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I am plotting out a sci-fi setting, and trying to figure out the consequences of a non-conventional form of time travel.

In the story, time travel has been achieved by means of temporal displacement. The principle is simple; the traveller enters a capsule, and everything inside of that capsule gets teleported to an earlier point of time. The traveller can then do whatever he wants in that past for a set duration, before returning to the capsule and going back to his own time.

This time travel operates on a rubber band effect; the traveller and all his belongings are temporarily moved into another timeline, and then later brought back to his original timeline. No matter what he does in the past - there is no effect on the original timeline.

As such, in the universe where we all exist, it is only possible to "leave", and never to "arrive". From a philosophical point of view, every time traveller arrives in an exact duplicate of the universe at a certain moment of time, which then diverges from that point onwards. As soon as he leaves, that universe effectively disappears. The displacement in time is strictly temporary.

Due to conservation of matter, though, absolutely everything that goes must return to it's original universe.

It's impossible to leave anything behind, and impossible to bring anything extra back. All displaced matter will be teleported back to the capsule once the duration of the temporal displacement ends.

The only thing that can change is the structure that the matter is arranged in.

Unfortunately, this teleportation must happen on a particle by particle basis. This doesn't work well with humans.

Let's say a time traveller eats and digests an apple while in the past. When he leaves the past, all matter that used to be that apple - including lumps of his cells and blood - will be left behind in the past. Therefore, the traveller will return with chunks of his intestines missing.

The same applies if the traveller goes to the toilet in the past - even though the waste isn't part of his body anymore, it will all be coming back with him. It gets messy.

Likewise for any oxygen in his lungs from the past, and for any skinflakes he sheds, or even any cells he picks up. Anything his body takes from the environment is gone.

After a set duration, everything will return to the capsule, and nothing else.

They want to get the most use out of this temporal displacement machine. So, with that in mind, what is the maximum duration that a time traveller could linger in the past, without suffering a messy death on his return?

Really, it depends on how much human bodies take in from their environment, and how unhealthy it would be if the matter making up their cells was suddenly 'sorted'.

Theoretically, the travellers could bring back whatever environmental suit, oxygen tanks, food supplies with them that are needed, but it costs power to run the machine. They only want to transport the very minimum amount of mass.

Edit:
For clarification; the universe that the traveller arrives in is not a 'real' universe. That universe (and timeline) effectively exists for only so long as the traveller is there. Once the displacement ends, that universe disappears and all that's left behind is the capsule, and the original matter. That original matter is the only thing that can return to our world.

As such, it means that (from the travellers point of view) the universe he arrives in is completely disposable to him. Nothing that happens there will have any effect on his universe. All he cares about is coming back alive to his own universe.

Effectively, the travellers can use the displacement to research the past and bring back information, but nothing else.

Since the question is now clarified to indicate that no actual other universe is involved, I'm revamping my answer thus:

Basically what this whole proposition boils down to is a kind of futuristic Virtual Reality experience, much like a holodeck from Star Trek. A "universe" is created into which a person may "travel" and he may interact with persons and objects created within that "universe". Whatever he takes within him has substantial existence (because its matter was created from Before within an actual universe): his own body; any tools or food he brings along; the "vessel" he uses to enter the VR universe. All the matter subcreated within the VR universe, having no substantial existence of its own, must dissipate when the user leaves. Since it is not real matter --- it may be directed energy that gives the appearance of matter --- it can not leave the VR universe. If he eats an apple there, he'll taste sweetness, experience the sensation of chweing and swallowing and his stomach will fell slightly distended. This is because the VR generator is "projecting directed energy" to give the appearance of matter. Once he leaves, the sweetness will disappear and the stomach will feel strangely empty again.

There being no actual, independent, universe external to the Traveller's own, I would say: there are no limitations because, in actuality, nothing that is brought inside the VR is "left behind"; and because everything within the VR is unreal, nothing can be taken away.

The ledger remains balanced because there's nothing on the other side of the equation to balance. There is no danger to his body because he has actually travelled nowhere and has interacted with nothing and has talked with noone.

Original answer for context:

I would say that, unless the universe the Traveller is going to is itself not only sentient but also intimately aware of every subatomic particle that comprises its corporeal existence, I believe you are placing yourself under an impossible yet also needless constraint.

My solution would simply be that, after wondering why so many early Travellers exited their machines dead and with random bits of fecal matter spattered all over the vessel interior, they would hit on the idea of cross-dimensional conservation of matter.

It would then be a relatively simple matter of installing a quantum scale that keeps track of all mass within the boundary of the spatio-temporal field down to weight of tiniest utron.

Whenever the Traveller is in transit, the vessel's computers take note of every atom that has come into the S-T field and stores that in a database. Once the Traveller does his business in the other universe and gets back into the vessel, the same computer runs a new scan, determines how many differences there are by comparing inbound and outbound databases. If the Traveller is "too light", a device will scoop up some matter from the environment equivalent to the inbound mass; if "too heavy", the vessel will sacrifice an amount of mass equivalent.

Both ledgers in balance, I think your Traveller should be okay and he'll return home with most of his original matter, but also with some foreign matter.

I don't see how a universe can "know" whether an oxygen molecule was made within itself or another universe. If it's a hard requirement that all original matter must leave with the Traveller, then I think you're going to run into insurmountable problems. Once he breathes the air of the other universe, his own universe's molecules get blown away in the wind. Once he decides to relieve himself, or sheds some dandruff or experiences a liaison with a local, well, there goes some more original matter that will be unrecoverable.

Such a hard requirement I think would cause too much damage not only to the Traveller but also to everything and everyone he comes in contact with.

However, if the requirement is hard and fast, then this might be a workable solution:

You say that S-T travel is kind of like an elastic band: the vessel uses energy to extend itself and its occupant into another S-T continuum (a different universe), and is then drawn back again after a set amount of time.

I'll posit an Elastic Field Effect. In order to conserve matter, prevent contamination (and stinky sequellae) and keep both sides of the equation balanced, I suggest that the same elastic band effect that allows the vessel to travel to the other universe also surrounds and conserves the original matter of the Traveller.

Basically, he will travel and interact with the other universe whilst operating within an elastic bubble. In this scenario, the Traveller never actually touches anything, never ingests anything, never leaves anything behind, never takes anything with him.

The elastic bubble field surrounds his body (and his excreta), allowing no contact with the other universe's matter. To the people and objects he interacts with, he might appear slightly abnormal: he might be kind of transparent; his voice might sound like it's coming from a great distance, all tinny and weak; it will appear that objects kind of "float" in his presence and their movements don't quite jive with his. He might appear like a ghost or an extradimensional being...

...oh. Wait. Right!

This is because, in effect, the Traveller and his vessel never actually left their home universe. The technology simply employs a device whereby a tiny depression is made along the boundary of the Void, which is then stretched until, pushing into a parallel elastic field within the other universe, it allows a Traveller to seemingly travel from one universe to another while never actually leaving his own.

This effect can be demonstrated by wearing latex exam gloves and pressing the finger of one hand into the stretchy material of the other glove. You'll be able to "feel" your finger pressing on your hand; the elastic field surrounding your finger will push aside the parallel field surrounding your hand. Two universes interact without ever colliding. No matter is introduced. No matter is left behind.

Ledgers balanced, the Traveller and his vessel quietly slip away as the energy inflating the elastic field dissipates. And best of all, the Traveller doesn't have to clean randomly applied poop from the interior of the vessel!

1. I will wade on on "virtual" vs "actual". We will say it is an actual universe. For all practical purposes it ceases to exist once the traveler leaves, because it is impossible to get back. That timeline is a parallel timeline of which there exist an infinite number. One might differ from the next because of a different splash of the waves in the Ordovician ocean. They are infinite, and on visiting a timeline that is substantively identical to the travelers own, there are an infinite number of which one is randomly chosen. There is an infinitesimal chance of revisiting that same one.

Of note: these other timelines will have travelers which are visiting yet other timelines. There is an infinitesimal chance of encountering one, or more. There is an infinitesimal chance of one visiting the timeline of the story.

2. /As such, it means that (from the travellers point of view) the universe he arrives in is completely disposable to him. Nothing that happens there will have any effect on his universe. All he cares about is coming back alive to his own universe/

The solution: he has no hope of coming back alive to his own universe. It will be a one way trip. Returning travelers die in various ways and speeds according to needs of the story. In return for their efforts their families collect a substantial sum.

Alternatively, the traveler's experience in the past could be the payment. The traveler fights his way into the headquarters of the Third Reich and murders Hitler with a plasma cannon. The traveler prevents the 911 disaster. The traveler parties hard with the Emperor Augustus. The traveler prevents his alternate self from making a terrible mistake. The traveler reunites with his lost loved ones. Then when they return they die.

There is so much grist for a narrative mill here that this could be a series on Syfy. It is a like a cross between Sliders and Looper but with one time temporary characters (I am reminded of Liz Taylor's role on Star Trek. What, you never saw that episode? Callow youth!). There would be action specific to the episode and also longer arc narrative threads. Oh yes.

• The traveler returns and fails to die, but has been changed in some other way.
  
  
  
  
  • The traveler figures out a way not to return, staying in the alternate timeline.
  
  
  
  


• The traveler does not wind up in a timeline nearly identical to her own, but someplace very different.


• A traveler visits from a different timeline and is captured, allowing the persons capturing him knowledge of a possible future (and temporary access to artifacts from that future).