# Have anybody considered travel with faster-than-infinite speeds?

• Anixx
In summary, the concept of infinite speed has been superseded by Special Relativity, which states that no physical matter can travel faster than the speed of light. Some theorists have proposed the existence of tachyons, particles that can travel faster than light, but they have not been observed. John Wheeler and Richard Feynman also proposed the idea of electrons and positrons being manifestations of a single entity moving backward and forward in time. However, such theories remain purely speculative and have not been proven. Ultimately, the concept of infinite speed remains a philosophical and theoretical concept, rather than a physical reality.
Anixx
Logically, it seems that if we arrive at the point of destination before we left the point of departure, we have traveled with greater-than-infinite speed.
So, I wonder whether anyone introduced faster than infinite speeds in a physical or mathematical theory.
Classically, it seems, for travel from point ##(x_0, t_0)## to ##(x_1,t_1)## along the ##x## spatial axis and ##t## temporal axis, the mean speed would be
$$s=(x_1-x_0){\mathcal {H}}\int_{t_1-t_0}^\infty \frac1{t^2} dt$$
But if we let the integral to be divergent without undertaking Hadamard regularization, the speed will be
$$s=(x_1-x_0)\int_{t_1-t_0}^\infty \frac1{t^2} dt=(x_1-x_0)\left((1-\operatorname{sgn}(t_1-t_0))\pi\delta(0)+ \frac{1}{t_1-t_0} \right)$$
Here ##\pi\delta(0)## formally represents the divergent integral ##\frac12 \int_{-\infty}^\infty \frac1{t^2} dt## in non-Hadamard-finite-part sense. In other words, intead of taking the Hadamard finite part integral and getting negative speed for negative travel time, we leave the integral divergent and get faster-than-infinite speed.
For instance, when a particle propagates in a direction, a virtual particle-antiparticle pair may arise ahead of it, with antiparticle moving in the direction to meet the original particle. Then the antiparticle may annihilate with the original particle, while the virtual particle becoming rea and travels in the original direction. This is how quantum tunneling works. For a side observer this may look like the distance between the pair birth and the annihilation points has been traveled by the particle faster than with infinite speed.

weirdoguy, davenn and PeroK
In the classical context, where particles cannot disappear and reappear, we can have no concept of a particle arriving earlier than it departed. If particle P is at position x1 at time t1 and position x2 at time t2 < t1 then we say the particle has traveled from x2 to x1 in the period [t2,t1]. No matter which way around we arrange the times and positions, under the classical paradigm we interpret that as traveling from its location at the earliest time to its location at the latest time, which must involve finite speed.

In the quantum context, we lose distinguishability of identical particles, so we cannot identify a post-annihilation particle with a pre-annihilation one.

Yes, you are right, in classical physics there is no faster-than-infinite speed. It quantum mechanics, it seems, it exists. But my question was more related to the philisophical concept of speed (we can model a world with faster than infinite travel in a computer game, for instance).

Anixx said:
But my question was more related to the philisophical concept of speed
I'm afraid we do not discuss any philosophy on PF. It leads nowhere, everybody has an opinion, few have knowledge, and nobody has any idea how an acceptable answer would look like.

Infinite speed is a concept that was thrown out when Classical Mechanics was superseded by Special Relativity theory where no physical matter can go faster than the speed of light.

Some theorists have posited the notion of tachyons, particles that travel faster than light but never travel slower than light. However, they have never been observed to exist.

https://en.wikipedia.org/wiki/Tachyon

John Wheeler and later Feynman theorized that electrons can travel back in time and we would observe them as positrons.

https://en.wikipedia.org/wiki/One-electron_universe

The one-electron universe postulate, proposed by John Wheeler in a telephone call to Richard Feynman in the spring of 1940, is the hypothesis that all electrons and positrons are actually manifestations of a single entity moving backward and forward in time.
...

Feynman was struck by Wheeler's insight that antiparticles could be represented by reversed world lines, and credits this to Wheeler, saying in his Nobel speech:
"I did not take the idea that all the electrons were the same one from [Wheeler] as seriously as I took the observation that positrons could simply be represented as electrons going from the future to the past in a back section of their world lines. That, I stole!"[1]
Feynman later proposed this interpretation of the positron as an electron moving backward in time in his 1949 paper "The Theory of Positrons" later applied it to all production and annihilation of particle-antiparticle pairs, stating that "the eventual creation and annihilation of pairs that may occur now and then, is no creation nor annihilation, but only a change of directions of moving particles, from past to future, or from future to past."
With that said, I think we've pretty much answered the OP's question that infinite speeds have been superseded by Special Relativity, and now it's time to close this thread.

Anixx

## 1. Can travel with faster-than-infinite speeds be possible?

Currently, there is no scientific evidence or theory that suggests travel with faster-than-infinite speeds is possible. The concept of infinite speed goes against the fundamental principles of physics, including the theory of relativity.

## 2. What are the potential benefits of faster-than-infinite speed travel?

If it were possible to travel with faster-than-infinite speeds, it could potentially revolutionize transportation and space exploration. It could significantly reduce travel time between distant locations and make space travel more efficient.

## 3. What are the potential risks associated with faster-than-infinite speed travel?

One of the main risks of faster-than-infinite speed travel is the potential for time travel and paradoxes. It could also have severe consequences for the human body, as it would require immense amounts of energy and could cause physical harm due to high speeds.

## 4. Are there any ongoing research or experiments on faster-than-infinite speed travel?

Currently, there is no known research or experiments on faster-than-infinite speed travel. Most scientists focus on exploring and understanding the laws of physics that govern our universe, rather than trying to break them.

## 5. Is there any evidence of faster-than-infinite speed travel in science fiction?

Faster-than-infinite speed travel is a common theme in science fiction, but it is purely speculative and not based on scientific evidence. It is important to remember that science fiction is not the same as science fact and should not be used as a basis for scientific theories.

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