Principle of Causality and Inertial Frames of Reference

[joigus]

As said, no way in hell that photons can "look like" muons in another frame of reference. This is incompatible with conservation of charge and covariance of 4-momentum to mention but the most outrageous.

Repeat: No way in hell. Maybe in parallel hells, as @KJW suggests.  

6 hours ago, Markus Hanke said:

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?

 

Very good points. Photons lead long lives; gluons live cryptic ones. And muons, blink and you missed them.

[andsm]

On 10/7/2024 at 11:24 PM, Mordred said:

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.

I'm trying to figure out what kind of mathematics you want to see, and proof of what you want to see.

First, what I believe has already been done within the framework of the hypothesis:

1.       It is shown that the hypothesis implies that events and causal relationships in different IFRs may differ. This is a direct consequence of independently applying the causality principle to different IFRs

2.       It is proven that from the observer's point of view, events in all IFRs are the same, even if in fact they are different

3.       It is proven that two types of transformations arise in the hypothesis when changing IFRs. The first type of transformation, the transformation from the observer's point of view, preserves events. The second type of transformation describes how events actually change.

4.       From the observer's point of view, events are preserved; the hypothesis derives a type of transformation with preservation of events. It follows that the hypothesis is compatible with all physical theories that fulfill the following conditions:

a.       Rely, directly or indirectly, on the causality principle

b.       It is assumed that events in all IRS are the same

The principle of causality in the hypothesis is considered in the most general form, without relying on any physical theories or any other principles.

It does not follow from the hypothesis that it is SR that describes the transformations from the point of view of the observer. SR satisfies the requirements to be compatible with the hypothesis. Galilean transformations also satisfy the requirements to be compatible with the hypothesis. Many other attempts to construct transformations, for example, with attempts to introduce small modifications to the Lorentz transformations, also satisfy this hypothesis.

SR is a well-tested and widely accepted theory. And this theory is compatible with the hypothesis. For these two reasons, I write that SR describes the transformations from the point of view of the observer. SR is not derived from this hypothesis.

QM/QFT also satisfies the described requirements. Therefore, it is also compatible with the hypothesis.

You can write that such and such a point is incorrect, for such and such reasons. But, if we do not argue with the written points 1-4, then this means that it has been proven that the hypothesis is compatible with SR and with QM/QFT

On 10/8/2024 at 8:37 AM, Markus Hanke said:

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)?

I would like to point out that these are no longer questions about the logical integrity of the hypothesis and how compatible it is with existing physical theories. These are questions about whether it is possible to construct a theory that would describe our Universe based on this hypothesis. In principle, one could try to refute this hypothesis if one could prove that there are no ways to construct such a theory.

I would like to point out that such a refutation would be a significant scientific achievement, because it would prove the fundamental nature of space-time. After that, one could continue to compose space-time from some parts, as in dynamic causal triangulation, but it would be clear that nothing deeper than space-time exists.

 

The question talks about the mapping between particles in different IFRs. Where does it follow that such a mapping should exist at all? A few messages above, I wrote equations that show how events in different IFRs are related to each other, given the presence of something more fundamental than space-time. And, as noted there, it does not follow from anywhere that the inverse operator exists at all. If the inverse operator does not exist, then it will be impossible to accurately determine the state of another IFR based on the state of one IFR.

Generally speaking, without the inverse operator, it is impossible to even say which space-time point in IFR1 corresponds to a space-time point in IFR2.

 

Can we say that it is impossible to create a theory based on this hypothesis? I do not see such evidence. I note that my task, as the author of the hypothesis, does not include proving that such a theory can be created. My task is only to prove that the hypothesis does not contradict widely accepted theories in their well-tested area, and to show that the hypothesis is, in principle, testable. Which, as it seems to me, I have done.

If anyone thinks that a theory based on this hypothesis cannot be created. The article with the theory provides an example of a model of a hypothetical universe in which this hypothesis is fully realized. So, the theory can be created, and this can be considered proven. What is not proven is that based on this hypothesis it is possible to create a theory that would describe our Universe. This is a question for further research, but already within the framework of attempts to build theories based on this hypothesis.

On 10/8/2024 at 8:37 AM, Markus Hanke said:

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

If the hypothesis is true, then all existing theories, including QFT and QCD as part of it, are not fundamental. They satisfy only the transformations from the observer's point of view. Therefore, they must be replaced by another, more fundamental theory, which will satisfy both transformations of this hypothesis.

On 10/8/2024 at 2:58 PM, joigus said:

As said, no way in hell that photons can "look like" muons in another frame of reference. This is incompatible with conservation of charge and covariance of 4-momentum to mention but the most outrageous.

And at the same time I prove that my hypothesis does not contradict modern widely accepted theories, including those mentioned. And somehow no one has yet shown where the error is in the proof that the hypothesis does not contradict these theories. The conclusions of the hypothesis are not liked, it is obvious, but it is not possible to show where exactly in the conclusions something is wrong.

[Mordred]

1 hour ago, andsm said:

I'm trying to figure out what kind of mathematics you want to see, and proof of what you want to see.

 

 

Let's put it bluntly show how your transformations can be incorporated into the transformation rules of SR.

What mathematics would be required to start from your transforms to arrive at the SR transformations.

Can you do that? 

If you cannot then there is no way to confirm your hypothesis does in fact have compatibility compliance with SR.

I never believe anything described verbally when it comes to physics. If it's not in the mathematics then it's not proven mathematically. It's that simple I don't take anyone's word regardless if it's from another PH.D in a professional peer review article of any declaration not shown in the math.

For example what limit is in your article for speed of information exchange between two states ? You have never answered that question when I asked it on page 1.

If you don't think that's important to your article then you must undoubtedly have a different definition of the causality principle from mainstream physics.

An inertial frame of reference includes vectors in regards constant velocity that is also missing in your article. So declaring your applying IFRs without applying vectors for velocity is rather pointless 

Edited October 9 by Mordred

[swansont]

2 hours ago, andsm said:

It is shown that the hypothesis implies that events and causal relationships in different IFRs may differ. This is a direct consequence of independently applying the causality principle to different IFRs

Repeating this does not make it true. You have asserted this, but provided no model and no evidence of it, as is required.

Further, you haven’t shown how any of this is an issue of causality. 

[Markus Hanke]

11 hours ago, andsm said:

I would like to point out that these are no longer questions about the logical integrity of the hypothesis

To be honest, I’ve been silently reading along this thread, and it is still not clear to me exactly what this hypothesis you’re referring to actually is. You keep talking about events and causality, and how they change between IFRs, but those are all concepts that already presuppose the existence of spacetime endowed with a connection and a metric. At the same time you refer to something “more fundamental than spacetime”, which is meant to be implied by the hypothesis. I’m so far failing to make the connection.

11 hours ago, andsm said:

The question talks about the mapping between particles in different IFRs. Where does it follow that such a mapping should exist at all?

I don’t know - it was you who made this claim:

Quote

The difference in events in different IFRs means that in one IFR, for example, a collision of two photons may occur. And in another IFR, this collision will not occur or, for example, there will be a collision of two muons.

If there’s no mapping (invertable or not) between those frames, there would be no transformation that relates them to one another; but you did say that such a transformation exists.

11 hours ago, andsm said:

Generally speaking, without the inverse operator, it is impossible to even say which space-time point in IFR1 corresponds to a space-time point in IFR2.

So you have two entirely separate patches of spacetime, each with their own set of events, which can’t be mapped into one another by any 1-to-1 map. These patches would thus each have their own independent histories, which are not guaranteed to be mutually compatible (see your own example above). Yet the patches are still somehow IFRs in a Minkowski spacetime, and thus related via the usual SR transformations?

Is that the idea?

[andsm]

On 10/9/2024 at 9:16 PM, Mordred said:

Let's put it bluntly show how your transformations can be incorporated into the transformation rules of SR.

What mathematics would be required to start from your transforms to arrive at the SR transformations.

Can you do that? 

If you cannot then there is no way to confirm your hypothesis does in fact have compatibility compliance with SR.

As I have already written, for any theory to be compatible with a hypothesis, it must satisfy the following two conditions:

• Rely on the principle of causality

• Assume that any event exists in all IFRs.

As is easy to understand, SR satisfies these requirements. Galilean transformations also satisfy these requirements. Generally speaking, it can be argued that any modern physical theory satisfies these requirements. The speed of information transfer, as is easy to notice, is not mentioned in the conditions.

The derivation of the above conditions for compatibility is given in the article, and has been written here in the topic many times. Therefore, they can be checked. If there are any comments on any steps of the derivation, they can be written. So far, I have not seen a single comment. If there were any, I would like to see them.

Returning to the question about mathematics. There are no comments on the derivation of the conditions described above. It turns out that you want a mathematical proof that SR fulfills the described conditions, that is, relies on the principle of causality and assumes the immutability of events when the IFR changes?

On 10/9/2024 at 9:56 PM, swansont said:

Repeating this does not make it true. You have asserted this, but provided no model and no evidence of it, as is required.

I have written, step by step, how the conclusions I write are made. These steps are easy to check, to show that this and that step contain errors. So, as far as I see, evidence is provided. Model was also provided. Not a single error was found. If you disagree with this statement, show the post where these errors are shown.

[Mordred]

Repeating the same thing isn't addressing the answer is it.

The question directly relates to 

can you verify your theory conforms to causality despite not having any limitation to signal delay as taught in the distinction between Galilean and SR.

 I do not see any vectors being applied with regards to a speed limit of information exchange.

Your transformations only apply to the coordinates they do not include any vectors. 

Without vectors describing constant velocity an inertial frame of reference serves absolutely zero purpose. You may as well just refer to your IFRs as nothing more than different coordinates.

 

 

 

Edited October 11 by Mordred

[andsm]

On 10/10/2024 at 7:29 AM, Markus Hanke said:

So you have two entirely separate patches of spacetime, each with their own set of events, which can’t be mapped into one another by any 1-to-1 map. These patches would thus each have their own independent histories, which are not guaranteed to be mutually compatible (see your own example above). Yet the patches are still somehow IFRs in a Minkowski spacetime, and thus related via the usual SR transformations?

Is that the idea?

The idea is not the same as described, although it is remotely similar.

The hypothesis assume that a single space-time, with a single set of events and cause-and-effect relationships, common to all IFRs, does not exist. Instead, each IFR has its own space-time, with its independent set of events and cause-and-effect relationships, with its own history. That is, instead of one space-time with its own history, our Universe consists of many space-times with their own events and with their own history of events. An observer observes only in one IFR - the one relative to which he is stationary. An observer can change his speed and move to another IFR, with its own space-time and cause-and-effect relationships. If events in different IFRs were completely independent, then a person would cease to exist when changing speed. Which obviously contradicts everyday experience. Therefore, events in different IFRs cannot be completely independent; there must be some dependence. For a person to exist, it is necessary that the smaller the difference in the speeds of two IFRs, the smaller the difference in events between these two IFRs.

Since an observer observes only in one IFR, he always observes a self-consistent picture. When the IFR changes, history, according to the described model, changes. An observer, when receiving information from another observer who is moving with some non-zero relative speed, cannot receive information about events that are not in his IFR. That is, the received signal may differ from the sent signal, and the received signal is always consistent with the cause-and-effect relationships of the IFR in which it is received. What arises is what can be called a weak information barrier between IFRs. The barrier is weak, because information about events that occurred in the IFRs of both the first and second observers can be transmitted.

It turns out that an observer, with any exchange of information, with any change in his speed, will receive only information consistent with the events and cause-and-effect relationships of his current IFR. As a result, this means that from the observer's point of view, events do not change when the IFR changes.

Two types of transformations arise. The first type, transformations from the observer's point of view. In this type of transformation, events are preserved when the IFR changes. The second type of transformations, direct transformations, describe what actually happens.

The causality principle says that based on the previous state, one can obtain the state at subsequent moments of time if all boundary conditions are known. The state here can also be a wave function, based on which one can obtain the probability of the system being in a certain state during measurement. A certain evolution operator arises, let's call it A. For the hypothesis, some properties of this operator are irrelevant as long as it is applied in some IFR. If, according to some physical theory, the operator must have some properties, and this theory implies that events in all IFRs are the same, then everything is fine, we say that this theory is not fundamental, based on transformations from the observer's point of view. If the hypothesis is true, then all existing theories, including SR/GR/QFT, are not fundamental. SR imposes some restrictions on the evolution operator, and SR implies the sameness of events in all IFR. Therefore, it is compatible with this hypothesis. The Minkowski space here is a tool of SR, and has nothing to do with direct transformations.

On 10/10/2024 at 7:29 AM, Markus Hanke said:

If there’s no mapping (invertable or not) between those frames, there would be no transformation that relates them to one another; but you did say that such a transformation exists.

The previous part of the answer consisted mainly of copying what was already written in the article or in other posts. Here I will simply give a link to the previous answer on this topic:  

 

14 minutes ago, Mordred said:

can you verify your theory conforms to causality despite not having any limitation to signal delay as taught in the distinction between Galilean and SR.

My hypothesis is based on the fulfillment of the principle of causality. In SR, when the speed of light is exceeded, as far as I remember, causality is violated. Anything that violates the principle of causality is incompatible with my hypothesis. The first point in the compatibility requirements says exactly this. Therefore, superluminal speed is incompatible with the hypothesis when fulfilling SR. But if we consider Galilean transformations, then superluminal speed does not violate causality, and Galilean transformations with superluminal speed are compatible with the hypothesis.

[Mordred]

Yes I understand that, that isn't the point of my question I am well aware how causality applies under SR. 

My question directly pertains to your hypothesis itself.

How do you have an inertial frame of reference without having any velocity term in your transforms ?

There is a significant difference between coordinate references, inertial and non inertial reference frames.

Obviously we have a difference in understanding what the Principle of Causality entails if you don't understand why I am asking these questions of your hypothesis.

https://en.m.wikipedia.org/wiki/Causality_(physics)#:~:text=Consequently%2C the relativistic principle of,the future of its cause.

Are you applying causality as per the inertial frame treatment,

See link

as you already stated your paper doesn't involve determinism ( see link) 

Or are you specifying causal structure (see link)

Edited October 11 by Mordred

[swansont]

4 hours ago, andsm said:

I have written, step by step, how the conclusions I write are made. These steps are easy to check, to show that this and that step contain errors. So, as far as I see, evidence is provided. Model was also provided. Not a single error was found. If you disagree with this statement, show the post where these errors are shown.

Your errors are omissions, so this is not possible. You show me where you’ve explicitly explained how causality is invoked. Show where you’ve provided a transform that changes a photon to a muon.

[Mordred]

Ok perhaps you can better explain the following.

in scenario 1 where neither observer or event has any velocity you state use equation 1.

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

You use L and prime L for each IFR fine no issue there as its just an identifier. You then state.

It can be noted that equation 1 alone is not enough for the causality principle. Let's say we know the state of the system in some inertial frame of reference (IFR). Let's denote this IFR 𝐿. Is it possible on the basis of this to find the state of the system in another IFR, 𝐿 ′ , moving at a non-zero speed relative to 𝐿? If this is not possible, then events in different IFR cannot be linked to each other. However, the practice of applying the principle of causality in modern theories of physics implies that, knowing the state of a system in one IFR, it is possible to obtain the state of a system in another IFR. Thus, in order to fulfill the principle of causality, the following equation must also be fulfilled, for each 𝜑𝑖 ′ and 𝑡𝑖 ′ , for an arbitrary 𝐿 ′ :

and then give equation 2.

\[\begin{cases}\acute{\psi}_i(\acute{L})=B_{\psi i}\psi(L)\\\acute{t}_i(\acute{L})=B_t t_i(L)\end{cases}\]

where \(\psi_i\) is one set of states in its IFR.

I will let you fill in the other details as quite frankly it is unclear to me what you are doing there prior to equation 3.

\[\psi(t+dt,L)=A_\psi(t,L)\]

is your equation 3.

I simply do not  get what you are describing as different time point in the same IFR ?????????

"The operator 𝐴, accordingly, translates the state of the system between different time points in the same IFR "

 

huh come again????

this is your equation 4 which you state is required to fulfill the principle of causality and you state you must simultaneously apply equation 2 and 3.

\[\begin{cases}\psi(t+dt,L)=A_\psi(t,L)\\\acute{\psi_i}(\acute{L}=B_{\psi i}\psi(L)\\\acute{t}_i(\acute{L})=B_tt_i(L)\end{cases}\]

"Equation 1 allows us to describe the principle of causality when we do not consider in detail the properties of transformations between IFR. Equation 4 is needed for a more detailed analysis of how the causality principle and transformations between IFR are related."

Now I did the work for you on porting your key equations here for everyone's interest without requiring them to use your article. Simply due to noticing your attempt to understand the latex format for this site.

I will let you describe how those equations work with regards to your IFR's as I certainly do not understand what you are doing above.

It almost sounds like your treating each state as being somehow quantum entangled. 

 

Edited October 12 by Mordred

[Mordred]

as a further assist I will latex over the other two equations best viewed in latex form. Your example on page 5 can be viewed well without needing latex.

\[fx=\sum^{+\infty}_{k=-\infty}\hat{f}_ke^{ik\frac{2\pi}{t}x}\]

\[\phi(l)=A\phi(0)\]

hopefully that helps... 

Please step us through the equations I ported over from your article 

 

Edited October 12 by Mordred

[Markus Hanke]

10 hours ago, andsm said:

The hypothesis assume that a single space-time, with a single set of events and cause-and-effect relationships, common to all IFRs, does not exist. Instead, each IFR has its own space-time, with its independent set of events and cause-and-effect relationships, with its own history. That is, instead of one space-time with its own history, our Universe consists of many space-times with their own events and with their own history of events. An observer observes only in one IFR

Ok, this is basically what I had in mind.

We now need to first make precise what we actually mean when we speak of observers and IFRs. I’m taking the following from Sachs/Wu, General Relativity for Mathematicians (1977), which is the standard formal definition.

We start with defining spacetime to be a singly connected, time-oriented Lorentzian manifold (M,g), endowed with the Levi-Civita connection and a suitable metric.

An observer on M is a future-pointing time-like curve with appropriate parametrisation.

A reference frame on M is a vector field, the integral curves of which are observers as defined above.

An inertial frame is one that is constant with respect to the covariant derivative. Thus, choosing an IFR means choosing a vector field on the manifold M that fulfils the above requirements. There may exist infinitely many such choices, or none at all, depending on the geometry and topology of M.

This definition is clearly inconsistent with your idea, since it makes no sense to speak of connections, metrics, integral curves, and vector fields that span multiple manifolds that don’t map their points into each other 1-to-1. The best you could do here is consider a foliation in some higher-dimensional space, where each spacetime is a hypersurface of some constant parameter. But it doesn’t look like that’s what you’re doing.

10 hours ago, andsm said:

An observer observes only in one IFR - the one relative to which he is stationary.

Since you say that each IFR is its own spacetime manifold, what does it formally mean to be stationary relative to spacetime? And what does it mean for a spacetime to be in motion relative to another spacetime?

10 hours ago, andsm said:

information about events that occurred in the IFRs of both the first and second observers can be transmitted.

If each IFR is its own spacetime manifold, and events on these manifolds don’t map 1-to-1, then transmitting information between such manifolds would be a clear violation of  local unitarity.

10 hours ago, andsm said:

An observer can change his speed and move to another IFR, with its own space-time and cause-and-effect relationships.

This explicitly implies 

\[\nabla_{\mu} T^{\mu \nu}\neq 0\]

on all manifolds involved.

10 hours ago, andsm said:

and SR implies the sameness of events in all IFR. Therefore, it is compatible with this hypothesis.

But you postulate that events are not the same in all IFRs, in the sense that there’s no 1-to-1 map between points on different manifolds.

10 hours ago, andsm said:

If events in different IFRs were completely independent, then a person would cease to exist when changing speed.

If different IFRs are different spacetimes, then accelerating means the test particle is leaving one spacetime and entering another. So it does cease to exist on the original spacetime, irrespective of any dependencies.

10 hours ago, andsm said:

Therefore, events in different IFRs cannot be completely independent; there must be some dependence.

How is this possible if there’s no 1-on-1 map between these manifolds? And what is the nature of these “dependencies”, since you also say that each IFR is subject only to its own causal relationships? There is a clear contradiction here. If the outcome of an experiment in an IFR is somehow dependent on non-local influences, we’d have spotted that by now. On the other hand, if there are no such influences, there is no mechanism to guarantee causal consistency between manifolds.

10 hours ago, andsm said:

this theory implies that events in all IFRs are the same

But this is precisely not what you’re claiming…? Refer to your earlier examples with the moon, and photons/muons.

 

Edited October 12 by Markus Hanke

[andsm]

On 10/11/2024 at 11:25 PM, Mordred said:

How do you have an inertial frame of reference without having any velocity term in your transforms ?

I have two types of transformations that follow from the hypothesis. The hypothesis shows their presence, but does not describe these transformations and does not describe their parameters. The first type, transformations from the observer's point of view, preserve events when switching between IFRs. We look to see if there are such transformations, and we easily find them - SR and Lorentz transformations. SR is not derived from the hypothesis, we can only show that the hypothesis is compatible with SR and Lorentz transformations. The second type of transformations, direct transformations, should be described by the theory based on the hypothesis. Finding the parameters and equations of direct transformation is not the task of this hypothesis.

On 10/11/2024 at 11:25 PM, Mordred said:

Obviously we have a difference in understanding what the Principle of Causality entails if you don't understand why I am asking these questions of your hypothesis.

https://en.m.wikipedia.org/wiki/Causality_(physics)#:~:text=Consequently%2C the relativistic principle of,the future of its cause.

As I have written many times, I consider only the principle of causality, without relying on any of the physical theories or any other principles. The principle of causality was formulated long before the advent of SR. For example, in Aristotle's "Metaphysics" one can find what can be called one of the early formulations of the principle of causality. I do not remember the exact formulation according to Aristotle now, I read it several years ago. The link provided does not set forth the principle of causality, but the relativistic principle of causality. This is the principle of causality based on SR. Obviously, it differs from what I am considering.

On 10/11/2024 at 11:25 PM, Mordred said:

Are you applying causality as per the inertial frame treatment,

See link

as you already stated your paper doesn't involve determinism ( see link) 

Or are you specifying causal structure (see link)

As I have already written, the hypothesis suggests that the causes and cause-and-effect relationships, including history, may differ in different IFRs.

On 10/12/2024 at 12:54 AM, swansont said:

Your errors are omissions, so this is not possible. You show me where you’ve explicitly explained how causality is invoked.

Do I understand correctly that when analyzing step-by-step the results of the hypothesis, logical errors, incorrect or unproven conclusions are not visible?

On 10/12/2024 at 12:54 AM, swansont said:

Show where you’ve provided a transform that changes a photon to a muon.

I have already answered this. The task of this hypothesis is to show the fundamental possibility of creating a new class of theories. Finding this transformation is the task of such a theory, but not the task of this hypothesis.

 

 

I don't have time to answer other messages today. I'll write a reply tomorrow.

[swansont]

13 minutes ago, andsm said:

The second type of transformations, direct transformations, should be described by the theory based on the hypothesis. Finding the parameters and equations of direct transformation is not the task of this hypothesis.

!

Moderator Note

Then you do not have material that fulfills the requirements of the speculations section

Do not reintroduce this subject