Can time travel paradoxes be avoided?

Cover of Fantastic SciFi with a
Porges story (The Shadowsmith)

In a science fiction story written in 1962 by Arthur Porges, entitled The rescuer, the inventors of a time machine discover that a man has entered the machine to travel back in time. To stop him, they destroy the machine with the man inside. When they are tried for murder and destruction of valuable property, they explain:

This man had taken with him a repeating rifle and five thousand rounds of ammunition. His intention was to arrive at Golgotha in time to rescue Jesus Christ from the Roman soldiers. In short, to prevent the crucifixion. And with a modern rifle, who can say he wouldn’t succeed? And then what?... What of the effect on the future, the entire stream of history, secular as well as religious?

The story is an excellent example of the paradox of predestination mentioned in a previous article, with several more that make us doubt the possibility of time travel. But is there no way to avoid the paradoxes? Is it possible to devise a theory that would remove them making time travel feasible, at least in principle? There have been several attempts to achieve this.

What does physics tell us about time travel?

In the previous article we considered a few paradoxes that could bring us to doubt the possibility of time travel. But what does physics say about this? Is there any theory that would make time travel possible? Is it true, as some say, that Einstein’s special theory of relativity implies that it will be possible to travel in time?

First of all, we must refute a fairly widespread misconception. We often hear people saying something like this:

If it were possible to travel at speeds greater than the speed of light, we would travel backwards in time, because the passage of time would become negative.

Is this true? Consider the equation that defines the relationship between proper time and external time for a body moving with a uniform rectilinear speed, according to the special theory of relativity:

Where t is the time experienced by travelers who move at speed v; t₀ is the equivalent external time (the time experienced by an object at rest); and c is the speed of light. 

We can see that, for v < c, the term inside the square root is positive and less than 1, its root would also be less than 1, and therefore t < t₀ (the time experienced by the travelers is shortened).

Will time travel be possible?

Hibernation in 2001, a Space Odyssey

The obvious answer to this question, such as it is formulated, is yes, of course it’s possible! We all travel in time at the rate of 24 hours a day.

Naturally, this is not what comes to mind when this question is asked. What is usually meant is this: will we be able someday to make sudden jumps in time, either forward (to the future) or backward (to the past)?

There are several schemes for traveling to the future. If they aren’t possible just now, one day they could become so. For example, perhaps human beings will be frozen and remain in suspended animation, to wake up and resume their ordinary lives a hundred years later. Or they could take passage on a spacecraft, make a trip at relativistic speed, and return to their starting point a century later, whilst for the travelers the elapsed time would have been just one year. In both cases, from the point of view of the persons in question, this would have been a trip forward in time, but in reality no sudden leap would have happened, for time would have kept going on for the hibernated body, though the mind would not be aware, and also for the relativistic traveler, although in this case time would have been accelerated.

But when we speak of time travel, we do not refer to these cases, which are possible in principle. We mean disappearing from the present and appearing in the past or in the future. Will we be able to do this someday?

Solution to the time machine problem

Answer to the problem posed in a previouspost, on August 18th 2014:

This is what happened in the second scenario: 

At 16:01, the original Max traveled to the future in the second time machine. When he arrived, he found there the second Max waiting for him with the first time machine. He moved to the other machine and traveled back to the past, arriving at 15:59. After changing machines again, he traveled to the future in the original time machine. He never returned.

Only these two scenarios are possible. Any other you may try to build would be inconsistent (try and you will see).

Consequences: 

It is easy to see that the world line for the machine is the same in both scenarios. What changes is the traveler’s world line.

1.            In scenario 1, the traveler does not change machines either in the present or in the future.

2.            In scenario 2, the traveler changes machines both in the present and in the future.

Therefore, if time travel to the past were possible, the traveler would not be free. What he does in the present logically determines what he must do in the future. If he changes machines now, he must change in the future. If he doesn’t, he mustn’t.

Conclusion: 

Nobody doubts that a human being is free to take an elementary decision such as changing chairs or not. 

Therefore time travel towards the past must be impossible.

Thematic thread on Time: Previous Next

Manuel Alfonseca

The time machine problem

I am posing here a problem with interesting consequences about the (im)possibility of time travel. I'll pose the problem by means of two science-fiction vignettes. If you decide to try your hand at solving it, you can describe your solution in a comment to this blog post. Next week I'll explain the solution and its consequences.

First vignette

At 15:55, Max told me:

“I have just invented a time machine. Do you want to see it?”

Of course, I accepted. 

• At 15:58, Max and I entered the room where the machine was. It looked like a simple metal chair. The machinery seemed to be located under the seat.
• At 15:59, while Max and I looked at the machine from the room’s door, a second exact copy of it suddenly appeared, just near the machine. In the second machine was seated an exact copy of Max. Amazed, Max and I looked at him.
• At 16:00, the original Max crossed the room, sat on the original machine, pressed a control and disappeared towards the future. The copy of Max, still sitting on the copy of the machine, observed attentively what he was doing.
• At 16:01, the copy of Max pressed a control in the copy of the machine and disappeared towards the future. Max and the machine never returned.

After thinking for some time, I deduced what had happened. At 16:00, Max travelled to the future in his time machine, but when he arrived he travelled back to the past, arriving at 15:59. He watched the original Max leaving on the original time machine at 16:00, went again to the future at 16:01 and never returned.

In the figure, the blue line represents Max, while the red broken line is the time machine.

Second vignette 

At 15:55, Max told me:

“I have just invented a time machine. Do you want to see it?”

Of course, I accepted. 

• At 15:58, Max and I entered the room where the machine was. It looked like a simple metal chair. The machinery seemed to be located under the seat.
• At 15:59, while Max and I looked at the machine from the room’s door, a second exact copy of it suddenly appeared, just near the machine. In the second machine was seated an exact copy of Max. Amazed, Max and I looked at him.
• At 16:00, the copy of Max stood up, went to the original machine, sat on it, pressed a control and disappeared towards the future. The original Max, near me, observed attentively what he was doing.
• At 16:01, the original Max crossed the room, sat on the copy of the machine, pressed a control and disappeared towards the future. Max and the machine never returned.

Please, kind reader, can you help me find out what had happened in this second scenario?

See solution
See Spanish version
Thematic thread on Time: Preceding Next

Manuel Alfonseca