Superluminal Time Travel + Time Warp Challenge Answer | Space Time

Superluminal Time Travel + Time Warp Challenge Answer | Space Time


Traveling faster than light
and traveling backwards in time are the same thing. Today I’m going to
prove that to you. Faster-than-light travel
is, understandably, a staple of science fiction. The reality of the vast
scale of our universe, even with our galaxy, is
inconvenient for tales of star-hopping adventure
or warring galactic empires. Enter the warp drive,
and hyperspace, and star gates, and the
infinite improbability drive. Plenty of ways to make traveling
across impossible distances as challenging as a
weekend road trip. And sci-fi makes instantaneous
communication a breeze. We have ansibles,
sophons, subspace relays, and tachyonic antitelephones. Actually, that last one
is a thought experiment that demonstrates that if you
communicate using tachyons, hypothetical faster-than-light
or superluminal particles, it’s possible to receive
and reply to a message before the message is sent. By choosing the right path
and the right reference frame, any superluminal motion can
lead to information or objects returning to their origin
before they depart. Today I want to show you
how to navigate such a path. To do that, we’re
going to need a map. We’ll do this in flat space,
so we need a flat or Minkowski spacetime diagram. We’re going to add
spacetime interval contours. We’ve spent some time talking
about how these contours define the flow of causality. If you aren’t familiar,
you should probably watch that episode first. In addition, today’s
episode is going to add to the recent time
warp challenge question. So spoiler alert. In the olden days, before
Albert showed us the way, time was thought
of as universal. It was assumed that the entire
universe exists simultaneously in a state of now, and that
all points move forward in time at a constant rate
for all observers, governed by one global clock. In the olden days, the same time
axis of a space time diagram would apply to
everyone, but no longer. Einstein showed us that
there is no universal clock. Instead, every
space time traveler carries their own clock. The tick rate of your clock and
your perception of simultaneity depends on your velocity. There’s no absolute
notion of velocity, so everyone can be
considered motionless from their perspective. Everyone draws their space
time diagram time axis parallel to their direction of
motion, because that’s their experience of stillness. The tick marks on that time
axis also depend on velocity and represent the speed of
everyone’s personal clock in their proper time. And everyone also has
a different space axis, representing chains
of simultaneous events according to their perspective. Those axes reflect symmetrically
around this 45 degree path, representing the
unvarying speed of light. Connect the ticks
of all possible time axes, and you get these
nested hyperbolae. These are contours of
constant spacetime interval. A straight line
journey to any location on one of these
contours seems to take the same amount of proper
time for every traveler. The spacetime interval is
special because every traveler will agree on which contours
a set of different events lie, even if they don’t agree
on the temporal ordering of those events. If we write the spacetime
interval for flat space with a negative sign in
front of the time part, then changes in
your space interval have to be negative,
as long as you travel at less than
the speed of light. So greater than 45
degrees on the diagram. Each contour is smaller
than the one before, and so forward
temporal evolution means rolling down
the causality hill. On the other hand,
superluminal paths, paths at less than
45 degrees, mean revisiting previous
contours, traveling uphill. That uphill journey is
equivalent to time travel. To prove it, let’s
think about the scenario that I proposed in the
recent challenge question. It went something like this. You’re in a race to claim a
newly discovered exoplanet 100 light years away. Your competitor immediately
launches a 50% lightspeed ship, the anti-matter
powered Annihilator. You decide to wait, taking
a century developing an Alcubierre warp drive. Your ship, the
Paradox, can travel at twice the speed of light. Let’s see what that looks
like on the spacetime diagram. We’ll plot the world
lines of these ships as recorded by someone
waiting back on Earth. Earth doesn’t move from
its own perspective. It just hangs out at x equals
0 and rolls upward in time. The Annihilator races off
towards the exoplanet, 100 light years this way. At 50% lightspeed,
the Annihilator would take 200 years to
reach its destination, from Earth’s perspective. Meanwhile, your own world
line remains on Earth as you build the paradox. However, when you
launch, you travel at twice the speed of light. And so you’ve
reached the exoplanet in 50 years from launch date,
also from Earth’s perspective. You overtake the Annihilator
at around the 67 light year mark and finish the race 150
years after the race began. Congrats, you win. I just hope your rejuvenation
tank is still working. But winning was
never the question. I’m really curious about what
the crew of the Annihilator sees at that moment
you pass them. Do they perceive you
as traveling in time? And now that you’ve mastered
faster-than-light travel, can you pilot the
Paradox back to a point before the race even started? To see what the
Annihilator sees, let’s transform the space time
diagram to their perspective. In fact, we need to do a
Lorentz transformation. Their time axis is
their own world line, and their space axis is
symmetrically reflected around the path of light. Now, add hyperbolic
spacetime into our contours. These are the
spacetime intervals as calculated from the zero
point in space and time, the beginning of the race. Because the
spacetime interval is invariant to Lorentz
transformations, when we shift to the velocity
frame of the Annihilator, we just make sure events
stay on the contours that they started on. The Annihilator perceives
itself as stationary and sees Earth racing away
in the opposite direction at half light speed, while its
destination races towards it at the same speed. We can figure out the
paradox world line because we know which
spacetime interval contours it’s on when it
departs from Earth and arrives at its destination. The Paradox still appears
to be traveling forward in time with respect
to the Annihilator, even though it’s traveling
faster than light. But what does this look like to
the captain of the Annihilator? Well, you just trace the photon
paths, assuming for a moment that an FTL ship doesn’t produce
infinitely red or blue shifted photons. The Paradox outraces
its own photons as it catches up
to the Annihilator, and then it continues to emit
light backwards behind it after it passes. So the Annihilator sees
a series of photons coming from both directions
that arrive simultaneously. The Paradox appears
to materialize out of nowhere and then
proceeds to split in two. One Paradox seems
to race onwards towards its destination,
while the other travels in reverse back towards Earth. Now, that looks a
bit like time travel, but a physicist
on the Annihilator would still infer that the
Paradox is moving forward in time, upwards according
to the Annihilator’s own time axis. However, there are perspectives
where time travel seems real. Let’s look at the perspective
of a different space time traveler, one traveling at
very near the speed of light. When we transform the
diagram to their perspective, we see that the
Paradox really does appear to travel
backwards in time according to this new time axis. But this is just
perspective, right? Well, no, not if we can find
a way to bring the Paradox back to a point in space
before it was built. To do that, we first
need to outrace photons that were admitted at
the space time point that we want to perceive. In this case, it’s
the start of the race. Let’s return to the reference
frame of the Earth to do this. We can keep flying the Paradox
until we cross this ominous 45 degree boundary. Let’s fill in the
space time diagram with all four quadrants. These ones represent the regions
inaccessible for sublight speed travelers starting
at the origin. Now we transform back to the
near lightspeed reference frame. In that frame, the
Paradox has moved into a region that appears to be
prior to the start of the race. If we assume that this
trajectory is valid, then there’s no limit to how
far into the past we can travel. If we travel far enough,
then when we finally turn the Paradox around, it’s
twice lightspeed movement will take us back to the
beginning of the race, long before the
Paradox was ever built. This seems like a trick,
and it sort of is. We constructed this time
traveling path using two different reference frames. In this case, Earth’s and
then a near-lightspeed frame. Normally, that would be fine,
because spacetime events marking the different stages
of a sub-lightspeed journey transform consistently
between these frames. However, when we introduce
faster-than-light travel, things get messed up. Superluminal paths
aren’t real worldlines Real worldlines don’t
point backwards in time under Lorentz transformations. While we can define a chain of
events that looks like an FTL journey, these aren’t paths
that real objects can take, and that includes us. Remember, we are
temporal creatures. Our experience of the
universe is a thing that emerges from the forward
causal evolution of the matter that we’re composed of. Reverse the flow of time, and
you reverse the flow of you. Even our fantasies of time
travel are just another pattern emerging from our
one-way trajectory through the temporal
part of spacetime. Thanks to everyone
who submitted answers to the timewarp challenge. If you see your name
below, we randomly selected your correct answer
to win a spacetime t-shirt. Shoot us an email at
[email protected] with your mailing address,
US t-shirt size– small, medium,
large, et cetera– and let us know which
of these T’s you’d like. Also, it’s that
time of year again, time for the annual PBS
Digital Studios survey. This is not a graded
quiz, nor will it tell you which Disney
princess you are, but it will really help both
Spacetime and PBS figure out what you guys are into and
what you want for the future. Click on the link
in the description to fill out the survey. It should only take
about 10 minutes, and we’ll be giving away PBS
shirts to 25 randomly selected participants.

100 thoughts on “Superluminal Time Travel + Time Warp Challenge Answer | Space Time

  1. I think I'm finally understanding how that tortoise won that race against the hare. #TemporalTestudinidaeDrive

  2. Ignoring the energy and length of time this would take; what if you were going twice the speed of light, then shifted your trajectory to be in synch with the outward expanding area of space time, then created a gravitational/ anti-gravitational force great enough to bend space time, somewhere out front of your ship, on the side facing earth, and then proceed to spiral in? Also, just for fun, what if you went the opposite direction, and spiraled out?

  3. Nobody can travel back in time, except may be the smallest particles.
    If you could go back and meet your own self as a baby, you’ll be breaking conservation energy law. You are made up of elements which were a part of something in the past. Each and every particle in you was a part of the universe. So going back in time is like having extra matter suddenly from nowhere or more precisely double amount of the particles you made up of, which is not possible. Energy cannot be created, only change from one form to another.
    So technically, if there was a way to go back in time, then you will arrive when you were born as a baby and be that baby just as it happened. And you will repeat your life and never know that you’ve been an adult. Nobody can change the past bcz we are in the closed system and every action has an effect on universe. To go back in time you have to rearrange entire universe back to the time you want to go, every particle. And even after doing that it won’t be useful as you will also be reversed ( along with you thoughts and memories)

  4. I'm afraid so many comic books have ruined your sense of reality. Really. Superluminal? Using the multidimensions in the arse of a wormhole?

  5. I have been thinking about this warp idea for a while. There are many papers about this but they all say the same thing I said in 1983 in seventh grade defending myself as a star trek fan from bullies on a school bus heading to school. Listen carefully because I accidentally got it right before the first real paper in the late '90s. Before that was a paper from the '60s which was used as the foundation for warp in the television show.

    I am going to use the term 'warp field' without defining what it means or how it is formed. Rather I am going to talk a out what it accomplishes.

    The warp field must squish space before it and stretch space behind it. This must be the case to balance time dilation. The ship need only move in the flat-ish region where the ship is and the two spatial distortions act like walking on a moving sidewalk.

    Now to go deeper than a 7th grader. You need to really take time to imagine this geometry. You are in a spherical field with an axis that forms a plane down the direction of motion. The squished space is a crescent along the inside leading edge of the plane and the stretched space is a crescent in the aft edge. Normal space is a circle in the middle where the port and starboard points are stretched to the edge of the field. This has a neccessary effect on the relative position of cosmological event horizon.

    It does not change along the axis that goes port to starboard because that is all normal space. Before you, you would see more stars than usual, come at you like in the show and they will be deeply blue shifted because the cosmological event horizon is extending further before the ship due to the squished space. The stars behind you will be fewer and deeply redshifted, not moving, and far far fewer because the stretched space is shrinking the cosmological horizon closer to the ship.

    Now, before we go further. Think about this geometry and one more thing. There will be a great deal more hawking radiation from the aft cosmological horizon because of how and why it is being drawn towards the ship. Also consider that this is only true for the observers in the ship itself. So maybe also consider how this ship will appear to other observers from different aspects.

    In this way, I have turned the 'warp ship' into an object as interesting as black holes. But if this ever becomes reality, I bet we will finally understand the real limits of causality. We may be able to go as if faster than light to some destination only to discover it really is impossible to go in any direction that would violate causality.

  6. i was never good at math so to be honest , i was trying to understand the whole "thing" but you lost me as soon as the two spacecrafts came into the play .

  7. I really didn't get how traveling faster than light is the same thing as traveling back in time. It seems that changing the reference frame do a trick but the Paradox itself doesn't travel back in time.

  8. No matter how i look at it, it feels overcomplicated and i learned that overcomplicated things are usually false.

  9. So…if superluminal paths aren't real world lines, what are they? Will ANY superluminal travel result in time travel to the past? I thought the warp bubble created by Alcubierre's and White's model would protect local time for the ship, or does this exploration not take that into account?

  10. when you see the stars, you see them in the past. the time it took light to reach your eyes. it is the same thing here. The annihilator sees the paradox in the past. the time it took light from the paradox to reach annihilator by the distance between the two. when the annihilator sees the paradox, it has already travelled the distance travelling twice the speed of light by the time it took light to reach the annihilator. real-time, they are not seeing each other travelling at their own speeds towards their own directions every second. real-time they are both traveling with every passing second. both ships experiences the same time. real-time they both exist on the same space at the same time.

  11. Use very fast forward velocity speeds to access dilated/left-over time,which is dimentional to reverse backward TimeTravel thru spacetime
    On earth taking ANY dead or alive object into an Earlier REAL-TIME! Work it out…

  12. Does that mean that a seemingly expanding universe could be actually collapsing on itself faster than light?

  13. Hmm… https://chrome.google.com/webstore/detail/threelly-ai-for-youtube/dfohlnjmjiipcppekkbhbabjbnikkibo

  14. What about traveling an entire light year per hour using teleportation? (it's slower than hyper-drive in 'Star Wars')

  15. I have always said that true space travel will be time travel through space, for example,…you want to go to Mars but the journey currently takes 6 month to 9 months depending on orbits but if you very precise calculations from the present on earth I you pick a point in space then calculate when Mars would have been there in the past then you bend space to that exact spacial point and to the casual observer you simply disappear but to Mars just seamed the be in front of you and earth is not, now when you want to go back you simply reverse your calculations and to the casual observer the will see you just appear where they saw you disappear, you would have effectively skipped over the say 18 month journey to arrive at the same time as you left,…. it's kinda a mind twist but you folded the space between earth and Mars and essentially walked through the door and back again with no aging or time dilation on earth by ftl

  16. Time travel only possible the way we do it now , dad by day, if time travel was possible we would be doing it since the beginning of time , as the future would of already existed!!!! U fucks!!!

  17. Make it too complicated, think of speed of sound. A jet takes off from California to NY. It travels at mach 6, 6 times the speed of sound. The pilot has to stay in contact with his home base in California. According to your theory no radio transmissions would be received until he started his return. So why if he is traveling that fast he is still receiving transmissions. Apply that simplicity to the speed of light, you just get there faster. Time doesn't change only the speed you got there. The faster you go decreases travel time.

  18. Even if the alcubierre drive were possible, how do we know the rate at which we can warp spacetime isn't bound by the speed of light? Is there some workaround for that?

  19. Why do all futuristic space crafts look aerodynamic? Theres no friction in space. So it could look like a cube, and still gorge same speed…..

  20. We could avoid all this minutes wasted by saying time is just a human invention a meassurement only. And look at how he said "Before Albert teached us the way" there were many other scientist before Albert with similiar equations but the guy was Jewish so, yep there you go, inserted on the history forever.

  21. I think you dont understand warping of space time .

    The hypothetical alcubiere warp drive which is also a theoretically possible one ,uses spacetime curvature to create a bubble field ,
    This bubble is then forced to expand and contract at front and back to travel through space time .

    It is possible ,and we are watching it every day on our own universr .
    The entire space time of universe is expanding faster than the speed of light .

    And warp drive is a much smaller process but still same in the action .

    The diagram is not sufficient to explain warpdrive since the ship paradox is temporarly disconnected from the whole of universe while it travels .

    It is still in the same timeline of universe .

  22. lmao what in the hell is this!!! I consider myself pretty technical and quick at understanding things and how they work. but this video is beyond even me lol.

  23. Unless that space ship is the size of the USA,I doubt we can ever build a sci fi like time machine faster than light. I mean,look at the Large Hadron Collider photos. Look at the wiring harnesses just for one. All to only break a few chips of atom. Not make a black hole or whatnot. Now try to scale the power.
    Yeah,I know what your thinking "future ways won't need a huge machine"..well,there is only so much future ways to advance and time machine isn't one.

  24. That was heavy. So your catching up and passing photons of an instance In space and time.
    I think I understand.

  25. I'm convinced this guy is just saying nonsense technobabble in these videos, but someone with authority says he's smart so we all nod our heads and pretend we understand a single word of this.

  26. Isn't the Alcubierre warp drive warping space time around itself but in a non-symetrical way (space is front of the ship is bent the "opposite way" compared to how space is bent at the back of the ship)? If so, since light is emitted from inside the warp bubble, it has to travel through those different regions of space time that have different geometries. It seems to me that it would affect the path of the light and therefore affect the time at which they arrive to the annihilator.

    The ship also crosses the same time hyperbola, what would it mean? That the observers in the ship see themselves going through the same instants, twice? It seems to mirror the fact of seeing the ship at two places at the same time.

  27. For some reason i watch a lot of your shows because im interested about the things these programs are about and then you pop up on the screen time and again so there is the single one and always the same question i end up with after i watched . What are you smoking?

  28. Holy shit you are crazy. You really need to see a doctor. This is real life here. You think you are in the movies. Just how much television have you watched as a kid? God i wish i could meet you take you around for the afternoon and talk to you damn i know i could help you . You're very very smart after all i just have to be able to bring you back to reality i know i can do it. Somebody do it you desperately need help.

  29. And how does the ship travel faster than light? Does it feed a Big Bang Expansion out its exhaust and so travel at any speed it likes? Lol!

  30. I want to see the diagram from the perspective of the Paradox. In particular, I want to see where the Earth goes.

  31. WRONG, you don’t travel back in time, you can only see back in time. If I am not mistaken Einstein’s clock thought experiment proves that.

    Please don’t kill me if I’m wrong haha

  32. You can't because nothing in spacetime is stationary everything is moving all of the time.
    The whole notion of time travel is pure speculation and theoretical.

  33. so really it isn't time so much what you're moving through, its you outrunning a photon packet that was emitted earlier then viewing it. But hasn't the time necessary to accomplish that still passed? You physically have not moved through time at all you just out ran an old photon that is now some distance away from its origination?

  34. There is no paradox. Sure you could go warp speed across the universe and sort of technically see the past (but you probably couldn't even see the sun that far), it's just some old light particles. And when you go back you might have aged less but the time passed just normally for others. Even if you talked with tachyon/entanglement telephone, you can't call the past, it's just trickery. You can only call the present and only when travelling under the speed of light,
    because going speed of light or faster would stop time for you.

  35. Great video, but I disagree with the statement that an observer on the Annihilator sees the Paradox travel forward in time. To get the velocity of the Paradox relative to an observer in the Annihilator, use the formula for velocity transform between relativistic reference frames and you get u' (velocity of Paradox relative to Annihilator) is infinite as observers on the Annihilator would see the Paradox leave the Earth and arrive at the destination at the same point in time in their reference frame. https://en.wikipedia.org/wiki/Velocity-addition_formula

  36. So in future when sun becomes red giant or big. so will the habitable zone get bigger. will mars become center of the habitable zone therefor habitable?

  37. No, Neo. I'm trying to tell you that when you're ready, you won't have to

    physically move yourself around the universe in a big metal spaceapartment.

  38. Time was represented by the rising and setting of the sun and is now represented atomically (the orbiting of particles around the nucleus of an atom). If time is based off these two situations then the only way to reverse time (time travel) is to reverse these two. It's impossible.

  39. Would it be true if you traveled in one direction faster than the speed of light you would see events in that location unfold in fast reverse if you looked behind you but if you looked ahead you would see things that happened in the past from that location but it would unfold in fast reverse starting from your current time (collection of photons that reach your eyes)?

  40. Let's say the Annihilator's captain had just observed the Paradox pop out of nowhere.

    Let's say the Paradox's copies move very slowly because the Annihilator had a speed of (1–1e-9)c relative to Earth, and the Paradox had a speed of (1+1e-9)c.

    Let's say the Annihilator's captain only spots a copy of the Paradox that moves towards Earth, and decides to pursue and prevent this copy from ever reaching Earth, because from the captain's perspective, this stuff is made of particles that have very strange spins, which the captain concludes to be dangerous for humanity.

    So he successfully pursues the Paradox, boards it, speaks to its captain, tries to explain the dangers of going to Earth, the other captain perfectly understands, and they both decide to go somewhere else. Happy ending for everybody.

  41. Alcubierre faster than light travel doesn't mean travel throught spacetime, but stretch and shrink of spacetime itself as a mean of transportation. I think Your explanation is faulty at root.

  42. I feel like every episode has a "you should watch this episode first". I mean I might as well just get a degree in physics to watch the show I guess

  43. There is a mistake. A Warp Drive doesnt produce time dialation, because no mass is moving FTL, which means the referenced clock isnt overcoming its own source. This only would apply to real FTL flight, which is prohibited by the dialation itself, because you would need infinite amounts of energy to make the referenced clock "slower" then zero. Same with Photons, from the perspective of a light particle, it needs 8 minutes to reach earth, same as we see it just after 8 minutes due to the fact that Photons have no mass. The Diagramm is correct, just the Alcubierre-Drive isnt working this way 😀 But besides that, really awesome Video !

  44. I know you're mister scientist, but if a mind can conceive something in reality does not reality contain the thought you say is impossible?
    "Imagination is more important than knowledge." -Einstein, I think he meant ultimate reality is the fullness of imagination.

  45. Is it possible to construct a cosmic speedometer by examining the properties of a particle moving with you on the ship …in an instant…no comparing to another measurement from a different time…?

  46. 10 minutes!?! that survey took over 30 minutes to do and most people quit before finishing….they need to learn their target audience. I don't watch TV. yet most of their questions revolved around…tv…great pbs is an entity that has no clue how to behave in the 21st century….hah television, as if.

  47. What if a time dimension doesn't exist, though? What if that's just something we put on our graphs and it doesn't mean anything to go forward or backward on that dimension because it simply doesn't exist.

    Yes, your relative clocks would be different, but no matter how fast you travel.. even if it's faster than the light that's being perceived you wouldn't be traveling in a different direction in time.

    Of course, there's other problems with superluminal speeds than traveling through time… but I don't think time travel is really a problem. I think that just comes from how we represent causality in our perception of reality. I don't think reality cares about the time axis on any of our graphs. Things just change how quickly events occur when you're moving at different speeds.

    At least, that's the way it seems to me from every experiment I've heard of.

  48. That FTL ship wouldn't actually be an Alcubierre drive: for an Alcubierre drive the flat spacetime Lorentz transformations wouldn't work because it's actually warping spacetime in such a way that its "effective velocity" seems faster than light but its "local velocity" is not.

  49. I'm not buying any part of this until you show the math that ties super-luminescence with REVERSAL of the law of entropy of the entire universe?!?!?!?!?!??????

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