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