The most devastating argument against the physical existence of tachyons is not that they require infinite energy to slow down to the speed of light, but that they inherently break the logical structure of the universe. This breakdown of cause and effect is best illustrated by a famous thought experiment introduced by physicist Richard Tolman in 1917: The Tachyonic Antitelephone.
1. The Relativity of Simultaneity
To understand the antitelephone, we must first understand a core pillar of Einstein's Special Relativity: the relativity of simultaneity.
In a Newtonian universe, time ticks away universally. If two events happen at the same time for Observer A, they happen at the same time for Observer B. Einstein proved this is false. Because the speed of light ($c$) is constant for all observers regardless of their relative motion, the perception of "now" is relative. Observers moving at different velocities will disagree on the chronological order of events separated by space.
For ordinary matter and light, this disagreement is harmless. Because nothing travels faster than $c$, no observer can ever see an effect happen before its cause. The temporal ordering of causally connected events is absolute.
2. The Setup of the Paradox
Imagine two observers, Alice and Bob, who are moving away from each other at a substantial fraction of the speed of light ($v$). Both are equipped with a hypothetical device capable of transmitting and receiving tachyon signals at a speed $u$, where $u > c$.
Let's walk through the sequence of events:
- Event 1: Alice sends a tachyon message to Bob. Let's say her message says, "Buy Apple stock." In Alice's reference frame, the tachyon travels incredibly fast, but it still travels forward in time.
- Event 2: Bob receives Alice's message. Immediately upon receiving it, he uses his own tachyon transmitter to send a reply back to Alice saying, "Message received."
Because Bob is moving away from Alice at a relativistic speed ($v$), the relativity of simultaneity severely distorts how the two observers measure time. According to the Lorentz transformations, if Bob sends a tachyon signal back to Alice at a speed $u$, and if the product of their relative velocity and the tachyon's velocity is greater than the speed of light squared ($v \times u > c²$), a mathematical catastrophe occurs.
If $v u > c²$, the term in the numerator becomes negative. This means that in Alice's reference frame, the time it takes for Bob's reply to reach her ($Δt_Alice$) is a negative number.
3. The Causal Loop (Grandfather Paradox)
The mathematics dictate a horrifying physical reality: Alice receives Bob's reply before she sends her original message.
This is the core of Tolman's paradox. The tachyonic antitelephone allows you to send a message into your own past. This creates a closed timelike curve, which immediately leads to logical paradoxes akin to the classic Grandfather Paradox.
Suppose Alice programs her tachyon transmitter with a simple logic gate: If I receive a reply from Bob at 11:59 AM, I will not send my message to him at 12:00 PM.
If she doesn't send the message, Bob never receives it, and therefore Bob never sends the reply. But if Bob never sends the reply, Alice's transmitter logic gate dictates she will send the message at 12:00 PM. The universe is thrown into an unresolvable logical contradiction.
Stephen Hawking's Chronology Protection Conjecture
To prevent the universe from dissolving into logical paradoxes, Stephen Hawking proposed the Chronology Protection Conjecture. It states that the laws of physics fundamentally prevent the macroscopic transfer of information into the past. In the context of tachyons, this conjecture implies that either tachyons do not exist at all, or if they do (like as field instabilities), they cannot be harnessed to encode and transmit localized information.
4. Feinberg's Reinterpretation Principle Revisited
As discussed in our physics section, Gerald Feinberg attempted to save tachyons from this paradox using the Reinterpretation Principle. He argued that a tachyon carrying negative energy backward in time must be physically reinterpreted by the observer as an anti-tachyon carrying positive energy forward in time.
If Alice sees a tachyon arriving from Bob before she sent her signal, Feinberg argues she should reinterpret this as her own transmitter spontaneously emitting an anti-tachyon toward Bob. However, while this clever mathematical trick restores local thermodynamic stability (so detectors don't spontaneously melt from infinite negative energy), most modern physicists agree it fails to resolve the macroscopic information paradox. A signal was still passed, and the causal loop remains unbroken.
Conclusion
The tachyonic antitelephone mathematically demonstrates that faster-than-light travel and time travel are exactly the same thing. Because special relativity is one of the most rigorously tested theories in the history of science, the inescapable conclusion of Tolman's paradox is that the universe strictly prohibits the superluminal transfer of information.