The transporter has a failsafe to replace missing atoms or molecules that didn't make the trip by pulling from reserves. It got a lock, attempted transport, then got an error saying 7x10^27 atoms didn't make it and replaced them, leaving the original Riker on the planet and constructing an entirely new Riker on the Potemkin's transporter pad. Thomas is the original, Will is the clone.

It took the mass from the replicator. Fewer tacos were served that day.

E=mc^2

Energy and mass are just different measures of the same thing. The transporters job is to take mass and turn it into something that it can more easily move around (a wave? Particle stream?) and back. So as long as the transporter is connected to the ship's energy supply it should theoretically be able to use that energy (instead of the energy from your body) to reassemble any pattern it wants without breaking the law of conservation of mass.

Riker is 6'4 let's say 200lbs, which is 8,153,369 terajoules.

DATA: Imagination is not necessary. The scale is readily quantifiable. We are presently generating twelve point seven five billion gigawatts per (an alarm goes off)

One watt is one Joule per second, there is some debate out there about the "per" part of the quote since watts already implies per second, but we probably assume the ship is capable of generating 12,750,000 terawatts, or 12,750,000 terajoules per second.

8,153,369/12,750,000 gets us about 0.64 seconds of the ships output to create our duplicate Riker.

However the quote above was when the ship was basically idling, (not actually at warp) so the actual output of the ship is likely exponentially larger.

Basically they have so much power available, that they can just rearrange it into whatever mass they want.

It did conserve his mass. Twice. At the same time.

And IIRC, some weird shit in the atmosphere during transport was the source of any extra energy needed to have created the new matter.

i always figured that the transporter was ultimately just a scanner and the beaming in process is the same as being replicated, but the replication has to be done while the scanner is running because there's simply too much data to actually store long-term unless you're willing to use the whole ship/station/whatever as a buffer, like that one DS9 episode. and i guess the scan requires a level of detail it can only get from the source destructively which is why it isn't a clone unless the beam gets reflected? or something? this is one of those things that makes less sense the more you try and figure it, and suddenly a literal matter stream somehow seems more feasible

maybe ships have Einstein Compensators or some shit allowing 1:1 matter energy conversion but it only works on transporters so you can't make a perpetual energy machine? i need to lie down

Pfft. Uh, hello reversed polarity?!

The real question is why didn't she recreate the accident to double Tuvix before splitting one of them back into Tuvok and Neelix?

It's the same way replicator technology works. They're reassembling matter that's been stored for that purpose. Two Rikers just means less matter is left in the storage buffer.

Can you imagine how much energy is stored in a transporter buffer?

I mean, they're flying around in a big engine that bends the fabric of space, so maybe it's not such a big deal a few hundred years in the future. I guess it's like comparing a furnace and bellows with a nuclear reactor.

Conservation of mass-energy only really applies if you rely on the old 21st century idea that the universe's fundamentals consist of time, space, matter, and energy.

Anyone who's had a secondary school education knows that that's an outmoded view of the universe. They didn't realise that subspace existed, in much the same way that they did not realise that surviving records show that 21st century humans did not know the Earth was round until Cochrane took to orbit in the late 2000s, and proved it.

The same way you killed Tuvix.

Oh boy now I'm vaklempt

Ahem: a second transporter beam locked on to his signal. Since the transporter uses that beam to convert physical matter into an energy pattern there were in essence 2 matter converted energy patterns. The energy came from the transporter.

Wasn’t there an energy fluctuation, so more energy could be entered into the system.

But also, Banach Tarski. On the subatomic level, maybe these types of shenanigans could manifest.

Edit: it turns out that copying a person requires a lot of energy, more than a heavy storm would have over years.

They cached 1 oz of 💩 from each of the previous 3000 transports.

Because of Quantum