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In the world that I'm building, life on Earth has gotten pretty unbearable for some. My first thoughts are over-population, pollution, war, etc. A company/government comes along and tells you and your family that they have the ability to resettle you, not to a new location, but to a fresh "new" Earth. They would do this by sending you back in time to an alternative Earth (no cause and effect relationship to cause paradoxes) where the travel was geographically fixed to a specific time.

The issue that most people would have, in my opinion, is that it is a one-way trip, with zero feedback to indicate if people arrived successfully or what was waiting for them. The company claims they were instructed by a message from a long lost civilization who accomplished something similar, but met an unfortunate fate early on (example: Atlantis).

Kind of reminds me of the television show, Terra Nova, but I'm putting a different kind of twist to the time travel portion.

How bad would things have to be for people to volunteer to be part of this program, given that they have no concrete evidence of their safety?

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    $\begingroup$ It indeed reads like the plot of Terra Nova. But people are willing to risk an awful lot for their children's future. $\endgroup$
    – Mormacil
    Apr 21, 2017 at 18:14
  • $\begingroup$ This is a good point. In my system, the energy required to send something back is directly related to the amount of mass, so children would be more likely candidates to repopulate a new world (assuming there was too many people wanting to go) and limited energy resources. $\endgroup$
    – curt1893
    Apr 21, 2017 at 18:29
  • $\begingroup$ In other words, how do you get people to drink the Kool-Aid? $\endgroup$
    – Hot Licks
    Apr 21, 2017 at 22:34
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    $\begingroup$ If the company is owned by Elon Musk, you will have people to sign right now... $\endgroup$
    – Taladris
    Apr 22, 2017 at 0:27
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    $\begingroup$ "Zero feedback" makes it a hard sell - how do you know it even works? Even expensive heavily rationed telegram messages would make it much less terrifying. $\endgroup$
    – pjc50
    Apr 22, 2017 at 9:20

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That's a hard question to answer because there are people who would go now and there are people who would never go.

Many conspiracy theorists would say that it is [some organization]'s attempt to get people to volunteer for euthanasia. The rest of the conspiracy theorists would say that the first set are backed by [some other organization] and are trying to keep people from the best thing since sliced bread. The majority of the people will believe whatever the news tells them to believe.

People who would go today:

  • Adventurers who would go just for the thrill (Mars One has already been mentioned)
  • There are those who just don't like being around people. Look at the off the grid folks in the US northwest (Montana, Wyoming, etc.) a bunch of them would go now just to get farther away from the crowds and the government.
  • Then you have those on the run (from the mob, police, debt collectors, ISIS, drug cartels, etc.). Some fraction of them would go because the unknown isn't as bad in their minds as the known.
  • Some people have starving families, if you tell them that they can have a plot of land to feed their family, many would go; especially from third world countries.

Then there is a spectrum. The worse things get the more people will go. What percentage of the population do you want to get rid of?

Finally, there are those who would never go. The devil you know isn't as bad as the devil you don't know.

A better question is, if they can't send back materials, who would bother paying for building and running this dimensional gate? England foisted off a lot of their riffraff on the US and Australia but they also got goods sent back and made a lot of money from it.

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Any situation where local perspective is negative will trigger emigration, even if the destination is a one-way ticket and the outlook is highly uncertain.

Overpopulation or famine in the source country will in itself already be sufficient.

Pull

Historically the US frontier was a place where women died in childbirth and people were lost in winter when the weather was more harsh than they were used to.

The body count was high, expectations however were sky high and provided a very strong motivation.

Census  Population
1790        3,918,000
1800        5,236,000
1810        7,036,000
1820      10,086,000
1830      12,785,000
1840      17,018,000
1850      23,054,000

Push

For example the Irish Great Famine triggered mass emigration and millions of people left the country, many towards the new world. The emigrants fled harsh conditions, died in numbers along the way and had trouble settling in the new country. This did not seem to stem the flow any bit, as the population fall in Ireland was as much as 50% down from some 8 million in 1841. enter image description here

References:
https://en.wikipedia.org/wiki/Demographic_history_of_the_United_States
https://en.wikipedia.org/wiki/American_frontier
https://en.wikipedia.org/wiki/Great_Famine_(Ireland)

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The answer really depends on how convincing the company is in their sales pitch. With complete lack of communication from the other side, you are putting 100% faith in the company's model of what they think is happening.

If this company has a history of taking knowledge from the Ancients and turning them into testable working products, the confidence in the company's position could be very high. On the other hand, if this is the first attempt at unlocking ancient technology, and the product looks like an oversized meat grinder or wood chipper, confidence will be very low. If the company can demonstrate scientific theories to show that it should work, that raises confidence. If it looks like you'd have to break a few popular scientific theories in order to get it to work, that lowers confidence.

There will always be takers. You may have to work hard to find them, but they're always there. If you go to a war torn country which is so impoverished that the locals have worked their way down the food chain from grains to grasses to mud cookies and fight over access to the best mud, you'll find people who are willing to take a risk. (And yes, mud cookies are actually a thing. In our world, there are populaces which are so far beyond starving that they indeed eat mud for its nutritional value)

There will also likely be religious cults that pop up using your device as proof of their life everafter. Those groups would be quite easy to toss into the woodchipper convince to undertake a less than certain fate, because while you would be uncertain they actually would be certain about where they were going.

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  • $\begingroup$ The wood chipper reminds me of Burroughs' Gods of Mars: the Therns, a white-skinned race of self-proclaimed gods, have for eons deceived the Barsoomians elsewhere by disseminating that the pilgrimage to the Valley Dor is a journey to paradise. Most arrivals are killed by the beasts of Valley, and the survivors enslaved or eaten by Therns. $\endgroup$
    – Willk
    Apr 22, 2017 at 3:22
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Remember Nigerian princes and Mars One have a working business model. Especially with increased population, unless you mean to be sending very large numbers of people you should be able to count on suckers.

Adventure and independence are powerful draws, during the settling of the American West people came thousands of miles to die in the desert on the hope of free land. Certainly they had some reports of previous people, but they included tales of gruesome murders, disasters and atrocities.

If you insist on rational trust; sharing a name with a popular organ transplant or dog food company may reduce the numbers of volunteers. Investing in training and resources for volunteers might aid their credibility.

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Lots of people will go, right now

enter image description here

Here are about 13.5 million volunteers. History has never been short of refugees, and I doubt the future will be, either.

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