Principle of Causality and Inertial Frames of Reference

[studiot]

Well you certainly don't understand STR if you think it is in any way connected to charge, or for that matter temperature.

If you are studying the motion (STR is all about motion) of a charge particle or particles then you have to consider charge as well as STR.

FYI Dirac was the first to do this successfully.

 

Please also reproduce your definition of 'causality' in relation to STR.

In mine the may or may not be a causal effect , STR simply defines the conditions under which such an effect can be observed or exist.

Edited September 30 by studiot
spelling

[swansont]

17 minutes ago, andsm said:

Independent application of the causality principle to different IFRs means that different IFRs can contain different events and different cause-and-effect relationships. The transition between IFRs ceases to be a simple change of coordinate system in the space-time continuum.

“And I explain how it is deduced from this that from the observer's point of view, events in different IFRs are the same.”

(emphasis added)

I can’t reconcile how they can be different events and also the same.

[andsm]

14 minutes ago, studiot said:

Well you certainly don't understand STR if you think it is in any way connected to charge, or for that matter temperature.

If you are studying the motion (STR is all about motion) of a charge particle or particles then you have to consider charge as well as STR.

What does conservation of charge etc. have to do with the hypothesis under discussion? If the hypothesis is true, then STR is only valid from the observer's point of view. This means that STR does not describe what actually happens when we transition between inertial frames.

14 minutes ago, studiot said:

Please also reproduce you definition of 'causality' in relation to STR.

I didn't understand the question. The fact that STR relies on the principle of causality is quite obvious. All modern physical theories, explicitly or implicitly, rely on the principle of causality. If you think that STR is an exception here, I would like to hear it.

6 minutes ago, swansont said:

And I explain how it is deduced from this that from the observer's point of view, events in different IFRs are the same.”

Here, to reach the conclusion described, several steps are required. We can go through each step one by one, discussing each in detail.

The first step is that the hypothesis implies that events in different IFRs may differ. Is this clear, or are there any objections?

[studiot]

12 minutes ago, andsm said:

I didn't understand the question. The fact that STR relies on the principle of causality is quite obvious. All modern physical theories, explicitly or implicitly, rely on the principle of causality. If you think that STR is an exception here, I would like to hear it.

Since you haven't told me what you understand the 'principle of causality' you cannot claim that any, let alone all theories rely on it.

My question was simply.

What is your version of 'the principle of causality ?'

I also told you in outline what I understand by it and in particular wha my version allows, namely that it allows tow event to be causally connected or not to be causally connected, yet be in the same light cone.
It tells when two events can be causally connected, but it does not tell you they have to be.

18 minutes ago, andsm said:

What does conservation of charge etc. have to do with the hypothesis under discussion?

You introduced uncharged particles apparantly changing into charged particles, not I.

[swansont]

1 hour ago, andsm said:

What does conservation of charge etc. have to do with the hypothesis under discussion? If the hypothesis is true, then STR is only valid from the observer's point of view.

You tell us! You’re the one violating the invariance.

1 hour ago, andsm said:

This means that STR does not describe what actually happens when we transition between inertial frames.

So we need a new transform to account for this. What is it?

 

1 hour ago, andsm said:

I didn't understand the question. The fact that STR relies on the principle of causality is quite obvious. All modern physical theories, explicitly or implicitly, rely on the principle of causality. If you think that STR is an exception here, I would like to hear it.

But you said this has nothing to do with relativity, and yet you acknowledge that you’re tossing it aside.

From your posts, it’s not clear you understand causality 

1 hour ago, andsm said:

The first step is that the hypothesis implies that events in different IFRs may differ. Is this clear, or are there any objections?

Events differing does not appear to be a causality issue

[Mordred]

7 hours ago, andsm said:

The answer was given in the topic above. What exactly is unclear about it, or what problems do you see in this answer?

 

 

Yes I see problems that are not being addressed so is everyone else seeing the same problems.

Let me know when you distinguish between an Observer and a reference frame or for that matter a global metric from a local metric in terms of causality.

Ask yourself the following under SR/GR light-cones which of the following does causality apply.

Timelike events

Spacetime events 

Null events 

Past/present/future.

Yes I recognize your trying to avoid relativity in particular SR but ignoring invariant quantities, the speed limit of information exchange to different observers which your entire paper mentions while not applying any of the transformation rules (either Galilean or Lorentz ) makes no sense whatsoever. 

Well I'm simply going to chalk this up to ignore all verbal descriptives and apply strictly the mathematics.

lets start with your math statement

\[\psi(t+dt)=A\psi(t)\]

you state A is some operator, \(\psi) being a state. Which you describe in the following statement

"includes the set of values that are necessary to describe the system. For example, to describe a system of objects based on Newton's law of universal gravitation, if we consider objects as material points, the masses, velocities and coordinates of objects are sufficient to describe the state. Accordingly, the value should consist of mass, velocity vector and object coordinates. According to the principle of causality, events without a cause do not exist. Someone might think that, for example, the radioactive decay of the nucleus of an atom has no cause. Let's look at equation 1. The radioactive decay of a nucleus is obviously described by this equation. Therefore, it also corresponds to the principle of causality. The principle of causality does not mean determinism. There are many discussions on this issue. Note that if there were at least one phenomenon that violates the principle of causality, then this would mean a refutation of this principle."

 

so How does the equation one describe radioactive decay of an atom ?

Simply by being a state ?

what state or system is causing the state above to change ? to give radioactive decay eliminating any uncertainty or probability function in determining its rate of decay ?

answer this with the following definition of causation. Particulalry since its been argued radioactive decay is acausal and not causal yet you claim otherwise above with the following statement

" According to the principle of causality, events without a cause do not exist."

since when ?

where is the reference that makes this declaration ? Other than your own 

 

Causality is the relationship between causes and effects.^[1][2] While causality is also a topic studied from the perspectives of philosophy and physics, it is operationalized so that causes of an event must be in the past light cone of the event and ultimately reducible to fundamental interactions. Similarly, a cause cannot have an effect outside its future light cone.

https://en.wikipedia.org/wiki/Causality_(physics)

 

 

 

Edited October 1 by Mordred

[Mordred]

As your new to this forum latex on this site uses \.[latex].\ simply remove the periods I used to prevent activation. So previous to the word latex \[

for inline latex \.( latex\.)

By the way the reason I was asking on Galilean as opposed to SR/GR is nowhere in your paper do I see any reference to proper time I only see coordinate time. I also don't see any second order time derivatives but we can ignore acceleration for now.

Then we have this statement

"Some events cannot affect other events, since they are separated by a space-like interval. In quantum physics, this is expressed as the absence of correlation of measurement results at points separated by a space-like interval."

true on spacelike separation but I am curious on what your understanding is on a correlation function which doesn't require any causation to begin with 

Edited October 1 by Mordred

[andsm]

There is simply no point in considering SR in the context of this hypothesis. Let me explain why.

Equation 1 is an equation describing the principle of causality. Usually, a number of restrictions are imposed on the operator A, including restrictions from the special relativity. As was written in the article a few sentences after the quoted text, I wrote that the properties of the operator A are not important for us and will not be considered. Accordingly, the hypothesis does not rely on the special relativity in any way. That is, the properties and restrictions of the operator A are not important for us. When considering the consequences of the hypothesis, we come to the conclusion that there must be two types of transformations. One of them, the transformations from the observer's point of view, preserves events when moving between inertial frames. The second type of transformation describes what is actually happening, and it does not preserve events. How is this possible, it seems, only one participant of this forum has understood so far. How is it possible that transformations from the observer's point of view preserve events, but in fact the events are different, it seems quite simple to understand, but it is very counter-intuitive, requires careful reading and analysis.

All I need to show in this hypothesis, in relation to SR, is to show that the hypothesis has transformations that preserve events. That's all, nothing more is needed. That is, the discussion of time like intervals etc. is meaningless, they do not concern the hypothesis in any way.

More about SR and the hypothesis, and about the aforementioned Minkowski space. It is obvious that in no space-time is it possible for events in different IFRs to differ. In any space-time, the transition between IFRs is just a change of coordinate system in the space-time continuum. Therefore, if the hypothesis is true, but space-time cannot be fundamental, there is something more fundamental. Thus, from the hypothesis it follows that space-time is not fundamental.

It may seem impossible to build a theory based on this hypothesis. In my article, I provide a model of a hypothetical universe in which this hypothesis is realized. This shows the possibility of building theories based on this hypothesis. But it is too early to discuss this example here, because there is no understanding of the hypothesis yet.

 

 

17 hours ago, Mordred said:

"Some events cannot affect other events, since they are separated by a space-like interval. In quantum physics, this is expressed as the absence of correlation of measurement results at points separated by a space-like interval."

true on spacelike separation but I am curious on what your understanding is on a correlation function which doesn't require any causation to begin with

As far as I remember the lectures on quantum physics, there is some kind of restriction imposed on the operator A, for the implementation of STR. Maybe there is a different formulation there. For the purposes of the hypothesis, this is completely unimportant, for the reasons described above. I will double-check the formulation and correct it if it is incorrect. Thank you for this remark.

22 hours ago, Mordred said:

"includes the set of values that are necessary to describe the system. For example, to describe a system of objects based on Newton's law of universal gravitation, if we consider objects as material points, the masses, velocities and coordinates of objects are sufficient to describe the state. Accordingly, the value should consist of mass, velocity vector and object coordinates. According to the principle of causality, events without a cause do not exist. Someone might think that, for example, the radioactive decay of the nucleus of an atom has no cause. Let's look at equation 1. The radioactive decay of a nucleus is obviously described by this equation. Therefore, it also corresponds to the principle of causality. The principle of causality does not mean determinism. There are many discussions on this issue. Note that if there were at least one phenomenon that violates the principle of causality, then this would mean a refutation of this principle."

 

so How does the equation one describe radioactive decay of an atom ?

Simply by being a state ?

On the principle of causality and radioactive decay. I have read many articles on this topic, all of them claim that it does not violate the principle of causality. There are no references to these articles in the hypothesis, because they relate to philosophy. I did not find any consideration of this issue in physics journals.

How does the equation describe radioactive decay? For the case where we consider a quantum system, the operator A must describe the evolution of the wave function. The probability of radioactive decay can be calculated based on the wave function.

22 hours ago, swansont said:

Events differing does not appear to be a causality issue

The answer is unclear. Is there an understanding that the hypothesis implies that events in different IFRs may differ, or is there no understanding? If you think that this hypothesis does not imply that events in different IFRs may differ, I want to see why.

22 hours ago, swansont said:

You tell us! You’re the one violating the invariance.

You can read my long answer above, about the hypothesis and SR

23 hours ago, studiot said:

Since you haven't told me what you understand the 'principle of causality' you cannot claim that any, let alone all theories rely on it.

My question was simply.

What is your version of 'the principle of causality ?'

Same as in textbooks. The difference is that while in textbooks the causality principle applies to events in all IFRs, my hypothesis is that it applies to each IFR independently.

Edited October 1 by andsm

[Mordred]

I understand that Minkoskii via SR isn't important but where it does become relevant is on how your defining the IFR particularly for causation.

Now when I saw the first equation my question that came to mind is what is it about A(t) that is operating on the state that determines the decay rate and try though I might except out of a scattering decay that ionizes the atom I could not think of any possibility.

Particularly since a neutral atom is also subjective to radioactive decay. 

Now its also apparent that your causation doesn't involve the usage of determinism as opposed to the relevant probabilities 

 

Am I correct on the last 

Keep in mind it isn't so much not understanding what's involved but challenging the article to see how well you can answer any issues and points raised. As well as pointing out portions that don't make alot of sense or lends to confusion.

Edited October 1 by Mordred

[andsm]

23 hours ago, Mordred said:

Now its also apparent that your causation doesn't involve the usage of determinism as opposed to the relevant probabilities 

 

Am I correct on the last 

Yes, of course. Quote from the paper with the hypothesis: “The principle of causality does not mean determinism.”

A bit off-topic. I think that at the fundamental level there are no randomnesses, everything is deterministic. At the same time, not so long ago, experiments confirmed the absence of local hidden variables. These experimenters received the Nobel Prize several years ago. The result is based on Bell's theorem. One more thing, Bell's theorem is not applicable to the class of theories based on superdeterminism. Therefore, the possibilities for determinism remain.

 

Returning to the hypothesis. The result obtained in the hypothesis that from the observer's point of view, events in all IFRs are the same, even if in fact the events between IFRs differ, makes the hypothesis fully compatible with all widely accepted physical theories. In this hypothesis, the operator A(t) is considered in the most generalized way, without relying on any of the existing theories. That is, the hypothesis does not rely on special relativity or quantum physics. Moreover, if the hypothesis is true, then all existing theories are not fundamental, and describe our Universe only from the observer's point of view. The hypothesis allows us to create a new class of theories that were impossible to create before it. The hypothesis is, in principle, testable. It is, in principle, testable, because it allows us to create theories based on it, and these theories, in principle, can be tested.

There is something that can be considered as an indirect confirmation that the hypothesis is true. All modern attempts to build theories beyond the Standard Model, such as string theory, LQG, dynamical triangulation, etc., are clearly unsuccessful. All these theories consider space-time as something fundamental. There are nuances, someone can say that in such and such a theory, for example, time at the macro level is emergent, derived from the dynamics of the micro level. But, if you look into it in detail, all these theories consider space-time as something fundamental. This hypothesis predicts that space-time is not fundamental. If it is really non-fundamental, then this explains the failure in building these theories. It is impossible to build a fundamental theory based on something that is not fundamental.

23 hours ago, Mordred said:

Keep in mind it isn't so much not understanding what's involved but challenging the article to see how well you can answer any issues and points raised. As well as pointing out portions that don't make alot of sense or lends to confusion.

Thank you, this is exactly what I would like. I can easily not notice some unclear and confusing moments simply because, as an author, the argumentation seems clear to me. In terms of argumentation, in terms of the logical integrity of the hypothesis, I have checked this more than once, looking for any possible problems.

[Mordred]

In so far as emergent spacetimes I would say you would need a considerable amount of additional details to the article to be useful for showing its applicability to determining an emergent spacetime particularly in regards to incorporation to QM/QFT.

I also feel that your article would be far better off if you included the invariant vs variant quantities in regards to causation rather than the verbal descriptive attempts with regards to your IFRs.

The other recommendation is to use examples that at least have some viability. You have seen the commentary on the examples you provided by others.  Poor examples that have no viability will be counter productive to any further interest in the article or hypothesis.

Those are some immediate suggestions granted more work on finding indirect means of testability would go along ways as well.

  For the record there were numerous points where poor descriptives and examples were extremely distracting from the articles goal. Several of those were already mentioned in this thread.

Think of it this way. If you, yourself was reading some paper that is poorly described and included examples with zero viability or has statements that doesn't conform with known physics 

Do you continue reading it ?

Now in the interest of article improvement in one regard I can offer some advise with regards to the causal vs acausal argument involving atoms.

Now Swansont may very well have a better treatment for dealing with half life decay but a method I'm familiar with is to treat the atom as a single state via a summation of all amplitudes using the Caasimer trick and then applying Breit Wigner distributions. This will give a reasonable decay rate for neutral atoms as well as ionized atoms. Obviously the formulas will vary between the two cases. Breit Wigner is typically in the CM frame but it does have the Lorentz invariance corrections.

However as that isn't the focus of the article whether or not you choose to include those details is up to you.

In terms of applying causality regardless of any specific relativity theory.

There are essential equations that all physics theories use. Regardless of the theory work with those in particular those relating to the equations of motion for causation. Good example is time ordering of events viewed from different observers (part of the proof for timelike observers as opposed to spacelike).

There's nothing incorrect about applying those lessons without involving SR directly.

Edited October 3 by Mordred

[swansont]

On 10/1/2024 at 2:36 PM, andsm said:

All I need to show in this hypothesis, in relation to SR, is to show that the hypothesis has transformations that preserve events

By all means show the transformations, but I thought that these events are not preserved. 

[andsm]

 

About invariants. Transformations from the observer's point of view coincide with the transformations of SR, here the invariants are clear. It is necessary to understand that these are not real invariants, but invariants from the observer's point of view. When moving to another IFR, they can be violated, although for the observer everything will look like the invariants are preserved.

Now let's consider direct transformations. Direct transformations should describe how everything changes in reality, and not from the observer's point of view. To begin with, what are the restrictions on these transformations? The presence in the hypothesis of transformations from the observer's point of view, under which events are preserved, means that the hypothesis is completely compatible with all existing physical theories. Therefore, direct transformations do not require any restrictions from existing theories. Further, there is a restriction described in the article, deduced from the fact of the existence of a human. If events in different IFRs are completely independent of each other, this means that a person, changing his speed, will cease to exist. When the speed changes, he will move from one IFR with some events to another IFR with completely independent events, and there is no reason for his body to continue to exist. This obviously contradicts everyday experience, so a limitation on the degree of difference of events in the IFR arises. The smaller the difference in the speed of the IFR, the smaller the difference in events should be. As the difference in the speed of two IFRs tends to zero, the difference in events between them should also tend to zero. It turns out that only this limitation affects direct transformations. Now, from the hypothesis it follows that there must be something more fundamental than space-time. Space-time and state must be derived from this something more fundamental, separately and independently for each IFR. Let's write an equation for this:

\[ \Psi(t) =B(L,t) \Omega \]

Here \[ \Psi \] is a state, \[ \Omega \] is that something more fundamental, \[ B(L,t) \] operator, which allows us to obtain the state at time t for the IFR \[ L \]. For another IFR, for \[ L^{'} \] , the equation will be:

\[ \Psi^{'}( t^{'})= B(L^{'},t^{'}) \Omega \]

In order to determine the state in another IFR from the state in the first IFR, we need to obtain \[ \Omega \]. But for this, the inverse operator \[ B^{-1} \] must exist, which does not follow from anywhere.

For an invariant to exist, this inverse operator must exist. But since its existence does not follow from anywhere, this means the absence of invariants and direct transformation. Invariants cannot exist in the general case, but for some \[ \Omega \], where the inverse operator exists, they can exist. We consider causality in the most general form, so the conclusion arises about the absence of invariants in the direct transformation. Are there any restrictions on \[ \Omega \] ? Yes, there are. Although, as a consequence of the hypothesis, modern widely accepted theories are satisfied only within each IFR. Within each IFR, the causality principle is satisfied: \[ \Psi (t+\Delta t) = A(t+ \Delta t) \Psi (t) \]. For the known physical theories to be satisfied, the operator \[ A \] must be subject to appropriate restrictions, although only within each IFR, without restrictions on the transition between IFRs. As a result, it must be true:

\[ \Psi (t+\Delta t) = A(t+ \Delta t) \Psi (t) = A(t+ \Delta t) \Psi (t)= A(t+ \Delta t) B(L,t) \Omega \]

Since \[ \Psi (t+\Delta t) = B(L,t+\Delta t)) \Omega \]

then

\[ B(L,t+\Delta t) \Omega = A(t+\Delta t) B(L,t) \Omega \]

As a result, a number of restrictions on \[ \Omega \] appear, based on which it is possible to calculate what is more fundamental than space-time.

Edited October 5 by andsm

[Mordred]

Use order \[ test \,] just remove the comma on last statement

[andsm]

On 10/3/2024 at 2:40 AM, Mordred said:

In so far as emergent spacetimes I would say you would need a considerable amount of additional details to the article to be useful for showing its applicability to determining an emergent spacetime particularly in regards to incorporation to QM/QFT.

It is shown that the hypothesis is compatible with SR. Modern quantum field theory relies on gauge symmetries. SR and U(1) symmetry are closely related. SR is a transformation from the observer's point of view. From this we conclude that U(1) symmetry is also satisfied only from the observer's point of view. And here an open question arises - can all other gauge symmetries of the Standard Model be derived from symmetries from the observer's point of view?

[Mordred]

All gauge theories are Lorentz invariant so yes they all are in accordance with  Observer effects factored in.

 From what I've seen thus far on your mathematics I don't see how your hypothesis complies under Lorentz invariants from what I've read of your article. Obviously under group theory all gauge theories must meet specific criteria which I don't see included in your article.

[andsm]

On 10/3/2024 at 2:40 AM, Mordred said:

Now Swansont may very well have a better treatment for dealing with half life decay but a method I'm familiar with is to treat the atom as a single state via a summation of all amplitudes using the Caasimer trick and then applying Breit Wigner distributions. This will give a reasonable decay rate for neutral atoms as well as ionized atoms. Obviously the formulas will vary between the two cases. Breit Wigner is typically in the CM frame but it does have the Lorentz invariance corrections.

I thought about expanding this part of the article, with a description of the causality principle.

The article was sent for review by many journals. One of the reviewers wrote in his review that for a radioactive atom, equation 1 from my article is not satisfied, the decay has no cause, therefore the hypothesis as a whole is not true. The journal does not belong to the first quantile of Scopus, but it is still surprising to see such a quality of review. After receiving this review, I expanded the description, explained that the causality principle is not violated here. I consider a more detailed and expanded description unnecessary, after all, the article is not written in defense of the causality principle.

[Mordred]

Lol if you recall I essentially asked that same question in regards to first equation  it's why I mentioned the decay being acausal.

 

 It's also one of the reasons for mentioning the choice of examples in the article.

In regards to gauge theories all Gauge theories must have symmetry invariance for both global and local symmetries. This includes Lorentz invariance under SO(3.1) Poincare group. Those details are inclusive in the covariant derivative for each gauge group.

Edit forgot to add that you may find other review turn downs as a result of the first equation. I would consider  eliminating that example altogether but that's just my advise. As the purpose of the paper also isn't to show a deterministic universe as a fundamental reality that example isn't really needed 

Edited October 5 by Mordred

[swansont]

3 hours ago, andsm said:

About invariants. Transformations from the observer's point of view coincide with the transformations of SR, here the invariants are clear. It is necessary to understand that these are not real invariants, but invariants from the observer's point of view. When moving to another IFR, they can be violated, although for the observer everything will look like the invariants are preserved.

That’s not what invariant means

3 hours ago, andsm said:

The smaller the difference in the speed of the IFR, the smaller the difference in events should be. As the difference in the speed of two IFRs tends to zero, the difference in events between them should also tend to zero.

There isn’t a continuum of options between a photon and a muon.

3 hours ago, andsm said:

It is shown that the hypothesis is compatible with SR.

Just saying this does not make it true. What is the transform that changes a photon into a muon?

On 9/30/2024 at 2:55 PM, andsm said:

The first step is that the hypothesis implies that events in different IFRs may differ. Is this clear, or are there any objections?

Not at all clear how that can be the case if “events in different IFRs are the same”

[andsm]

On 10/5/2024 at 10:58 PM, Mordred said:

 From what I've seen thus far on your mathematics I don't see how your hypothesis complies under Lorentz invariants from what I've read of your article. Obviously under group theory all gauge theories must meet specific criteria which I don't see included in your article.

In this article, I do not aim to derive the SR. The aim is only to show that the hypothesis is compatible with the SR. But it is not difficult to show how to derive the SR.

Let us verify whether the special theory of relativity, taken together with the corresponding transformations, is transformations of space-time-fields from the viewpoint of observer.

Let us list the conditions under which it will be possible to assert this univocally:

1.       Events are same in all frames of reference, from the viewpoint of observer

2.       The principle of causality connects events in all frames of reference, from the viewpoint of observer

3.       Physical laws are the identical in all frames of reference

4.       The speed of light in vacuum is the same in all frames of reference

It can be easily seen that the conditions listed above describe the explicit and implicit postulates of the special theory of relativity.

3 and 4 are implemented through restrictions on the operator A in each of the IFRs

 

On 10/6/2024 at 2:23 AM, swansont said:

That’s not what invariant means

The invariants of SR, from the observer's point of view, are fulfilled exactly. Events, from the observer's point of view, are preserved exactly, not approximately, when transitioning between IFRs. You trying to evaluate the hypothesis by some part of its consequences. At the same time, ignoring other consequences that resolve the apparent contradiction to observations.

On 10/6/2024 at 2:23 AM, swansont said:

There isn’t a continuum of options between a photon and a muon.

The hypothesis implies that space-time is not fundamental, that there is something more fundamental than space-time. Particles exist in space-time. Since space-time, according to the hypothesis, is not fundamental, it is not clear how particles can be fundamental. It follows that perhaps there is a continuum of options between a photon and a muon.

On 10/6/2024 at 2:23 AM, swansont said:

Just saying this does not make it true. What is the transform that changes a photon into a muon?

Are there arguments showing that there are errors in the conclusion of the statement that the hypothesis is compatible with SR? If there are, I would like to see them.

If there are no such arguments, then answering the second part of the question - this is a direct transformation. The task of finding equations describing these transformations is the task of creating an theory based on this hypothesis. This hypothesis only shows the possibility of constructing such a theory.

On 10/6/2024 at 2:23 AM, swansont said:

Not at all clear how that can be the case if “events in different IFRs are the same”

 

On 10/6/2024 at 2:23 AM, swansont said:

Not at all clear how that can be the case if “events in different IFRs are the same”

I suggested considering step by step the conclusion that events, from the observer's point of view, are the same in all IFRs, although in fact the events differ. But you, in fact, rejected such a proposal. In this question, the conclusion of the hypothesis and, in fact, the hypothesis itself are confused.

The hypothesis itself, I will write once again, is that the principle of causality is applied to different IFRs independently. Further consequence - Independent application of the principle of causality means that from the fact that such and such an event occurred in some IFR, or that there is such and such a cause-and-effect relationship there, it does not follow that in another IFR there is this event or this cause-and-effect relationship.

[Mordred]

Well as there isn't any equations that use either Galilean or SR transformations in your article. All transforms are specific to your article including those where you separated spacetime into two 2d planes we can only take your word of complying with Lorentz invariance. 

None of your equations has proper time from what I see but only the coordinate time.

The mathematical proofs are not included for Lorentz invariance not from what I see in the article. Verbal declarations are insufficient by themselves.

For example I don't see a single covector when you require a minimum of a covector and vector to maintain lorentz invariance once you have any curvature term.

That includes the curvature terms that arise from inertial observers.

Your more than welcome to show your transformations here to show how I'm incorrect with the above in point of detail I invite you to show how I would be incorrect in my assessment using those transformations that you have in your article.

I would also argue that spacetime is simply the metric where time is given dimensionality of length via the ct interval and not fundamental as it's only a volume where the time components involve the SM fields. For example it's not some fabric or eather as many try to make it out to be.

So if your trying to find some fundamental aspect to spacetime all I can say is good luck on that.

Edited October 7 by Mordred

[andsm]

46 minutes ago, Mordred said:

Well as there isn't any equations that use either Galilean or SR transformations in your article. All transforms are specific to your article including those where you separated spacetime into two 2d planes we can only take your word of complying with Lorentz invariance. 

None of your equations has proper time from what I see but only the coordinate time.

The mathematical proofs are not included for Lorentz invariance not from what I see in the article. Verbal declarations are insufficient by themselves.

I consider causality in the most general way, not relying on anything except causality. This means that I do not rely on either STR or QM/QFT. Therefore, I do not need to derive STR, I only need to show that the hypothesis is compatible with STR. To do this, all that is needed is to show the presence of transformations that preserve events.

After reading what you wrote above, I have a question. Is it clear how this hypothesis derives that from the observer's point of view, events in different IFRs are the same?

47 minutes ago, Mordred said:

I would also argue that spacetime is simply the metric where time is given dimensionality of length via the ct interval and not fundamental as it's only a volume where the time components involve the SM fields. For example it's not some fabric or eather as many try to make it out to be.

If space-time is fundamental, then the transition between IFRs is just a change of coordinate system. During such a transition, events and cause-effect relationships cannot change. The hypothesis assumes that during the transition between IFRs, events and cause-effect relationships can change. Therefore, this hypothesis and the fundamentality of space-time are incompatible.

[swansont]

1 hour ago, andsm said:

The hypothesis implies that space-time is not fundamental, that there is something more fundamental than space-time. Particles exist in space-time. Since space-time, according to the hypothesis, is not fundamental, it is not clear how particles can be fundamental. It follows that perhaps there is a continuum of options between a photon and a muon.

No, I don’t see how that follows, and given all the events observed at accelerator/collider labs, not having any evidence whatsoever of this continuum means this is pretty much already experimentally falsified

1 hour ago, andsm said:

I suggested considering step by step the conclusion that events, from the observer's point of view, are the same in all IFRs, although in fact the events differ. But you, in fact, rejected such a proposal. In this question, the conclusion of the hypothesis and, in fact, the hypothesis itself are confused.

You say the events differ and that they are the same. This might make sense to you, but not to me.

 

1 hour ago, andsm said:

The hypothesis itself, I will write once again, is that the principle of causality is applied to different IFRs independently. Further consequence - Independent application of the principle of causality means that from the fact that such and such an event occurred in some IFR, or that there is such and such a cause-and-effect relationship there, it does not follow that in another IFR there is this event or this cause-and-effect relationship.

You still haven’t explained how this is an issue of causality. An event happens. Causality only enters into the situation if you look at what caused the event, and you haven’t done that. 

[Mordred]

1 hour ago, andsm said:

I consider causality in the most general way, not relying on anything except causality. This means that I do not rely on either STR or QM/QFT. Therefore, I do not need to derive STR, I only need to show that the hypothesis is compatible with STR. To do this, all that is needed is to show the presence of transformations that preserve events.

 

No you need to show how anyone else can employ what you have to incorporate an SR/GR treatment to confirm what you have complies with SR/GR.

Not merely state that it does. This whole article mentions examples where different IFR's will disagree on what is being measured.

To the point where they cannot even agree on what particle is being measured.

How can that possibly comply with Lorentz invariance ? This is a point mentioned numerous times on this thread by others 

1 hour ago, swansont said:

 

You say the events differ and that they are the same. This might make sense to you, but not to me.

 

 

Example here.

So that should answer the clarity question on your article. In essence lack of clarity.

Edited October 7 by Mordred

[Markus Hanke]

11 hours ago, andsm said:

this is a direct transformation. The task of finding equations describing these transformations is the task of creating an theory based on this hypothesis. This hypothesis only shows the possibility of constructing such a theory.

I don’t see what such a transformation could possibly look like.

For starters, massless particles have no rest frame (inertial or otherwise) associated with them, so it is not clear at all what it actually is that you’re mapping between.

Furthermore, what would be the parameters of the map? It can’t involve v, since v=c for all IFRs, so the map would be 1-to-many. But if it’s not v, what else could it be, since that’s the only parameter whereby IFRs are related to one another?

Also, there’s more than one massless particle in nature. What is it that determines that a particular set of IFRs map a muon into a photon, and not a gluon (or hypothetically a graviton)?

And what about the fact that muons decay, and gluons are QCD-confined, whereas photons are free and stable?