Claudio Marchesan Who knows! Perhaps in the future this paradox, with its implications for causality and the nature of communication, will be presented to students in a philosophy lesson, just as today we analyze Zeno's paradox of Achilles and the tortoise to explore the limits of our intuition about the continuous.

To me, the crux of the matter arises from the very nature of the calculation system: does the tachyon break clocks synchronization? This paradox is an invitation to rethink our logical foundations.

But how can the synchronization of clocks belonging to the same light cone be broken?

This story suggests that a tachyonic telephone cannot connect regions within the same light cone: their ability to communicate would produce a causality paradox. However, quantum entanglement exists, and whether or not we call it “tachyon” changes little; therefore, our conclusion is that some form of superluminal communication can occur regardless of the frame of reference. It is evident that whatever the nature of this “mediator”, it does not respect the Lorentz transformation: the gamma factor is imaginary. In Alice's frame of reference, she cannot calculate when Bob will receive the signal, but this does not imply that Bob will not receive it. To know when, she only needs to ask Bob with a traditional communication.

From all this, compact dimensions are not necessarily deduced, and the undivided universe is not excluded.

In the case of entanglement, the measurement performed on particle A causes the collapse of the state of the other, B. This represents a cause-effect relationship, in reference frame B. Here, the cause triggered by A precedes the effect on B, and from this perspective the tachyon cannot reverse the arrow of time, thus preserving causality.

The no-communication theorem, about the impossibility of transmitting information superluminally via entanglement, doesn't change the fundamental issue of its non-local correlations, which remain puzzling in the context of relativity.

Hi Claudio,
I enjoyed your deep analysis of the issue. However I disagree that tachyonic communication within the same light cone would cause a causality paradox. In my model (previously described in various essays) all particles (fermions) are superluminally entangled via their em field. (in essence a tachyon is my virtual gluon). Quantum measurements that collapse the wavefunction (destroy the coherence between entangled fermions) preserve causality as you suggest. But the decoherence also occurs naturally without measurements being made. That is a big issue with quantum computers. How do we preserve entanglement over large distances and times? In fact it is interesting to consider how we actually entangle a system in the first place. I think it may be possible in the future to use magnetic fields for faster than light communication (breaking the no communication theorem) since my model allows superluminal fields as distinct from em radiation which is limited to c in a vacuum, or <c in other mediums.
Synchronization of clocks in relativity is via light (em radiation) which is subject to c, and hence has simultaniety issues.
I think of time, for each defined volume of space, as being proportional to the inverse of the energy in that volume of space. Hence time interval is a scalar property of each defined volume of space, which is bristling with energy from fields and particles traversing through it, as well as from its inherent cosmological energy. This makes a natural NOW impossible (except for LaPlace's demon), unless we use the tick of a master clock as the expansion of the aether, about which we currently know very little. All of our 'intended' communication is via em radiation which thus subject to relativity, hence having simultaneity issues. Causality is only broken if we allow time to flow backwards. Superluminal whatevers do not mean backward in time!
My FTL communication will only work if I am correct about the distinction between fields and radiation. Having worked in EMC for over 40 years, I now consider fields to be part of every fermion (hence field particle duality, although I think of it as unity) Modulation of a field produces em radiation. However it may be possible to modulate the magnetic component only and receive a signal before the em disturbance arrives at the speed of light. This may become an active area of research in the future I hope.
Cheers
Dave

    Lorraine Ford Why bother with hypothesizing that particles might exist that move faster than the speed of light and travel backwards in time?

    What is time anyway? And what is a particle anyway? And what about “laws of nature” which are relationships that, obviously, definitely exist, but are independent of categories like time and space and mass, and are not subject to restrictions like the speed of light?

    "Laws of nature" exist, they seemingly in effect create time and space and mass, but they clearly can't exist IN time or space or mass. Do people ever take law of nature relationships seriously, or do people want relationships to exist IN time and space, hence hypothesizing that "signalling" is required?

    Hi Lorraine,
    Good questions that I guess we all grapple with.
    In my reductionist thinking there are only particles and force laws. I have it simplified down to two types of particle and two force laws (attraction and repulsion). Everything else is emergent. Still, as we "emergent creatures" exist in our "emergent time and space" it is only natural that we think in terms of relationships that require signalling and causality.
    Our modelling of our emergent universe is done both with mathematics and algorithmic calculations. What seems to be important in my thinking is that we skuld or sentient creatures can choose to "stop" whereas our calculation systems aka computers cannot choose.
    Cheers
    Dave

        Hi Dave,
        Thanks for your thoughtful and stimulating reply. I'm still not fully equipped to explore the quantum mechanical aspects in depth, but I'm currently studying them to eventually propose a hypothesis—related to my model—for the quantum vacuum. In fact, if you've published anything on the vacuum, I’d be very interested in reading it.

        I found your remarks on decoherence and entanglement particularly stimulating. It’s striking that entanglement can degrade even without measurements, simply through interaction with the environment. This natural decoherence presents a major challenge for quantum computing and also raises fundamental questions about how entanglement is established in the first place. Perhaps this difficulty in both preserving and creating entanglement reflects a deeper complexity in how particles interact with the quantum vacuum and their surrounding energy fields.

        As for causality and communication, I believe the Tolman paradox concerns the type of relativistic calculation that can no longer be applied in this context. However, quantum entanglement undeniably exists. Whether or not we call the "mediator" a tachyon may be just a matter of naming. The correlations it enables are superluminal and frame-independent.

        Whether entanglement collapse is triggered by a measurement or by some spontaneous event affecting one particle, that event is the cause, and it precedes the effect on the other particle (even if "simultaneity" in this context is disturbing). You also seem to reject the notions of simultaneity and absolute time.

        That said, I think we should be very clear about what violating relativity implies. There’s no doubt that the Lorentz factor is imaginary in these scenarios—so perhaps the implications go beyond just communication issues.

        Your assertion about superluminal fields and their distinction from EM radiation is intriguing and will require some time on my part to study carefully.

        If you can, I’d also love to see a link to any of your publications on FTL communication.

        Best,
        Claudio

        DAVE
        Hi Dave,
        You claim that things emerge. But, in fact, you need to input/ inject, often repeatedly input/ inject, something new into a system if you want something else new to emerge in the system.

        The only things that you could potentially input to the system are new equations involving entirely new categories, or you could input modified equations, and/or you could assign new numbers to one or more categories (e.g. mass or position) in the existing equations. In other words, nothing mysteriously emerges out of the blue, for no reason.

        To represent the above you need to use algorithmic/ logical connective symbols to represent any input/ injection into the system, as well as the usual symbols for equations, categories and numbers.

        But then these algorithmic/ logical connective symbols, which represent what is driving the system, clearly represent entirely different, but necessary, aspects of the real-world system, aspects that are not covered or represented by the “law of nature” equations.

            Lorraine Ford
            One of the dodgiest ideas of science and mathematics is the idea of emergence, the idea that order emerges out of chaos.

            But, despite any superficial appearances, outcomes have no order, order DOESN’T emerge.

            Order exists on the inside, not on the outside: the ONLY order exists in the underlying equations, the number assignments, and the algorithms that drive a system.

              Via experiments, physicists have basically found nothing more than relationships between categories (categories like mass and position etc.), and they represent these relationships with equations.

              But it is completely laughable to believe that equations alone can represent a complete and viable moving real-world system.

              In fact, physics has no CAUSE, no reason for the numbers (that apply to the categories in the equations) to ever move or jump.

              Instead, physics ASSUMES that number movement occurs, assumes that there is a system that moves. lol.

              ..................................................................................................................

              AGENCY:

              And this is the issue with agency/ free will/ creativity: who or what is moving/ jumping the numbers?

              NON-RIGOROUS people seem to be perfectly happy with superficial appearances. They subscribe to the idea that if it superficially looks like agency/ free will/ creativity, then it IS agency/ free will/ creativity. In fact, that view of agency/ free will/ creativity is no different to non-agency/ non-free will/ non-creativity: it is all superficial appearances.

              But a RIGOROUS view of agency/ free will/ creativity asks: who or what is moving/ jumping the numbers?

              Only genuine agency/ free will/ creativity, i.e. the ability of matter to jump some of its own numbers, can “[breathe] fire into the equations”, and create a viable moving real-world system:

              “Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe? The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe.” Stephen Hawking, A Brief History of Time.

                Lorraine Ford
                The point is that physics only has “just a set of rules and equations”, as Stephen Hawking put it (see above).

                Physics doesn’t have any causes. Physics has no cause for the real-world relationships (represented by equations with delta symbols) to ever exist. And physics has no cause for the real-world to ever move. I.e. physics has no cause for (what we would symbolically represent as) the numbers to start smoothly moving or jumping, and no cause for the numbers to keep smoothly moving or jumping.

                In other words, physicists can’t reasonably make any claims about agency/ free will/ creativity at all, because physics doesn’t have any cause or reason for the numbers to move: the equations of physics merely ASSUME that number movement exists.

                So, when physicists make claims about agency/ free will/ creativity, it is clear that they have made invalid assumptions about the real-world: they have ASSUMED number movement without having any cause or reason for number movement.

                  Re "Does AI Already Have Free Will?", Sabine Hossenfelder, 20 Jun 2025, youtube.com/watch?v=YdL3QDzaPrE:

                  Sabine Hossenfelder, and the philosopher Frank Martela, have a very superficial view of “agency” in the real world:

                  (1:41) How much agency a system has depends on how much of its behaviour can be predicted by external input. The more predictable, the less agency. The behaviour of a toaster for example is strongly determined by external input. You push a button, it toasts. Therefore, philosophers would say, a toaster has no agency, it has no free will. If you push a human being, results are varied and only rarely toast. So, humans have a lot of agency. … (4:34) … humans don’t have real agency because our ultimate goals were determined by the laws of nature. …

                  So, this “agency” is a merely superficial description, which is made up of a combination of the inability to predict “random [elements] that [come] from quantum effects”, and the inability to predict outcomes if a part of the system (e.g. a human being) is too complex.

                  Similarly, Frank Martela’s “criteria for free will” are superficial high-level descriptions of situations, and he includes the very dodgy concept of “choice”.

                  But there is a problem with these views, because physicists and philosophers have wrongly assumed that physics already has a complete model of a viable, functioning, moving real-world system.

                  But physics DOESN’T have a complete model of a functioning real-world system, because physics has no causes or reasons for the numbers to ever jump/ change; physics just assumes number change. Physics only has “just a set of rules and equations”, as Stephen Hawking put it:

                  “Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe? The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe.” Stephen Hawking, A Brief History of Time.

                  Agency is not a superficial description; genuine agency is all about who or what causes low-level number jumps/ number movement in the real-world system.

                  Hi everyone,

                  the relativistic propagator of a massive particle in quantum mechanics assigns a non-zero probability amplitude even for spacelike intervals. This implies that, regardless of whether the particle can be precisely localized, there is a non-zero probability that it may be detected at a separation implying a superluminal velocity.

                  As a result, observers within a timelike interval might record the emission of the particle at a time t₁ and its detection at a time t₂ with t₂ > t₁ — preserving a cause-effect ordering. However, other observers, equally valid under Lorentz transformations, might observe the reverse temporal order, with t₁ > t₂.

                  If we want to uphold the principle that causality cannot depend on the observer, then we must recognize that what is being questioned is not causality itself, but rather our ability to calculate the order of events when the model we rely on — such as special relativity — becomes insufficient or breaks down.

                  In other words:
                  the cause always precedes the effect, but our model might no longer be able to determine exactly when and how. This does not imply that causality is violated — only that our calculational framework has reached its limit of applicability.

                    Claudio Marchesan
                    Hi Claudio,

                    You have used high-level human words to describe something about the world. But isn’t it true that you can’t describe the underlying low-level world using high-level human words? That is why, as a result of experiments, physics represents the world mathematically, i.e. in terms of categories, relationships/ equations and numbers.

                    But these categories, relationships and numbers can’t explain the following aspects of the world:

                    1. How come the world knows (observes?) its own categories, relationships and numbers? What aspect of the world knows?
                    2. How come the numbers are moving? What aspect of the world is continually initiating number movement?

                    These aspects of the world can only potentially be represented using algorithmic/ logical connective symbols: using high-level human words is sure to cause philosophical-type problems.

                      Hi Lorraine,

                      Thanks again for your reflections. From the standpoint of physics, I believe I’ve already addressed most of your points in my previous posts. Many of the further questions you raise—such as what it means for the world to "know" its own categories or for numbers to "move"—go beyond what physics, as currently formulated, can answer. These questions are closer to the realm of philosophy, and while certainly fascinating, they lie outside the domain I’m focusing on.

                      In my last post, I mentioned the relativistic propagator — a version that doesn't allow us to distinguish between a positive-energy particle moving forward in time and a negative-energy one moving backward. That example was meant to highlight that even in physics, things are not always as intuitively clear or settled as they may seem. We should not always take physics as self-evident or complete.

                      With that said, I think I’ve already shared what I can in this context. Thank you again for your engagement.

                      Best regards,
                      Claudio

                        Claudio Marchesan
                        Dear Claudio,

                        If you will forgive me, your “observer” remains a vague, high-level, human-level, philosophical concept. Unless, that is, you can represent your “observer”, or represent the observer’s observation of what is currently true from his/ her/ its point of view, in low-level mathematical and algorithmic terms.

                        And, if you will forgive me, you also seem to have lifelike, active, agents in there that propagate “a massive particle”; that assign “a non-zero probability amplitude”; that detect or precisely localize a particle; and that record “the emission of the particle”. These hidden agents, or their hidden agency, also needs to be represented in in low-level mathematical and algorithmic terms.

                        Cheers,
                        Lorraine

                            Lorraine Ford
                            Despite the fact that “law of nature” relationships (represented by equations) seem to exist, it is a logical fallacy to infer from the existence of these laws that the real-world system is ruled by these laws/ equations.

                            And the logical fallacy is:

                            1. Mathematics, and mathematical equations, can’t even exist without the consciousness and agency of human mathematicians.
                            2. So, it is/was wrong to ever assume that the equations of physics could represent a system WITHOUT the system having aspects that correspond to human consciousness and agency.

                            So, though people do it all the time, I think it is completely unacceptable to write or talk about the low-level world, that physics investigates, in terms that would inevitably suggest that freewill conscious agents are involved, and then try to pretend that we are actually talking about a system ruled by deterministic equations.

                              10 days later

                              My unified field theory holds that the essence of the universe is a holographic, dynamic, and tunable information field (the etheric field). All matter, energy, events, and consciousness are “slices” or “resonance modes” of the etheric field under different parameters such as frequency, phase, and spin. Causality is not a simple linear chain, but rather the result of overall feedback and resonance within the multi-dimensional structure of the information field. There are three types of causal phenomena: “cause precedes effect,” “cause and effect coexist,” and “effect precedes cause.”

                              In my theory, the universe’s essence is this holographic, dynamic, and tunable information field. Every event we experience and every act of consciousness is a “slice” or “resonance mode” of this field under various parameters like frequency, phase, and spin. Causality, in essence, is the flow and feedback of information within this multi-dimensional field and is not necessarily unidirectional.

                              The “cause precedes effect” phenomenon that we are familiar with arises when the information field evolves linearly along its fundamental frequency, following the arrow of time. For example, when you make a decision and a result follows, this causal chain is most common in the macroscopic world and forms the basis of classical physics.

                              However, the information field is fundamentally holographic and nonlocal. This means that some causes and effects can resonate synchronously across different regions and parameters of the information field, manifesting as “cause and effect coexist.” Phenomena such as quantum entanglement, synchronous intuition, and empathetic experiences are examples where the information states of different nodes are instantaneously correlated, transcending the limitations of traditional spacetime.

                              There is also the situation where “effect precedes cause.” Through multidimensional feedback and holographic projection within the information field, some future outcomes (such as a premonition, dream, or inspiration) can appear as attractors, manifesting in the present ahead of time. Subsequently, your choices and experiences in reality become the paths that self-consistently realize these “effects.” This reverse causality is actually a natural manifestation of the information field’s overall self-organization and closed-loop feedback.

                              Therefore, in my theory, these three causal phenomena are all normal occurrences at different levels and structures within the information field. Together, they constitute the richness of the universe’s causal network and allow us to approach the relationship between reality and consciousness with greater openness and diversity.