Monday, August 18, 2014

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?


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