Hi Dave,

Alice is using relativity to establish when Bob sent the message. In my opinion, the mistake that creates the paradox is that, in the presence of tachyons, time can no longer be compared using traditional methods. It’s not that causality breaks, but that the system for measuring time, as we normally understand it, is no longer applicable. In other words, the paradox arises because we try to use a scheme of synchronization and temporal ordering that doesn’t work with superluminal signals.

Hi Dave, hi everyone, I have thought long about Tolman’s paradox.

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.

  • DAVE replied to this.

    Thanks for the tip! I had no idea my tachyonic musings were eligible for premium academic support. Do you guys offer faster-than-light proofreading too? That would really help me get feedback before I even write the post.

    • DAVE replied to this.

      Hi Claudio,

      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?

      • DAVE replied to this.

        Hi Lorraine,

        That’s a really intriguing way to put it. I agree that we often take for granted that all relationships must happen “in” space and time, when maybe those very frameworks emerge from deeper structures. But I’m curious — how can we investigate or even describe such relationships without using the language of signaling, time, and space? Isn’t some framework always required?

          We study physics not just to know, but to do, to build, and to continually improve our world. And in doing so, we are compelled to confront the deepest questions about the nature of reality itself, fostering a profound interplay between scientific discovery and philosophical inquiry that drives both practical innovation and fundamental intellectual advancement.
          Beyond its practical applications, the study of physics is profoundly intertwined with ontology, the philosophical study of the nature of being and reality. And you're absolutely right: this isn't just an academic exercise in knowledge acquisition.
          I personally do not believe that any branch of physics can progress without a deep understanding of what the laws we have formulated actually represent. For physics to truly advance, it's not enough for our laws to merely "work", that is, to accurately predict experimental outcomes. We must also grapple with what those laws ontologically signify.

          Claudio Marchesan
          What is a signal? If, when driving a car, red light interacts with our eyes, we know it means to stop the car; if green light interacts with our eyes, we know it means we can start moving the car again.

          I think, at the particle level, an interaction between low-level matter with a red-light particle or a green-light particle can have no “extra” meaning, i.e. there can be no signals at the low-level matter or particle level. So, there could potentially be knowledge, on the part of low-level matter or particles, of categories like frequency or wavelength, and of the associated numbers, but there could be no extra meaning on top of that which would allow the definition of “signal”.

          Re framework: My framework is that, by definition, we live in a standalone, self-sufficient world (universe), with no meddling from the outside because there IS no outside to the world. At the foundations of the world there is no mathematical system etc., there is only something (not a God, with all the nonsense baggage that that entails) that created and knows the mathematical system etc.. And I think that matter (particles, atoms, molecules and living things including human beings) can only be small parts of this whole thing.

            Hi Lorraine,

            As you might have guessed, I tend to respond from the perspective of physics. You're absolutely right: concepts like particles, mass, and even “signal” (which I’d relate here to wave phenomena) are far from obvious. And this is exactly where quantum mechanics becomes essential.

            The double-slit experiment, in particular, challenges our most basic intuitions about the nature of objects and the independence of reality from the observer. In this context, a “signal” isn’t something with intrinsic meaning — but rather an emergent, interpretable pattern within a probabilistic framework.

            For a physicist, it’s not enough that Schrödinger’s equation predicts the interference pattern. The desire to understand what the laws actually represent — ontologically — is what drives new theories like hidden variables or many-worlds interpretations. The double-slit experiment is, in a sense, the archetype of this ongoing and necessary interaction between physics and ontology.

            Thank you again for your thoughtful message — I truly appreciate this kind of exchange.

              Claudio Marchesan
              Hi Claudio,

              Re "In this context, a “signal” isn’t something with intrinsic meaning — but rather an emergent, interpretable pattern within a probabilistic framework.":

              That is exactly what I was saying: no signal or symbol has intrinsic meaning. The problem is: who or what interprets a signal? People interpret signals. But particles and other low level matter don't interpret signals, because it requires a bit of high-level analysis and collation to interpret a pattern or a signal, as we know, e.g. from the number of steps required in computer programs to interpret patterns or signals. And also, the "meaning" or interpretation of patterns or signals doesn't Platonically float in the air, ready to be plucked. So, obviously, low-level matter interacts with other low-level matter; but are you claiming that low-level particles or matter could be signalling each other?

              Also, there is a calculatable probability for everything, e.g. the number of people who will be bitten by dogs in a particular town in a year, or something like that. So, Schrödinger’s equation is about probable outcomes; but the equation doesn't predict actual real-world outcomes. The real question is: who or what is assigning new numbers to categories, like the relative position category, in a real-world particle outcome?

                Mathematics, with its man-made symbols, can’t exist without the consciousness and agency of mathematicians. However, mathematicians and physicists continue to delude themselves that a viable real-world mathematical system could exist without aspects describable as “knowledge/ consciousness” and “agency/ creativity/ free will”. A viable moving system needs more than just a pile of equations and numbers.

                So, a viable moving real-world system, or small parts of the system, needs to have a low-level on-the-spot knowledge/ consciousness of itself, i.e. knowledge of what categories, numbers and relationships are currently true. And matter, with its categories, numbers and relationships, already has an intrinsic, in-built, on-the-spot true interpretation/ meaning from the point of view of itself and other matter.

                But while matter might have an intrinsic, in-built true interpretation/ meaning, there are no ARRANGEMENTS of matter that have an intrinsic, in-built, interpretation/ meaning. Signals and symbols are deliberate arrangements of matter, but whether these arrangements are deliberate or not: arrangements of matter have no in-built true interpretation/ meaning.

                So, who or what is interpreting arrangements of matter? Obviously, a higher-than-base-level consciousness, that is capable of a bit of analysis and collation, is required to interpret signals and symbols.

                Hi Lorraine,

                You’re absolutely right — there’s no intrinsic meaning in signals or symbols. Interpretation, as you say, is a complex act, and this is exactly where the interesting questions begin. Low-level matter doesn’t “interpret” in the human sense, but it can — at least in some physical models — respond consistently to patterns that, at a higher level, become interpretable as information.
                That’s why, in contemporary physics, information is often seen as an emergent property. What we call a “signal” may simply be a useful description at a certain level of abstraction. But what happens when, in some quantum systems, we observe correlations that seem to “carry information” (as in entanglement)? Is the structure of the theory itself enforcing a kind of coherence that resembles communication?

                Perhaps the most surprising part is that, despite all these deep questions, physics works.

                As for your second question — who or what assigns definite outcomes in the real world?
                When we assign a value to a physical quantity, like a particle's position or momentum, we do so within a system of agreed-upon units (like meters or kilograms). These units are not arbitrary; they are meticulously defined and internationally agreed upon to ensure consistency and comparability of our observations.
                At the current stage of our understanding, mathematics remains our best, and perhaps only, tool to describe and model reality, even if it may not capture its full essence.

                Perhaps we've all wandered a bit off topic, and it might be time to return to the original thread theme: causality.

                  Claudio Marchesan
                  Hi Claudio,

                  Re the off-topic bit:
                  What is “information”? People seem to have difficulty conceptualising and explaining what “information” is.

                  I’m contending that low-level information is subjective; information doesn’t objectively/ Platonically exist. Low-level information is just another word for low-level on-the-spot knowledge/ consciousness, and this low-level information is symbolically representable in something like the following form:

                  (category1=number1 IS TRUE) AND (category2=number2 IS TRUE) AND (category3=number3 IS TRUE.

                  I’m saying that the above is the way to symbolically represent information about an on-the-spot situation. But this type of information doesn’t emerge from a system; instead, it is a necessary part of the functioning of a system.

                  (The same types of symbols (e.g. IF, AND, OR, IS TRUE, and THEN), which seem to represent something about the real world that equations can’t represent, are the symbols one would use to represent the analysis of patterns. And also, these symbols (together with the symbols for categories and numbers) are the symbols one would use to represent the assignment of new numbers to categories, like the relative position category, in a real-world particle jump outcome, in response to a symbolically represented situation.)

                  However, if something new emerged from a system then it would only be because something else new had been ADDED to the system, e.g. new equations/ relationships between categories, or new numbers had been assigned to existing categories. This seems to happen in the plot of the Mandelbrot set, where something new seems to emerge, but this is only because the man-made algorithm is made to repeatedly and systematically ADD something new to every point on the plane on which it is plotted.

                  Re causality:
                  Without any explanation for why anything ever moves, causality assumes a moving system. But I don’t think it is valid to assume that a system would just automatically start to move, or continue to move.

                    1. The underlying infrastructure of the world is symbolically represented in terms of equations (“laws of nature”), categories like mass or position, and numbers that apply to these categories. But “information” is a word that is bandied around a lot, so how should “information” be symbolically represented?
                    2. What use is information to a system, if any?
                    3. Is it true that the symbols IF, AND, OR, IS TRUE, and THEN represent aspects of the world that can’t be represented by equations?
                    4. Is it true that nothing new can emerge from a system unless something else new is added to the system?
                    5. Before considering "causality", why does a system ever move, and why does a system continue to move?

                    Increasingly, it seems, there is talk of consciousness being a fundamental aspect of matter. But there is not much talk about the nature of this consciousness.

                    I contend that consciousness is a functional aspect of matter; consciousness is the necessary information, about matter and its local surroundings, that a viable system needs in order to operate. This type of basic-level consciousness can be symbolically represented in something like the following form:

                    (category1=number1 IS TRUE) AND (category2=number2 IS TRUE) AND (category3=number3 IS TRUE),

                    where the categories are basic-level categories like mass and position.

                    However, how come that where 2 entangled particles are separated by large distances, a change in one of the particles A could have a physical effect on the other particle B? (As I contended above, both A and B only have information about themselves and their local surroundings.)

                    Without resorting to wildly hypothesising that a new type of particle which would violate causality, tachyons, must exist, it is clear that “law of nature” relationships between categories, while they are an integral part of the structure of the world, they are independent of space and time. These “law of nature” relationships between categories, taken seriously, are seemingly the only things that could potentially explain an A-B outcome that is independent of distance and time.

                    Is physics taking these “law of nature” relationships between categories seriously, when it comes to causality?

                    It seems truly absurd that physicists don’t yet see any difference between a pile of equations and a genuine viable system.

                    A pile of equations is pretty useless because, despite the optimistic use of delta symbols, nothing moves.

                    Physicists might themselves move the equations and numbers in their minds, or by writing another line of symbols on paper or screen, but they never seem to notice that their own mental and physical involvement is required to make it all work.

                    The difference between what is represented by a pile of equations and a genuine viable moving system lies in the aspects of the real world that are represented by the following types of symbols: IF, AND, OR, IS TRUE, and THEN. These symbols represent the causal properties that animate systems and subsystems.

                    These multipurpose logical/ algorithmic symbols can be used to represent the necessary causal aspects of the real-world system. And they can also be used, together with other types of symbols, to represent the necessary inputs to the system, that are required in order to build the vertical hierarchy going from atoms to particles to molecules to living things.

                    (People have been labouring under the mistaken idea that “emergence” just naturally happens. But in fact, the plot of the Mandelbrot set shows otherwise: something new seems to emerge, but this is only because the man-made algorithm is made to repeatedly and systematically input something new to every point on the plane on which it is plotted.)

                    There IS input to the world. A quantum number jump, by a particle or other matter, in response to a situation, IS the input of new number information to the world, where this number applies to a category like the position category.

                    A number, that applies to a category, is not the type of thing that can morph into another number.

                    So, it seems that number jumping is the ONLY way that the world can move forward, because the equations, i.e. the relationships between the categories, can only implement number movement IF some other number movement has been initiated for the other categories in the equations.

                    The only way that the world can move forward is by the input of new information to the world, where this new information is a natural ratchet on the system: there is no going backwards in time.

                    How does the world work/ function?

                    A set of equations and numbers, on paper or screen, does not model or represent how the world works.

                    A set of equations and numbers, on paper or screen, mentally and physically controlled by a human being (e.g. a mathematician or physicist) can more closely model how the world works.

                    It is the consciousness and agency aspects of human beings (that can be symbolically represented by algorithmic/ logical symbols) that allow a set of equations and numbers to work as a system.

                    I.e., the world requires consciousness-like and agency-like aspects in order to work/ function.

                    While people continue to look for special, amazing, equations that will explain the world, the fact is that there are aspects of the world, including aspects of the low-level mathematics of the world, that are not covered by equations.

                    “Law of nature” equations, i.e. relationships between categories, with their associated numbers, are necessary to the world, but they CAN’T explain what happens in the world.

                    Looking at the nitty-gritty step-by-step mechanics of how mathematics itself works: mathematics can only ever work because of non-mathematical aspects of the world.

                    These necessary non-mathematical aspects can be represented using algorithmic/ logical connective symbols. But these algorithmic/ logical connective symbols represent aspects of the world that can’t be explained: they can’t be broken down into component parts.

                    So, it is not enough to describe the world in terms of equations/ relationships and numbers. At the heart of what is happening in the world, the following aspects are necessary if you want to have a viable moving real-world system (and these aspects can be represented using algorithmic/ logical connective symbols):

                    • The matter of the world (particles, atoms, molecules, cells and other living things including human beings) needs to know itself and its surroundings; and
                    • The matter of the world needs to initiate movement by jumping its own numbers (whereby other numbers also jump due to the “law of nature” mathematical relationships between the categories).

                    I guess it is because they are not also professional Systems Analysts, that professional Mathematicians, Physicists and Philosophers seem to have no idea why a set of physics’ equations and numbers cannot represent a viable moving system.

                    A viable moving system needs aspects whereby the system can interrogate or know its own numbers, and a viable moving system needs aspects whereby the system can jump its own numbers. These separate, necessary, aspects are not covered or dealt with or represented by physics’ equations and numbers, even when the equations include delta symbols.

                    A computer with its computer programs can symbolically represent a viable system. But in a computer, the numbers and equations are symbolically represented by organised arrangements and arrays of higher and lower voltages and transistors: these are not the form in which the real-world numbers and equations exist.

                    When, oh when, are Mathematicians, Physicists and Philosophers going to perform a systems analysis on the real-world moving system?

                      Lorraine Ford
                      (

                      Re my above paragraph: “A computer with its computer programs can symbolically represent a viable system. But in a computer, the numbers and equations are symbolically represented by organised arrangements and arrays of higher and lower voltages and transistors: these are not the form in which the real-world numbers and equations exist.”

                      It should be remembered that the real-world categories, equations (relationships between the categories) and numbers are what physicists represent with their special man-made symbols.

                      But the real world doesn't "know about" the symbols; the real world only “knows about” the actual real-world categories, equations and numbers.

                      Except for human beings, nothing knows about man-made symbols, on paper or screen, or inside the workings of computers/ AIs. Only people know what man-made symbols are meant to represent.

                      Man-made symbols can be re-represented with other man-made symbols. But the real-world original source of the symbols is not itself a symbol, it is the real world. The real world is different to man-made symbols of the world. Duh.

                      When are the people, who make comments on these FQxI blogs, going to stop ascribing knowledge/ consciousness of man-made symbols to computers/ AIs?

                      )