Is Causality Fundamental?

Hi Dave,
I generally agree with your position, and I would add that—based on Tolman's explanation of the twin paradox—I personally avoid getting involved in trying to refute other relativistic paradoxes or in discussing time travel, even though I acknowledge their complexity and fascination. In my view, the key issue is not so much the arrow of time, but rather the question of simultaneity and, in the context of speculative theories, the tachyon.

Regarding the so-called Andromeda paradox, I also believe it is often misunderstood: it seems more like a problem in how we conceptualize the “present” than a true physical contradiction. The relativity of simultaneity, as you point out, doesn’t imply objective divergences in events, but only differences in how events are coordinated across reference frames—without measurable effects in the absence of interaction.

I'm currently working on a model related to galactic recession, and in exploring some of the conceptual aspects tied to cosmology, I looked into the idea of tachyons to see if they could be included as part of a broader conjecture within the speculative context I’m exploring — one that involves a fourth spatial dimension (though I didn’t find a viable way to do so).

Causality, in my view, has both physical and philosophical implications — physics and philosophy are inseparably linked (just think of Popper’s criterion of falsifiability). What I consider essential is that we both share a belief in the necessity of causality, and that, according to Einstein, causality is as fundamental as physics itself. Let's leave it to philosophers to further explore this point.

As for me, I’ve set aside the idea of tachyons for now in the context of my model. However, I don’t believe tachyons should be dismissed in speculative theories. Regardless of how one chooses to describe them, their essence seems to be implicitly present in the phenomenon of quantum entanglement.

I personally lean toward compact dimensions as a way to interpret near-instantaneous interactions, but I regard both approaches as having the same physical dignity.

Hi, Allow me to share some perspectives on the interrelationships between time, entropy, and causal laws:
Beyond human perception, causality refers to the inherent ordering principles governing sequences of cosmic transformations. If we model the universe's changes as a partially ordered set , then the internal ordering rules of this poset constitute the law of causality.

According to thermodynamic time rules, each subsequent transformation exhibits higher entropy than its predecessor. Thus, the set of cosmic transformations can be mapped onto the poset of increasing entropy. From this perspective, one fundamental causal law underlying the universe is the Second Law of Thermodynamics—the principle of entropy increase.

Of course, other fundamental causal laws also govern cosmic transformations, including the conservation of energy and the principle of least action in path selection.

Here is the preprint version of my article for sharing, if permitted by the forum . [Time-Entropy Mirroring via Space Transformation] (https://doi.org/10.20944/preprints202505.0270.v1)

Zou

zzk
No matter how you intellectualise it, or represent it with delta symbols and/or special, ingenious equations, things like equations CAN’T explain why the world is moving: i.e. why the numbers ever moved, or why the numbers continue to move. It can't be assumed that the numbers that apply to the categories in the equations (e.g. the relative position category) are fully covered by the equations.

If you want to represent the extra elements necessary for a viable moving real-world system, you need to use logical connective/ algorithmic symbols (like IF, AND, OR, IS TRUE, and THEN), which obviously represent very different aspects of the real-world system to the aspects of the real-world system represented by the equations.

ON COMMANDING EQUATIONS TO FLY

[Physicist] Christopher Fuchs recounts (in an email from Dec. 1997, reproduced on p. 292 of “My Struggles with the Block Universe“, 2014):

a little anecdote about [physicist] John Wheeler that I heard from [physicist] John Preskill a few days ago. In 1972 he had Wheeler for his freshman classical mechanics course at Princeton.

One day Wheeler had each student write all the equations of physics s/he knew on a single sheet of paper. He gathered the papers up and placed them all side-by-side on the stage at the front of the classroom. Finally, he looked out at the students and said,

“These pages likely contain all the fundamental equations we know of physics. They encapsulate all that’s known of the world.”

Then he looked at the papers and said,

“Now fly!”

Nothing happened. He looked out at the audience, then at the papers, raised his hands high, and commanded,

“Fly!”

Everyone was silent, thinking this guy had gone off his rocker. Wheeler said,

“You see, these equations can’t fly. But our universe flies. We’re still missing the single, simple ingredient that makes it all fly.”

…

[Physicist] Wheeler appears (cf. [physicist] Blake Stacey, Jan 2016) saying:

There’s nothing deader than an equation. You write that down in a square on a tile floor. And on another tile on the floor you write down another equation, which you think might be a better description of the Universe. And you keep on writing down equations hoping to get a better and better equation for what the Universe is and does.

And then, when you’ve worked your way out to the end of the room and have to step out, you wave your wand and tell the equations to fly.

And not one of them will put on wings and fly.

Yet the Universe flies!

It has a life to it that no equation has, and that life to it is a life with which we are also tied up.

(From https://ncatlab.org/nlab/show/John+Wheeler)

Hi, I'm currently not in a position to contribute at your level — I'm developing a cosmological model based on Galactic Recession, and still deepening my understanding of quantum mechanics to ensure it's consistent with all branches of physics. I've been following the discussion in the hope that other experts might join and offer their perspectives.

Hi Claudio,
Thanks for your interesting reply. I had not heard of the Tolman paradox and so I have been reading about it, and working on a reply regarding the paradox which I place on this forum when I have completed the exercise. So far I cannot see how tachyons break causality.
I am curious about your 'compact dimensions'. Are they extrinsic spacial dimensions or are they mathematically intrinsic dimensions, like how infinitessimals are non-standard numbers which cannot be measured?
I personally do not like defining things that cannot be measured, although they can have their uses mathematically.
I cannot see why we need to invoke extra dimensions when our three spatial dimensions can carry the tachyonic information linking cause and effect, as you put it. (Again, you would need to read my last two FQXI essays).
I am suggesting that fields (EM, gravity) transmit their influence faster than c, not to be confused with disturbances in the fields, which are limited to c.
On another note, cosmological in nature, I believe what we call the hot big bang, was actually preceded by a cold big bang. Well the words are wrong here, not a big bang but a phase change in the primordial energy field (whatever that means) where initially everything was extremely cold with low entropy. This cold matter state soon changed to a hot dense matter state as particle annhilations produced lots of electromagnetic radiation which soon jostled the matter to extreme temperatures. Hence the hot "big bang'.

Hi Dave,

thank you for your message — I’d like to focus on one key point: the question of causality in relation to tachyons.

Personally, I don’t think that tachyons necessarily violate causality, although I realize this is not the most common position. As explained in the Wikipedia article on tachyons, many interpretations suggest that a tachyon, seen from a different inertial frame, could appear to travel backward in time — leading to a supposed causality paradox.

The compact dimensions I previously mentioned were just a way of expressing that — like you — I don’t think tachyons break causality. I see them more as geometrical tools to represent distant connections without requiring physical propagation through standard space-time. I originally proposed them as a more structured alternative to Bohm’s “everything is connected” view, which I personally find less satisfying because it seems to give up locality altogether.

That said, maybe we don’t even need such constructs, if the near-instantaneity required by certain physical processes doesn’t imply almost truly infinite speeds.

Thank you for sharing your approach — it's certainly full of original insights and challenges to the traditional view. I must admit that some of your claims require more time for me to reflect and study — especially regarding the role of time, the reinterpretation of fundamental interactions, and the concept of a discrete aether.

Personally, I still find many aspects of relativity and the current quantum formalism to be indispensable, although I remain open to consistent reinterpretations that preserve the predictive structure of modern physics.

All the best,
Claudio

Claudio Marchesan
“Causality” is a vague, imprecise, philosophical term.

Seemingly, you are talking about number change, where the numbers apply to categories like relative position, that in turn apply to matter like particles, atoms etc.

Physics assumes that number change occurs in the world, without being able to say exactly why number change would ever occur in the world.

Except that IF number change occurs, THEN other number change occurs, due to the relationships between the categories.

So, all the equations in the world can’t explain number change. But then again, all the equations in the world don’t constitute a system.

As computing has shown, number change is a systems aspect of the world, where the difference between a set of equations and a system is represented via the use of logical connective/ algorithmic symbols. These logical connective/ algorithmic symbols represent aspects of the real-world system that CAN’T be represented by equations.

Lorraine, I read the little anecdote about Wheeler — but honestly, I didn't quite grasp the point.
It's too easy to reply that our plane flies, because the key phrase seems to be: “We’re still missing the single, simple ingredient that makes it all fly.”
I’m not sure where Wheeler was going with that (maybe he meant that we're still missing that simple, profound ingredient that unifies all the forces of nature into a single coherent framework, something that would bind all the equations to a deeper, fundamental principle), but to me, that is the real subject worth discussing.

zzk
Hi Zou,
It is a very interesting article you have posted. It resonates with many of my own ideas on a first read. I think that I will do a deeper dive into it at a later date after I have concluded my tachyonic studies.
Best wishes
Dave

Claudio Marchesan
Hi Claudio,

Sure, devices like light-cone structures and conservation laws and consistency are seemingly needed e.g. to check the validity of mathematical models, and to predict or narrow down possible outcomes of a model. Light-cones don’t actually exist, except as a concept in the minds of physicists; but they are a useful device.

So, this “causality” that you seem to be describing seems to be mainly about physicists trying to model and predict outcomes of a complicated and slightly unruly real-world system that they are observing.

But that is not genuine causality at all, in the sense of physicists trying to understand and represent the actual causal inner workings of the real-world system. Maybe physicists have given up on that ambition!

I think that the valid point that Wheeler was making is that a set of equations, no matter how many equations, no matter how ingenious the equations, can’t ever represent a viable, moving system. It is just the nature of equations: they can’t do it.

I think Wheeler was in effect saying that if physicists ever had the ambition of representing the actual components needed to make a viable moving (“flying”) real-world system, then something entirely different to equations would be needed, as well as the equations.

DAVE
Hi Dave,

Good luck with your TOE and your tachyon studies !

Claudio Marchesan
Hi Claudio,
I had a look at Wikipedia on tachyons, particularly the Tolman paradox you suggested.
Below is a quote from that article on two way tachyonic communication (with paradox), together with my version using a single frame (with no paradox). Am I missing something?
From Wikipedia, the free encyclopedia
A tachyonic antitelephone is a hypothetical device in theoretical physics that could be used to send signals into one's own past. Albert Einstein in 1907[1][2] presented a thought experiment of how faster-than-light signals can lead to a paradox of causality, which was described by Einstein and Arnold Sommerfeld in 1910 as a means "to telegraph into the past".[3] The same thought experiment was described by Richard Chace Tolman in 1917;[4] thus, it is also known as Tolman's paradox.
A device capable of "telegraphing into the past" was later also called a "tachyonic antitelephone" by Gregory Benford et al.[5] According to the current understanding of physics, no such faster-than-light transfer of information is actually possible.

Tachyonic telephone paradox – two way communication example from Wikipedia in italics.
When Alice's clock shows that 300 days have elapsed since she passed next to Bob (t = 300 days in her frame), she uses the tachyon transmitter to send a message to Bob, saying "Ugh, I just ate some bad shrimp". At t = 450 days in Alice's frame, she calculates that since the tachyon signal has been traveling away from her at 2.4c for 150 days, it should now be at position x = 2.4×150 = 360 light-days in her frame, and since Bob has been traveling away from her at 0.8c for 450 days, he should now be at position x = 0.8×450 = 360 light-days in her frame as well, meaning that this is the moment the signal catches up with Bob. So, in her frame Bob receives Alice's message at x = 360, t = 450. Due to the effects of time dilation, in her frame Bob is aging more slowly than she is by a factor of , in this case 0.6, so Bob's clock only shows that 0.6×450 = 270 days have elapsed when he receives the message, meaning that in his frame he receives it at x′ = 0, t′ = 270.
When Bob receives Alice's message, he immediately uses his own tachyon transmitter to send a message back to Alice saying "Don't eat the shrimp!". 135 days later in his frame, at t′ = 270 + 135 = 405, he calculates that since the tachyon signal has been traveling away from him at 2.4c in the −x′ direction for 135 days, it should now be at position x′ = −2.4×135 = −324 light-days in his frame, and since Alice has been traveling at 0.8c in the −x direction for 405 days, she should now be at position x′ = −0.8×405 = −324 light-days as well. So, in his frame Alice receives his reply at x′ = −324, t′ = 405. Time dilation for inertial observers is symmetrical, so in Bob's frame Alice is aging more slowly than he is, by the same factor of 0.6, so Alice's clock should only show that 0.6×405 = 243 days have elapsed when she receives his reply. This means that she receives a message from Bob saying "Don't eat the shrimp!" only 243 days after she passed Bob, while she wasn't supposed to send the message saying "Ugh, I just ate some bad shrimp" until 300 days elapsed since she passed Bob, so Bob's reply constitutes a warning about her own future.

Now let us look at this with a universal clock since this problem has nothing to do with the sending and receiving of light signals. As both Bob and Alice know their velocity is 0.8c, let us say they both install a universal clock in their spaceship that adjusts for the time dilation factor (ie. It runs faster by 0.6). Now let’s use the universal time clock and distance coordinates in days and light days (t’’, x’’) for a similar scenario but with a much faster tachyonic phone speed of 4c (so as to keep the numbers smaller).
When Alice's UT clock shows that 300 days have elapsed since she passed next to Bob, she uses the tachyon transmitter to send a message to Bob, saying "Ugh, I just ate some bad shrimp" (x’’ = -240, t’’ = 300). At t’’ = 450 days in the UTC frame, she calculates that since the tachyon signal has been traveling away from her at 4.0c for 150 days, it should now be at position x’’ = 4.0×150 -240 = 360 light days in UTC frame (x’’ = 360, t’’ =450), and since Bob has been traveling away from her at 0.8c for 450 days, he should now be at position x’’ = 0.8×450 = 360 light-days in UTC frame as well, meaning that this is the moment the signal catches up with Bob. So, in the UTC frame Bob receives Alice's message at x’’ = 360, t’’ = 450.
When Bob receives Alice's message, he immediately uses his own tachyon transmitter to send a message back to Alice saying "Don't eat the shrimp!".
225 days later in the UTC frame, at t’’ = 450 + 225 = 675, he calculates that since the tachyon signal has been traveling away from him at 4c in the −x′ direction for 225 days, it should now be at position x′ = −4×225 +360 = −540 light-days in the UTC frame, and since Alice has been traveling at 0.8c in the −x direction for 675 days, she should now be at position x’′ = −0.8×675 = −540 light-days as well. So, in the UTC frame Alice receives his reply at x’’ = −540, t’′ = 675. Thus causality is preserved.
I think the paradox arises in the original (italicised) version because of the assertions that “Time dilation for inertial observers is symmetrical, in her frame Bob is aging more slowly than she is, and in Bob's frame Alice is aging more slowly than he is, both by the same factor of 0.6.” In fact Bob and Alice age at the same rate in this example as they are both travelling at the same relativistic speed. Their knowledge of each others time via their UTC’s is in essence the same as having an instantaneous tachyonic phone.

These paradoxes are always incredibly complex and fascinating, so I might be wrong — but I wonder: if Alice and Bob are in relative motion, how can they both have the same UTC clock, at rest with respect to them, to synchronize their time? According to special relativity, a universal time shared between observers in relative motion shouldn't exist.

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.

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.

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?