OK, so why do they say time will turn back if we travel faster than the speed of light?
It works this way.
Lets say we travel to A Centauri. 4.67 Light Years, and we travel at the speed of light.
There is this huge clock on Earth and we can see the time, date and years.
As we travel away from Earth, we will see the clock stands still, because we are travelling with the light as we departed from Earth.
However, If we travel at 2X C, the rocket will gain on the light that was travelling at C from the Earth, and it will seems as if this clock is turning in reverse,...
Using the formulas of Lorentz, it seems as if Time dilated!
No, it did not, all that happened is that the light we observed in our reference frame, was light we gained on as we traveled and gained on.
You need to do something else in order for time travel to show up. Let's take a more extreme example. Suppose our FTL drive travels along a world line's line "Now" — that is, if we have a bunch of clocks spread all over the universe that are both synchronized with our home clock and comoving with our own clock, the FTL drive will arrive at a new clock that reads exactly the same time as the clock it left. But if this FTL engine obeys relativity, then it will be able to arrive at that clock at that time ONLY if that clock was initially comoving with the ship carrying the drive.
We now set our space ship to travel to Alpha Centauri using the FTL drive. Because our clocks are synchronized according to us (a very important qualifier), the FTL drive will arrive at Alpha Centauri when it left. Everyone will agree that when the space ship leaves at Jan 1, 2018 12:00:00.0 AM according to the Earth clock, it will arive on Jan 1, 2018 12:00:00.0 AM according to the clock we arranged to put on Alpha Centauri.
So far so good, but what if the Vogons are cruising along at some appreciable v ≤ c (assuming they can) directly away from Earth. They will see that the FTL ship departs from Earth on Jan 1, 2018 12:00:00.0 AM according to Earth's clock, and arrive at Alpha Centauri on Jan 1, 2018 12:00:00.0 AM according to our Alpha Centauri clock,
BUT the Vogons think that our clocks are out of synch, and any duration deduced from them over any notable distance will need adjustment. They have their
own set of clocks scattered throughout the universe, synchronized and comoving with them, and use
them to decide how much time has passed between the departure of the FTL rocket from Earth and its arrival at Alpha Centauri.
Suppose that the Vogons are traveling at ~1c, just to make things neat and tidy. Then if they pass Alpha Centauri on Jan 1, 2018 12:00:00.0 AM according to the ship's onboard clocks, then because of time dialation, they must have passed the Earth on Jan 1, 2018 12:00:00.0 AM according to the ship's onboard clocks, too. But they know that Alpha Centauri is 4.67 light years away, so it took them actually ~4.67 years to travel that distance, so they had seen the Earth's clock read sometime in May 2013 when they passed it. So Jan 2018 on their clock translates to May 2013 in Earth time, and thus Alpha Centauri time, and the Alpha Centauri clock placed by earth is BADLY out of synch with Earth time. (They are valid in thinking this, because length contraction —which occurs hand-in-hand with time dialation— places Alpha Centauri much much closer to the Earth, according to the Vogons.)
Nothing unusual has happened so far, because according to the Vogons, the FTL ship has left Earth after they did, and arrived at Alpha Centauri just as they do. But let's suppose that the Vogons immediately take on the FTL drive (thus making it comoving with their own clocks) and send it back. Because the FTL drive obeys relativity, it travels only to a place if a comoving and synchronized clock in the area reads the same time as the place it started. The clocks the FTL ship is now comoving with are the Vogon's clocks, so it travels to places where a Vogon clock reads Jan 2018, and the clock buzzing past Earth at the time reading Jan 2018 when Earth's own clock is reading May 2013.
And
there is the time travel. The FTL ship left the Earth in Jan 2018 (Earth time), but returned to the earth May 2013 (Earth time).
Of course, this is only possible if FTL works as advertized. We don't see real FTL travel or communications in our universe, so causality is preserved.
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How about building the clocks on the Earth, load it on a rocket, blast all 3 into space, stop halfway, send the clocks with the same speed to the Moon and Earth with smaller rockets that travel at snailpace to both positions.
Why all the fuss to try and show that speed will have an effect on a clock?
We don't need any
fuss to show that. We can
see it on atomic clocks on commercial airliners, but only to the tune of 50 nanoseconds or so over many flight hours. It is a subtle effect, which is why we don't see much of it in our ordinary lives, but it's there and is detectable clear as day with sensitive experiments.
Also, very sensitive technologies have to account for it, too. The GPS satellites (and similar geopositioning systems) have to take into account both special and general relativity when keeping time. Otherwise, time on earth and on the satellites would get badly out of synch and introduce horrible errors into positional accuracy, many tens of meters. When you have to take it into account with a real technology, it's a thing.
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I think you missed out when I wrote, lets do this experiment again, but from the time-frame of the Moon.
I want us to be clear about my claim.
If the observer on the Moon looks at the Earth at 12H00, when the rocket also blasts off from the Earth at 12H00, the observer on the Moon will see the clock on the Earth and the clock on the Rocket are both one second before Noon.
"Looking" requires light, which travels at the speed of light. Therefore, the very instant (according to the Earth and the Moon — that qualifier is very important) that the rocket leaves the Earth, the person looking from the moon sees the rocket on the pad at T-minus 1 second, and the Earth's clock reads 11:59:59, because the light of the Earth clock reading 12:00:00 and the rocket launching
hasn't reached them yet. He doesn't
see the launch at 12:00:00 Earth time until a second later Earth time.
If light takes a substantial amount of time to travel from place to place, you kinda have to take that into account.If Moon time is synched with Earth time, then he will
see the launch at 12:00:01 Moon time, but
observe the launch at 12:00:00 Moon time because he can do math and he knows the clocks are synchronized.
The clock on the Moon will move forward for one second, and the rocket will arrive at the same instance.
Yes, it takes one second for the rocket to travel from Earth to the Moon by Earth's observations, and one second for the rocket to travel from the Earth to the Moon by the Moon's observations. They are both comoving with each other, and will measure time the same way. It's only with objects moving
relative to each other that time dialation shows up. The Earth and Moon are not moving relative to each other in our gedanken, so no dialation there.
The clock on the Earth will appear to be noon, but both the Rocket and Moon clock will show one second past Noon.
The rocket's clock is moving relative to both the earth and the moon. To say that the rocket's clock shows one second past noon is begging the question. It's what you have set out to prove; you can't take it as a given.
Therefore, the Earth clock seems to be late with 1 second to the one on the moon,
Well, yeah, but they
also know that the Earth clock is exactly one second ahead of what it seems from the Moon, because everyone in your model knows physics.
Again, if light takes a substantial amount of time to travel from place to place, you kinda have to take that into account.and the clock on the Rocket seemed to have moved forward 2 seconds on its journey of one second.
No.
That's the exact bone of contention. The guys on the moon can see
perfectly well that the rocket launches when the clock on Earth (which is near the rocket) reads 12 noon. They
see this image at 12:00:01 moon time, but they know that the light they see left Earth one second earlier.
Once again, if light takes a substantial amount of time to travel from place to place, you kinda have to take that into account. Indeed, this image arrives at the moon and is seen at almost exactly the same time the rocket itself arrives (because they're traveling at almost the same speed, remember?). The moon sees that the rocket launched at exactly 12 noon, as measured by the local Earth clock (which is in synch with their own) and by the shipboard clock (which was
at that moment in synch with their own), and arrives at one second past noon at the Moon.
The rocket will observe that they launch at 12 noon on Earth, and arrive at one second past noon on the Moon, according to Earth-Moon synchronized clocks. Their own shipboard clock remains at about 12 noon during the trip, however, because to the ship and everyone on it, the trip took less than a second and started at 12 noon. They deduce from this that the moon all of a sudden became much much closer than one light second away (because they were traveling near the speed of light for much much less than a second), yet the moon registered about one second for them to make the trip — ergo, the moon's clock slowed down, and since the moon clock stared and remains in synch with the Earth clock, the Earth clock must have slowed down, too.
Under no circumstances will
anyone observe that the rocket's clock advances by two seconds. Earth doesn't observe it. The moon doesn't observe it. The rocket doesn't observe it.
Now, the moon suddenly becoming much closer is unphysical, but then, instantaneous acceleration to speed is equally unphysical. I've already given you that gimme, so you can't ding me for hand-in-hand gimme of the apparent teleportation of the moon.
