossible, and thus SR can be overthrown without having to think about the time dilation formula at all. This then is the basis of my approach to toppling the theory of special relativity.
The proper conclusion is that the ends of the rulers coincide simultaneously in all reference frames, not just inertial reference frames. In other words simultaneity is absolute, not relative.
I think this is enough to start off the discussion. At the very least, this should help you understand how come the conclusions of SR are so weird. My current paper goes into clock rates, inertial reference frames, synchronicity, location of measurements in a frame, derivation of the length contraction formula and time dilation formula using the basic postulate of SR which is that the speed of light is the same in all inertial reference frames, and a few other things which could be regarded as new. I refer to the new theory as state theory, and regard it as the only alternative to relativity theory.
I will start the thread by asking a question. Who here understands the logic of my argument, which is that we needn't worry about the time dilation formula in our approach to overthrowing SR?

Thanks
 
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  • #2
Originally posted by TheAtheistKing
This should be regarded as impossible, and thus...

Unfortunatly, we cannot just say "this should be impossible".

The problem you described is only a problem if we assume there exists some universal "correct" order that events happen. But this is not an assumption we make in relativity.
 
  • #3
Unfortunatly, we cannot just say "this should be impossible".


Fortunately an algebraic proof can be constructed.

The problem you described is only a problem if we assume there exists some universal "correct" order that events happen. But this is not an assumption we make in relativity.

We don't need to assume anything other than lorentz contraction, in order to arrive at an algebraic contradiction.
 
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  • #4
Originally posted by TheAtheistKing
You are wrong again, since you don't need to assume anything other than lorentz contraction, in order to arrive at an algebraic contradiction.

This isn't an algebraic contradiction. Algebra doesn't say anything about "simultaneity should work this way". In fact, algebra doesn't say anything about time at all.
 
  • #5
What I've shown you here can be converted into an algebraic argument, and there will be a clear contradiction. I didn't say this was the algebraic argument, only that there is one.
 
  • #6
Originally posted by TheAtheistKing
What I've shown you here can be converted into an algebraic argument, and there will be a clear contradiction. I didn't say this was the algebraic argument, only that there is one.

But all that will show is that one of your assumtions is false. In order to overthrow SR that way, you need to assume only special relativity. But that wasn't the only assumption you made.
 
  • #7
What I've shown you here can be converted into an algebraic argument, and there will be a clear contradiction. I didn't say this was the algebraic argument, only that there is one.
--------------------------------------------------------------------------------



But all that will show is that one of your assumtions is false. In order to overthrow SR that way, you need to assume only special relativity. But that wasn't the only assumption you made.

You aren't following the logic of my argument correctly. Here is the argument form I use:

If X then (Y and not Y); therefore not X

where X is the length contraction formula. I only use SR, binary logic, and algebra in the proof. You have not seen the algebraic proof yet. You are making false statements about my assumptions.

Look at the issue the following way.
Let A denote the length contraction formula, and let B denote the time dilation formula, now consider the following fact taken from binary logic:

If A and B then A

So if we can show that "if A then (X and not X)" SR is overthrown.


Hence the time dilation formula need never be assumed, in order to overthrow SR, and certainly SR uses binary logic and algebra, so they can be considered assumptions of SR as well.

You really should just say you want to see this supposed algebraic proof that simultaneity is absolute and not relative, rather than simply cling to a very misguided theory. Additionally, I am glad you are interested in the topic.
 
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  • #8
I understand the logic you're using. But you're making two assumptions, not one. You're assuming:

1. That SR is true.

2. That if A and A' coincide before B and B' in one inertial reference frame, it cannot happen the other way around in another inertial frame.


The contradiction you've shown is only a contradiction is you assume both 1 and 2. But that only proves that either 1 or 2 is false.
 
  • #9
I understand the logic you're proving. But you're making two assumptions, not one. You're assuming:

1. That SR is true.
2. That if A and A' coincide before B and B' in one inertial reference frame, it cannot happen the other way around in another inertial frame.


Ok, now we are getting somewhere. The state diagrams which you looked at aren't an argument, they are state diagrams. However, what I am saying is that we can quickly see what it is about common sense that the theory of relativity contradicts. In other words, the state diagrams lead to a clear algebraic argument, the diagrams themselves aren't the argument. Succincly put, the algebraic argument doesn't make assumption two above. Here, I will give you a clue. In the algebraic argument, only one state diagram is used and it is this:


Initial state
R1: A...B
R2:_____A`...C.....B`

Intermediate state
R1:_______A...B
R2:_______A`...C...B`

Final state
R1:__________________A...B
R2:_______A`...C...B`
 
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  • #10
Originally posted by TheAtheistKing
Ok, now we are getting somewhere. The state diagrams which you looked at aren't an argument, they are state diagrams. However, what I am saying is that we can quickly see what it is about common sense that the theory of relativity contradicts. In other words, the state diagrams lead to a clear algebraic argument, the diagrams themselves aren't the argument. Succincly put, the algebraic argument doesn't make assumption two above.

In that case, I would certainly like to see that algebraic argument.


However I should mention that just about everyone who understands relativity knows that it contradicts most common sense. But common sense is a guide, not the absolute truth. And since relativity works better than any other theory we currently have, we use it.
 
  • #11
In that case, I would certainly like to see that algebraic argument.


However I should mention that just about everyone who understands relativity knows that it contradicts most common sense. But common sense is a guide, not the absolute truth. And since relativity works better than any other theory we currently have, we use it.


If SR ends in contradiction then no one undestands SR.

It will take me a lot of time to post the algebraic proof here, because I don't know how to place mathematical symbols here.

P.S.: Really, we have a decision that doesn't seem to be able to be made by the physics community, and that decision is on whether or not simultaneity is absolute or relative. The issue has remained unsettled for years, and without rigid adherence to binary logic, the issue can never be resolved.
 
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  • #12
Originally posted by TheAtheistKing
[BIf SR ends in contradiction then no one undestands SR.[/B]

But it only contradicts common sense, not itself.

Common sense is just a heuristic that evolved to help humans make quick decisions that are accurate most of the time. It may not be possible to replace relativity with a theory that doesn't contradict common sense. Unless you're willing to sacrifice accuracy.
 
  • #13
But it only contradicts common sense, not itself.

Common sense is just a heuristic that evolved to help humans make quick decisions that are accurate most of the time. It may not be possible to replace relativity with a theory that doesn't contradict common sense. Unless you're willing to sacrifice accuracy.


Forget about common sense, I am telling you if the lorentz contraction formula is true, then you can derive a contradiction algebraically. This has nothing to do with common sense whatsoever, the contradiction can be made explicit, or as you would say "SR can be shown to self contradict".
 
  • #14
Originally posted by TheAtheistKing
P.S.: Really, we have a decision that doesn't seem to be able to be made by the physics community, and that decision is on whether or not simultaneity is absolute or relative. The issue has remained unsettled for years, and without rigid adherence to binary logic, the issue can never be resolved.

Most physicists agree that simultaneity is relative. Particularly since this is a requirement of SR. If SR didn't agree with the evidence the way it does, people would probably prefer to throw it away and assume simultaneity is aboslute.
 
  • #15
Originally posted by TheAtheistKing
Forget about common sense, I am telling you if the lorentz contraction formula is true, then you can derive a contradiction algebraically. This has nothing to do with common sense whatsoever, the contradiction can be made explicit, or as you would say "SR can be shown to self contradict".

As I said, I would have to see that. It might be easier for you to post it if you use LaTeX.
 
  • #16

Most physicists agree that simultaneity is relative. Particularly since this is a requirement of SR. If SR didn't agree with the evidence the way it does, people would probably prefer to throw it away and assume simultaneity is aboslute.


What does it matter if they all agree, if SR ends in contradiction?
What conclusive evidence is there that SR is correct? The experiment which must be done to determine whether or not simultaneity is absolute is well known to be beyond our current ability to experimentally determine. No physicist wants to assume simultaneity is absolute, and no physicist wants to assume simultaneity is relative, they want to know which it is.
 
  • #17
Originally posted by TheAtheistKing

What does it matter if they all agree, if SR ends in contradiction?
What conclusive evidence is there that SR is correct? The experiment which must be done to determine whether or not simultaneity is absolute is well known to be beyond our current ability to experimentally determine. No physicists wants to assume simultaneity is absolute, and no physicists wants to assume simultaneity is relative, they want to know which it is.

Of course, we don't know SR is correct, in any absolute sense. But we do have evidence, like the fact that the GPS works, to indicate that it is, as far as we know, accurate.

Since we need simultaneity to be relative for SR to work, we accept that it is. If someone comes up with a better theory than SR that requires absolute simultaneity, well use that. But currently, the theory that requires relative simultaneity gives the best results.

As for SR having a contradiction, I'll believe that when I see it.
 
  • #18

Since we need simultaneity to be relative for SR to work, we accept that it is...

As for SR having a contradiction, I'll believe that when I see it.


Ok, it is time for the proof, but It's going to be hard to get it all out on this thing. How about if you and I slowly go through the argument one piece at a time. I will post a little, and then you comment on whether you are following the argument so far. Let me start off the algebraic argument.

Consider two rulers which have identical lengths when at rest, which are now in uniform relative motion with speed v. Let the length of either ruler at rest be denoted by L0, and let the length of either ruler in relative motion be denoted by L. Let c denote the speed 299792458 meters per second.

Assumption 1: L=L0(1-v^2/c^2)^1/2

Consider an event where the rulers move by each other. The event is to begin with the universe in the following state:

R1:A...B
R2:____A`......B`

This state is characterized by the end B of ruler one coinciding with the end A` of ruler two.

Now, suppose there is a clock stationed at A`. An observer there can clearly note his clock reading when B passes by. Later on, the point A will pass by him, and he can again note what his clock reads. He will thus have made two readings, one reading made before the other. Suppose his first reading is x, and that his second reading is y, on a digital clock. Since the clock isn't being subjected to any forces, let us say that this single clock can make an inertial time measurement Delta t of the event which begins when B coincides with A` and ends when A coincides with A`. The time of the event as 'inertially' measured is:

Delta t = y-x

Do you follow the argument so far?
 
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  • #19
Originally posted by TheAtheistKing
Do you follow the argument so far?

Yes.
 
  • #20
Assumption 1: L=L0(1-v^2/c^2)^1/2

Consider an event where the rulers move by each other. The event is to begin with the universe in the following state:

R1:A...B
R2:____A`......B`

(the rest of the argument insert here)

The time of the event as 'inertially' measured is:

Delta t = y-x

Ok so, in time Delta t, the point A has moved some distance in this frame. The question now, is what is this distance? Well, in time delta t, the entire ruler 1 has moved by A, so that the distance traveled MUST be L (by assumption that lorentz formula is true). Hence the speed of A relative to A` is:

Vaa` = L/delta t

Any questions so far?
 
  • #21
Originally posted by TheAtheistKing
Any questions so far?

No. It's still good.
 
  • #22
Assumption 1: L=L0(1-v^2/c^2)^1/2

Consider an event where the rulers move by each other. The event is to begin with the universe in the following state:

R1:A...B
R2:____A`......B`

(the rest of the argument insert here)

The time of the event as 'inertially' measured is:

Delta t = y-x

Ok so, in time Delta t, the point A has moved some distance in this frame. The question now, is what is this distance? Well, in time delta t, the entire ruler 1 has moved by A, so that the distance traveled MUST be L (by assumption that lorentz formula is true). Hence the speed of A relative to A` is:

Vaa` = L/delta t

If ruler one has length contracted, then in this frame the point B on ruler one coincides with some point C` on ruler two as follows:

R1:____A...B
R2:____A`...C`.....B`

Now, the location of the point C` relative to A` must be as follows:

The distance between A` and c` is equal to L. This is so because we have assumed that the Lorentz Fitzgerald length contraction formula is true. And by simple algebra, the distance from C` to B` is none other than L0-L.

Still following?
 
  • #23
Originally posted by TheAtheistKing
Still following?

Yes
 
  • #24
Assumption 1: L=L0(1-v^2/c^2)^1/2

Consider an event where the rulers move by each other. The event is to begin with the universe in the following state:

R1:A...B
R2:____A`......B`

(the rest of the argument insert here)

The time of the event as 'inertially' measured is:

Delta t = y-x

Ok so, in time Delta t, the point A has moved some distance in this frame. The question now, is what is this distance? Well, in time delta t, the entire ruler 1 has moved by A, so that the distance traveled MUST be L (by assumption that lorentz formula is true). Hence the speed of A relative to A` is:

Vaa` = L/delta t

If ruler one has length contracted, then in this frame the point B on ruler one coincides with some point C` on ruler two as follows:

R1:____A...B
R2:____A`...C`.....B`

Now, the location of the point C` relative to A` must be as follows:

The distance between A` and c` is equal to L. This is so because we have assumed that the Lorentz Fitzgerald length contraction formula is true. And by simple algebra, the distance from C` to B` is none other than L0-L.

Let me change notation here and instead of writing delta t for the time let me write delta t1. So, in this frame thus far, the point B is located in the middle of ruler two, it coincides with the point C`, and the time this has taken as measured by a stationary clock located at A` is delta t1.
Ok now here is what to do next. Consider things onward from C`. So we have a state in which B coincides with C`. We are now interested in the time it will take the point B to reach the point B`. Let us denote that time by delta t2, therefore in time delta t2, the point B will have traveled a distance L0-L so that it now coincides with B`. The speed of B relative to B` is

Vbb` = (L0-L)/delta t2

Ok so far?
 
  • #25
Originally posted by TheAtheistKing
Ok so far?

I think so.
 
  • #26
Originally posted by TheAtheistKing
Ok so far?
--------------------------------------------------------------------------------



I think so.


Ok let's do this again. We have an event, it begins when B coincides with A`, and ends when B coincides with B`. Now this event is going to take some amount of time according to clocks at rest in ruler two's frame.

So let us say that we have three clocks, one stationed at A`, another stationed at C`, and a third stationed at B`. As the point B moves along ruler two, observers stationed at the clocks can make readings.
Now, let us assume that all three clocks have identical readings when the event begins, thus they are synchronized. So for simplicity, let all three clocks read zero, at the exact moment when B coincides with A` (which is the beginning of the event).

Now, as the point B moves along ruler two, all three clocks will be ticking. Let us suppose that all three clocks are of identical construction, therefore they all tick at the same rest rate. So let us suppose that at the moment when B coincides with C`, that the clock stationed at C` reads r. Well, since all three clocks tick at the same rate, and since they were synchronized when the event began, they are still synchronized. This means that when B coincides with C` all three clocks read r.

So eventually, the point B will coincide with B`, and a clock reading there can be made. Suppose that reading is h. Thus, the time it took for the point B to move from C` to B` is :

delta t2 = h-r

Are you still there?
 
  • #27
Originally posted by TheAtheistKing
Are you still there?

Yes. I went back over it. I understand what you're saying.

[tex]v=\frac{L}{\Delta t_1}=\frac{L_0-L}{\Delta t_2}[/tex]
 
  • #28
Let me clean up the notation for you and me.

Here is the state diagram (for help):

Initial state
R1: A...B
R2:_______A`...C`...B`

Intermediate state
R1:_______A...B
R2:_______A`...C`...B`

Final state
R1:______________________A...B
R2:_______A`...C`...B`


Focus on the time it takes for B to move from A` to B`. Let us agree to denote that time by delta t`. Thus, the total time of the event is being denoted by delta t`. In fact, let us agree to refer to all measurements or computations in the primed frame using a prime symbol. Now, the whole event is composed of two sub events. The first sub event begins when B coincides with A` and ends when B coincides with C`, and the second sub event begins when B coincides with C` and ends when B coincides with B`. Let the time of the first sub event be denoted by delta t1`, and let the time of the second sub event be denoted by delta t2`. Thus it follows that:

delta t` = delta t1` + delta t2`

Do you understand the forumla above?
 
  • #29
Originally posted by TheAtheistKing
Do you understand the forumla above?

Yes.
 
  • #30
Ok I really really need to know how to make those math symbols, then this will be simple, can you explain that to me?


I'm reading the PDF file on latex now.

What would I type to write

Delta t

Using the symbol for delta?
 
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  • #31
Originally posted by TheAtheistKing
Ok I really really need to know how to make those math symbols, then this will be simple, can you explain that to me?

I can't explain it any better than the "Introducing LaTeX Math Typesetting" thread in the General Physics forum.
 
  • #32
We are going to consider the following event:

Initial state
R1: A...B
R2:_____A`...C`...B`

Intermediate state
R1:_______A...B
R2:_______A`...C`...B`

Final state
R1:__________________A...B
R2:_______A`...C`...B`

Let the total time of the event in this frame be denoted by


[tex] \Delta t' [/tex]

This time corresponds to the amount of time it takes B to move from A` all the way to B`. The distance traveled in this frame is L0, which is the rest length of the ruler. Thus, the speed of b relative to b` is

[tex] v(bb') = \frac{L_0}{\Delta t'} [/tex]

Assumption 1:

[tex] L= L_0 \sqrt{1-\frac{v^2}{c^2} [/tex]

Now consider things from ruler one's perspective. Suppose there is a stationary clock located at B. It will note when A` coincides with B, and later this same clock will note when B` coincides with B. Thus, this clock can make an inertial time measurment of this event which I will denote by

[tex] \Delta t [/tex]

Now, the distance that the point B` traveled in ruler one's frame is L. Thus, the speed of B` relative to B is

[tex] v(b'b) = \frac{L}{\Delta t} [/tex]

And since the speed is relative, we must have

[tex] v(b'b) = v(bb') [/tex]

Hence, we must have

[tex] \frac{L_0}{\Delta t'} = \frac{L}{\Delta t} [/tex]

From which the time dilation formula follows. I will pick this up later, I have to go right now.
 
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  • #33
In other words:


Diagram as drawn in the primed reference frame (that of ruler 2):

Code:
Time t'0:
         A  B
Ruler 1: |--|
Ruler 2:    |--|---|
            A' C'  B'


Time t'1:
            A  B
Ruler 1:    |--|
Ruler 2:    |--|---|
            A' C'  B'

Time t'2:
                A  B
Ruler 1:        |--|
Ruler 2:    |--|---|
            A' C'  B'

The two rulers, AB and A'B' have the same proper length, [itex]L_0[/itex].

At (primed) time [itex]t'_0[/itex], B and A' are at the same event of space-time.

At (primed) time [itex]t'_1[/itex], A and A' are at the same event.

The point C' is defined to be the point on ruler 2 which is at the same event as B at (primed) time [itex]t'_1[/itex].

At (primed) time [itex]t'_2[/itex], A and B' are at the same event.


You've defined [itex]\Delta t' := t'_2 - t'_0[/itex].

The velocity, [itex]v[/itex] of ruler 2 (as measured in the primed system) must be [itex]v = L_0 / \Delta t'[/itex].

By length contraction, we know the length [itex]L[/itex] of ruler 1 as measured in the primed coordinate system; it is [itex]L = L_0 \sqrt{1 - v^2/c^2}[/itex].


Now, we consider things in the unprimed reference frame (that of ruler 1):

Code:
Time t0:
         A      B
Ruler 1: |------|
Ruler 2:        |--|
                A' B'


Time t2:

         A      B
Ruler 1: |------|
Ruler 2:     |--|
             A' B'

You define [itex]\Delta t := t_2 - t_0[/itex].

The velocity of ruler 2 (as measured in the unprimed system) must be [itex]v = L / \Delta t[/itex].

By (insert favorite reason here), these two velocities must be the same, thus:

[tex]\frac{L}{\Delta t} = \frac{L_0}{\Delta t'}[/tex]

Okay...
 
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  • #34
Hey Hurkyl, your diagrams are better than mine so I will change, but please if you can, edit your third state diagram. You have the event ending when A coincides with A`, but the event I am analyzing ends in a state where B coincides with B`. As for your usage of the word 'event' in spacetime, in state theory the word 'state' is used, to clearly differentiate between which theory is being used. In state theory, a state is a moment in time, a point of time, and instant, and as such has no duration. In contrast, in state theory an event must have a duration, an event must last for some amount of time. An event has a beginning, and an ending. The beginning of an event is a state, and the end of an event is a state, and there is a binary relation on the set of states 'before' such that the following statement is true in any reference frame:

Let [X,Y] denote an event. X denotes the beginning of the event, and Y denotes the end of the event. The following binary relation holds:

X before Y

Undefined binary relation on the set of states: before
In state theory, this binary relation is not defined logically, instead an operational definition is used. That means that some experiment serves to give meaning to the term. For example, consider the dropping of a stone and a feather in the Earth's gravitational field. Suppose the two are released simultaneously from the same height above the Earth's surface. The experimental result is that the stone hits the ground BEFORE the feather hits the ground every time. Hence, such an experiment can be used to 'operationally define' the binary relation 'before'. Now, on the moon both objects would hit the ground simultaneously because there is no air resistance, but this need cause us no concern, because on the moon the experiment would be that we release the feather BEFORE the stone, from the same height, and the result will always be that the feather hits the ground before the stone hits the ground.
In state theory there are two defined binary relations on the set of states they are:

Let X denote a state, and let Y denote a state.
Definition: X simultaneous to Y if and only if (not(x before Y) and not (y before x))
Definition: X after y if and only if y before x

Some axioms are:

Axiom 1 (Non circularity):
For any state x, and any state y, not (X before y and y before x)

Axiom 2 (Transitivity):
For any states x,y,z: If x before y and y before z then x before z.

Axiom 3 (Quantum Hypothesis QH):
For any state x, there is at least one state y, such that x before y AND not (there is at least one state z, such that x before z and y before z)

Axiom 4 (First state):

There is at least one state A, such that for any state B, if not (A simultaneous to B) then A before B.

There are others, but you get the idea. Basically, state theory models time using the natural number system. In other words, in state theory there is an absolute order to the states of the universe, which is totally independent of reference frame, inertial or otherwise. At any rate, unless relativity is overthrown, I don't see state theory being seriously worked on by the physics community, even though a whole host of intuitively true statements about time can be derived from a very small set of axioms.

The quantum hypothesis is the statement that there is at least one possible next state of the universe (from which it follows that time cannot end, or equivalently that relative motion cannot cease, which fact is obvious via the senses, thermodynamics, or even derivable from Newton's laws of motion). The statement that there is at most one possible next state is called the determinism conclusion DC, and is one of the theorems of state theory. In order to reach the determinism conclusion, the mathematical theory of probability is used. I don't wish to discuss state theory further, because I consider it more important to address whether or not simultaneity is absolute. It isn't until after you are certain that simultaneity is absolute and not relative, that you should begin seriously considering the temporal modal logic that is used in state theory.
 
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  • #35
Consider the uniform motion of C' from A to C, as illustrated below:

Code:
Initial State
         C'
Ruler 1: |
Ruler 2: |------------|
         A            C

Intermediate state

              C'
Ruler 1:      |
Ruler 2: |------------|
         A    B       C

Final State

                      C'
Ruler 1:              |
Ruler 2: |------------|
         A    B       C

Suppose that there are four clocks, one at each of the four locations A,B,C,C`, and that clocks A,B,C are not moving relative to one another, and tick at the same rate. Now consider time readings. When C' coincides with A, clocks C' and A read something, when C' coincides with B, clocks C' and B read something, and when C' coincides with C clocks C' and C read something. Let us presume that clocks A,B,C are synchronized at the beginning of the event. Therefore, when C' coincides with A, clocks A,B,C all read X. When C' coincides with B, clock B will read somewhat greater than X, say it reads [tex] X+ \Delta t_1 [/tex]. Therefore, the total time of travel of C' from A to B can be computed by subtracting the reading of clock A when C' coincided with it, from the reading of clock B when C' coiincided with it. Thus:

[tex] (X+\Delta t_1) - X = \Delta t_1 [/tex]

When C' coincides with C, clock C will read somewhat greater than [tex] X +\Delta t_1 [/tex], say [tex] X + \Delta t_1 + \Delta t_2 [/tex]. Therefore, the total time of travel of C' from B to C is computed by subtracting the reading of clock B when C' coincided with it, from the reading of clock C when C' coincided with it. Thus:

[tex] (X+\Delta t_1 + \Delta t_2) - (X+\Delta t_1) = \Delta t_2 [/tex]

The total time of travel of C' from A to C in the unprimed frame is

[tex] \Delta t = \Delta t_1 + \Delta t_2 [/tex]


Let [tex] L_0 [/tex] denote the distance from A to C in the unprimed frame. The speed of C' relative to C is

[tex] V(C'C) = \frac{L_0}{\Delta t}[/tex]

Now consider things from the point of view of clock C'. Suppose that when C' coincides with A, clock C' reads X', and when C' coincides with B, clock C' reads [tex] X' + \Delta t_1 ' [/tex]. Therefore the total time of travel of C' from A to B in the primed frame is given by:

[tex] (X' + \Delta t_1 ') - X' = \Delta t_1 ' [/tex]

Now when C' coincides with C, clock C' will read an amount [tex] \Delta t_2 ' [/tex] more than what it read when it coincided with B. Therefore, the total time of travel of C' from A to C in the primed frame is given by:

[tex] \Delta t' = (X' + \Delta t_1 ' + \Delta t_2 ') - X' = \Delta t_1 ' + \Delta t_2 ' [/tex]

Let L denote the distance between A and C in the primed frame. The speed of C with respect to C' is:

[tex] V(CC') = \frac {L}{\Delta t'} [/tex]

Let it be stipulated that clock C' is of identical construction to clocks A,B, and C. Therefore clock C ticks at the same rest rate as they do. In other words, when clock C' and clock A are both at rest with respect to each other, one tick of clock A corresponds to one tick of clock C'. Now, assuming that the rate of clock C' does not change when clock C' is in relative motion to clock A, [tex] \Delta t_1 = \Delta t_1 ' [/tex] and [tex] \Delta t_2 = \Delta t_2 ' [/tex]. In which case, [tex] \Delta t = \Delta t' [/tex], from which it follows that the relative velocity computations will be equal if and only if [tex] L=L_0 [/tex]. If clock C' ticks at a constant rate [tex] \gamma [/tex] which is different from the rate that clocks A,B,C tick at when C' is in relative motion to them then:

[tex] \Delta t_1 = \gamma \Delta t_1 ' [/tex]
and
[tex] \Delta t_2 = \gamma \Delta t_2 ' [/tex]

In which case:

[tex]

\Delta t = \Delta t_1 + \Delta t_2 = \gamma \Delta t_1 ' + \gamma \Delta t_2 ' = \gamma (\Delta t_1 ' + \Delta t_2') = \gamma \Delta t' [/tex]

Thus, the relative speed calculations will be equal if and only if

[tex] L = \frac {L_0}{\gamma} [/tex]

Notice how the readings of the clocks fall out of the analysis, and only 'amounts of time' in a frame are left. A reading on a clock corresponds to some particular state of the universe, it is differences in readings that are used to make computations of 'amounts of time'.

Also notice that the previous conclusion is completely independent of the theory of relativity as well as the Lorentz Fitzgerald length contraction formula. The previous conclusion would hold for any formula for L, not just the Lorentz Fitzgerald one.

Mathematical Analysis Of Simultaneity

Let us consider an event where two rulers of identical rest length [tex] L_0 [/tex] move past each other in uniform relative parallel motion, as shown in the state diagrams below. Let the relative speed be denoted by v, and let c denote the speed 299792458 meters per second. Let it be supposed that there are four clocks of identical construction, at the ends of both rulers. Thus, the rest rate of all the clocks is the same. It can be stipulated that at the beginning of the event all four clocks have the same reading without loss of generality, since clock readings inevitably fall out of the analysis. What we end up doing is comparing the amount of time of an event [X,Y] in one reference frame to the amount of time of the same event [X,Y] in another reference frame.

Code:
Initial State (B coincides with A' in all reference frames)
         A      B
Ruler 1: |------|
Ruler 2:        |--|
                A' B'

Final State (B coincides with B' in all reference frames)
         A      B
Ruler 1: |------|
Ruler 2:     |--|
             A' B'

Stipulation 1: The relative speed between the two reference frames is constant, hence if either reference frame is inertial, so is the other.
Stipulation 2: Neither ruler is subjected to any external forces, hence each ruler is in an inertial reference frame. Hence clocks in a frame tick at their rest rate.
Stipulation 3: All four clocks are synchronized at the beginning of the event, in other words they all read the same number, for simplicity let all four clocks read zero at the beginning of the event. There is nothing objectionable to this stipulation, since clock readings fall out of the analysis.
Stipulation 4: The rest rate of all four clocks is identical, thus clocks in a frame remain synchronous at all moments in time.
Stipulation 5: The two rulers, AB and A'B' have the same proper length, [itex]L_0[/itex].

Assumption 1:
Let L denote the length of the moving ruler, as measured in a rest frame. Let us assume the Lorentz Fitzgerald length contraction formula is a true statement about the length of a moving ruler. Therefore,

[itex]L = L_0 \sqrt{1 - v^2/c^2}[/itex].

From the previous analysis:

[tex] L = \frac {L_0}{\gamma} [/tex]

Hence, we must have

[tex] \gamma = \frac{1}{\sqrt{1 - v^2/c^2}}[/tex].

Let us define g such that:

[tex] g = \frac{1}{\gamma} = {\sqrt{1 - v^2/c^2}} [/tex]


(I am still working on this, ignore everything below)





Diagram as drawn in the primed reference frame (that of ruler 2):

Code:
Time t'0:
         A  B
Ruler 1: |--|
Ruler 2:    |--|---|
            A' C'  B'


Time t'1:
            A  B
Ruler 1:    |--|
Ruler 2:    |--|---|
            A' C'  B'

Time t'2:
                A  B
Ruler 1:        |--|
Ruler 2:    |--|---|
            A' C'  B'

The two rulers, AB and A'B' have the same proper length, [itex]L_0[/itex].

At (primed) time [itex]t'_0[/itex], B and A' are at the same event of space-time.

At (primed) time [itex]t'_1[/itex], A and A' are at the same event.

The point C' is defined to be the point on ruler 2 which is at the same event as B at (primed) time [itex]t'_1[/itex].

At (primed) time [itex]t'_2[/itex], A and B' are at the same event.


You've defined [itex]\Delta t' := t'_2 - t'_0[/itex].

The velocity, [itex]v[/itex] of ruler 2 (as measured in the primed system) must be [itex]v = L_0 / \Delta t'[/itex].

By length contraction, we know the length [itex]L[/itex] of ruler 1 as measured in the primed coordinate system; it is [itex]L = L_0 \sqrt{1 - v^2/c^2}[/itex].


Now, we consider things in the unprimed reference frame (that of ruler 1):

Code:
Time t0:
         A      B
Ruler 1: |------|
Ruler 2:        |--|
                A' B'


Time t1:

         A      B
Ruler 1: |------|
Ruler 2:     |--|
             A' B'

You define [itex]\Delta t := t_1 - t_0[/itex].

The velocity of ruler 2 (as measured in the unprimed system) must be [itex]v = L / \Delta t[/itex].

By (insert favorite reason here), these two velocities must be the same, thus:

[tex]\frac{L}{\Delta t} = \frac{L_0}{\Delta t'}[/tex]

Okay... [/B][/QUOTE]
 
Last edited by a moderator:
<h2>1. What is the concept of "non relativity of simultaneity"?</h2><p>The non relativity of simultaneity is a concept in physics that states that the concept of simultaneity, or two events happening at the same time, is not absolute and can vary depending on the observer's frame of reference. This means that what is considered simultaneous for one observer may not be simultaneous for another observer.</p><h2>2. Who first proposed the idea of "non relativity of simultaneity"?</h2><p>The concept of non relativity of simultaneity was first proposed by Albert Einstein in his theory of special relativity in 1905. He showed that the perception of simultaneity is relative and depends on the observer's frame of reference.</p><h2>3. How does the "non relativity of simultaneity" affect our understanding of time?</h2><p>The non relativity of simultaneity challenges the traditional understanding of time as a universal and absolute concept. It suggests that time is relative and can be perceived differently by different observers depending on their relative motion.</p><h2>4. Can the "non relativity of simultaneity" be observed in everyday life?</h2><p>Yes, the non relativity of simultaneity can be observed in everyday life. For example, if two people are standing at different distances from a clock tower, they will perceive the time of the clock's strike differently due to the time it takes for light to travel to their respective positions.</p><h2>5. How does the "non relativity of simultaneity" impact our understanding of the universe?</h2><p>The non relativity of simultaneity is a fundamental concept in the theory of special relativity, which has significantly impacted our understanding of the universe. It has led to the development of the theory of general relativity, which explains the effects of gravity on the fabric of space and time. This concept has also been applied in the field of cosmology to study the origin and evolution of the universe.</p>

1. What is the concept of "non relativity of simultaneity"?

The non relativity of simultaneity is a concept in physics that states that the concept of simultaneity, or two events happening at the same time, is not absolute and can vary depending on the observer's frame of reference. This means that what is considered simultaneous for one observer may not be simultaneous for another observer.

2. Who first proposed the idea of "non relativity of simultaneity"?

The concept of non relativity of simultaneity was first proposed by Albert Einstein in his theory of special relativity in 1905. He showed that the perception of simultaneity is relative and depends on the observer's frame of reference.

3. How does the "non relativity of simultaneity" affect our understanding of time?

The non relativity of simultaneity challenges the traditional understanding of time as a universal and absolute concept. It suggests that time is relative and can be perceived differently by different observers depending on their relative motion.

4. Can the "non relativity of simultaneity" be observed in everyday life?

Yes, the non relativity of simultaneity can be observed in everyday life. For example, if two people are standing at different distances from a clock tower, they will perceive the time of the clock's strike differently due to the time it takes for light to travel to their respective positions.

5. How does the "non relativity of simultaneity" impact our understanding of the universe?

The non relativity of simultaneity is a fundamental concept in the theory of special relativity, which has significantly impacted our understanding of the universe. It has led to the development of the theory of general relativity, which explains the effects of gravity on the fabric of space and time. This concept has also been applied in the field of cosmology to study the origin and evolution of the universe.

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