# Random topic: Time travel

Let’s talk about timey-wimey stuff

Although my degrees are in computer science and computer engineering, as an undergraduate I switched my major over from physics after my first year. Before switching, I went through five quarters of undergrad physics, with my last class being relativity. I also had the pleasure of watching — and mocking — the Star Trek TNG series finale in a room full of other physics majors.

I love science fiction, not only for escapism, but also because it is fun to explore the hypothetical possibilities that science could make possible but hasn’t. Various topics like time travel and artificial intelligence have come up this year on The Non-Prophets, and I will usually drop into that kind of speculation at the drop of a hat.

I got a message this morning from someone asking:
I was wondering if you could help me with a scientific question. Recently, a friend of mine and I were discussing time travel. He stated that time travel is a proven fact and that there is evidence of this when you are driving in your car. If you look closely, time speeds up. I disagree but I cannot for the life of me remember the details, scientifically, on why this isn’t possible. Can you help me?
Here’s my reply:
Time travel can have a lot of different meanings. In a trivial sense, we are always “traveling” in time, that is to say, we are moving forward at the rate of one second every second.
Your friend is actually correct… one of the weird findings of relativity is that time can be compressed when moving at high speeds. There are a lot of equations which represent how much this happens. At normal speeds it’s not likely to be noticeable at all, but as you get close to the speed of light a few things happen:
1. Your mass increases.
2. The energy required to speed you up more increases (that’s a necessary consequence of #1)
3. Your localized time slows down.
The standard example is: you have a pair of twins. One stays on Earth, the other flies far from the Earth at 99% speed of light, and then returns. When they get back, the Earth-bound twin is old, while the flying twin hasn’t aged nearly as much.
But… this doesn’t cover all kinds of time travel that science fiction writers like to talk about. The plots of movies like Back to the Future and Terminator require people to move backwards in time, arriving at an earlier point than they left. As far as we know, that’s not possible, and time only moves forward for real world objects.
But when I say “real world objects” I mean things with mass. There are some hypotheses about things called tachyons, which have negative imaginary mass (see the comments section and/or the linked Wikipedia article for clarification). If tachyons exist then they could travel backwards in time. In fact they could ONLY travel backwards in time, never forward.
Compressing time is still forward time travel, but most scientists are pretty confident that backward time travel is impossible, because it would violate causality. Sci-fi stories that allow time travel are free to make up their own rules that address the causality issues, like traveling to parallel universes, or branching universes, or requiring altered time to form a closed loop, or (as in BTTF) allowing the timeline to gradually update the timeline… giving Marty a whole week to arrange his parents getting together before he disappears.
But real life isn’t fiction. We have no idea how violations of causality would be resolved, because we’ve never seen it happen and have no way to test it.

### Comments

1. Tod says

With regards to the violation of causality issue, something I watched Sean Carroll talking about might solve that, but also change our idea of time travel…

I might get this wrong, but Sean seems to go along with the many worlds interpretation of Quantum Theory, where every time there are 2 options they both actually happen and you simply find yourself in one world or the other..

When you mix that idea with something I saw Brian Cox explaining where basically at every moment (maybe use planck time here?) any electron in orbit around a nucleus in any atom in the entire universe could move position.. or not, and you end up with an infinity of worlds dispersing out every moment of planck time…

Then we add in the whole “going back in time and accidentally stepping on a butterfly” idea…

Now you might start to see the problem (and the solution I propose :))… Let’s say you can go back in time through a wormhole, it’s not a matter of worrying about accidentally killing your granddad (or impregnating your grandmother hehe).

The very instant you arrive in the past the universe would be splitting through the multiverse, over and over, an infinite number of other worlds, with most of that infinite number consisting of this exact universe but with a slightly different atom in another galaxy somewhere…

Forget trying not to do something that might upset “your future”, try navigating the splitting of the universe you arrive in as it splits infinitely every moment so that you follow the exact same path through the many worlds as you did prior to your time travel…

This resolves all paradoxes of time travel as anything you do, you do in another of the “many worlds”, and so can be normal canon in that version of the universe, where when time arrives at the present it doesn’t matter if you manage to recreate the time travelling or not as that happened in another universe…

So how does this change our idea of time travel?

Well if the many world interpretation is correct, then you are not really travelling through time at all, maybe at first, but as soon as you arrive you are really travelling through the many worlds, so it should be many world travel instead hehe 🙂

2. Rob Grigjanis says

There are some hypotheses about things called tachyons, which have negative imaginary mass.

Negative mass could give rise to exotic physics, like the Alcubierre drive, but that’s not tachyons.

If tachyons exist then they could travel backwards in time. In fact they could ONLY travel backwards in time, never forward.

Since any two points on a tachyon’s path have a spacelike separation, there is no unique way to define time order, backwards or forwards. They could be used to send messages to the past, but that’s not the same as only traveling backwards in time.

Anyway, introducing tachyons into a quantum field theory renders the theory unstable, and restabilization gives a theory with no tachyons, but possibly interesting new features. An example is the Higgs mechanism, which gives masses to some of the particles in the Standard Model.

3. Orion Silvertree says

There are some hypotheses about things called tachyons, which have negative mass.

Actually, tachyons (if they exist) are even weirder than that: their rest-mass values aren’t negative, they’re imaginary.

4. CompulsoryAccount7746, Sky Captain says

“when you are driving in your car. If you look closely, time speeds up.”

Here’s my reply:
Time travel can have a lot of different meanings.

Book: Traffic, Why We Drive the Way We Do

experiments have been focused on exit ramps because they are a statistically dangerous part of the highway. One crucial reason involves a particular illusion we face in traffic: “speed adaptation.”

Have you ever noticed, when driving from a rural highway onto a village road with a lower speed limit, how absolutely slow it feels? […] The longer we drive at high speeds, the harder it is for us to slow down. Studies have shown that drivers who drove for at least a few minutes at 70 miles per hour drove up to 15 miles per hour faster when they hit a 30 miles-per-hour zone than drivers who had not previously been traveling at a higher speed.

The reason, as Robert Gray, a cognitive psychologist at the University of Arizona, explained to me, is something that might be called the “treadmill effect.” After running on a treadmill for a while, you may have noticed that the moment you stop you may briefly experience the sensation of moving backward. As Gray describes it with driving, neurons in the brain that track forward movement become fatigued as a person looking ahead drives at the same speed for a time. The fatigued neurons begin to produce, in essence, a negative “output.” When a person stops (or slows), the neurons that track backward motion are still effectively dormant, but the negative output of the forward neurons fools you into thinking you’re moving backward – or […] into thinking you have slowed more than you actually have. This illusion cuts both ways, studies suggest: We underestimate our speed whe asked to slow down and overestimate our speed when asked to speed up.
[…]
The reason we have speedometers, and why you should pay attention to yours, is that drivers often do not have a clue about how fast they’re actually traveling – even when they think they do.

Article: Wikipedia – Motion Aftereffect

after viewing a moving visual stimulus for a time (tens of milliseconds to minutes) with stationary eyes, and then fixating a stationary stimulus. The stationary stimulus appears to move in the opposite direction to the original (physically moving) stimulus. The motion aftereffect is believed to be the result of motion adaptation.

For example, if one looks at a waterfall for about a minute and then looks at the stationary rocks at the side of the waterfall, these rocks appear to be moving upwards slightly. The illusory upwards movement is the motion aftereffect. This particular motion aftereffect is also known as the waterfall illusion.

5. Curt Cameron says

I also like those kinds of scifi stories. Speaking of which, have you seen the animated show Rick and Morty? It’s full of plotlines that use ridiculous takes on time travel and infinite universes. A quick example is the one where Rick’s tinkering went bad and that resulted in the destruction of the Earth. Next thing you know, we see Rick and Morty tinkering in the garage, when something goes bad and it kills both of them. Just then, a vortex appears and another Rick and Morty jump into the scene – they just found another universe where they were killed but everything else was the same, and started living in that one. Later in the show you see two graves in the back yard.

6. verruca says

Time travel is one of those subject that fascinates physicist and non-physicist alike but I think the real puzzle (as far as physicists are concerned) is time itself.
Although we can see ways to move forward in time there seems to be no way to move backward. I don’t just mean in terms of an actual experiment. There’s just no theoretical, mathematical basis for the idea. It’s similar to the concept of probability that’s used in Quantum Mechanics in that probability is always positive. The idea of a negative probability just makes no sense.
In quantum mechanics. we deal with this behavior of probability by working always with a thing called the ‘amplitude’, which has to be squared mathematically to give probability values. The square is always positive regardless of the sign of the amplitude. This is true even when using complex numbers (if we define the ‘square’ of a complex number as the product with the complex conjugate). In that way, negative probability can’t happen in the theory, just like we always see in the real world.
So what about time? should we regard time as the ‘square of something’? Maybe. But it’s interesting to note that in Einstein’s equations of relativity, squares and square roots appear an awful lot.

7. Chikoppi says

Counterpoint: the “religious right.”

If it weren’t possible to travel backwards in time how do you explain the social ideologies they espouse?

I believe that’s check and mate, physicists!

8. L.Long says

Let’s say time travel is do-able. So what!? what would you do with it? Varify jesus is real? Why? true believers would deny what ever you don’t find and say you made it up! Change the past? Why? Killing Hitler? Well would that change anything for the better? How do you know? Go back an live in a better time? ANd when is that?
It may be fun as a discussion point for physicists & philosophers to masturbate with.

9. CompulsoryAccount7746, Sky Captain says

@L.Long #8:

Let’s say time travel is do-able. So what!? what would you do with it? Verify jesus is real? Why? true believers would deny what ever you don’t find and say you made it up!

Steal the body while it’s dead.
Tada! Proof.
Bonus: Jesus returns. Sorry about the mess.

10. Russell Glasser says

Yes. I would absolutely, definitely go check out the details on the life of Jesus. Probably nobody would believe me, but I’d know. This is my number one priority if I ever get to go back in time. I’ve given this some thought before.

11. EnlightenmentLiberal says

Uhh, most of the OP’s description of relativity is questionable at best, and close to outright wrong.

He stated that time travel is a proven fact and that there is evidence of this when you are driving in your car.

Going forward in time, yes. For example:

> Time Travel Face Bag | Metalocalypse | Adult Swim
https://www.youtube.com/watch?v=ZknFhQftrug

If you look closely, time speeds up. I disagree but I cannot for the life of me remember the details, scientifically, on why this isn’t possible.

Consider if you had a pendulum clock with you, at your side. No matter what crazy stunts you do, no matter what scenarios you have in the context of general relativity, you will always see that pendulum clock tick at the same, normal, everyday rate.

Can you help me?

Yes, but it’s going to be hard. You have to “forget” a lot of what you learned in high school physics and geometry classes.

Let me work through some of Russell’s questionable replies.

At normal speeds it’s not likely to be noticeable at all, but as you get close to the speed of light a few things happen:
1. Your mass increases.

Suppose you hop in a spaceship right now, then accelerate for a while, so that you’re moving at 99% c (aka 99% of the speed of light) relative to Earth. Suppose you weighed yourself, or part of yourself, or otherwise determined the mass of you and your spaceship. Everything would be normal. The measuring device would properly report that your mass, and the mass of your spaceship, is entirely unchanged. What Russell says here is not entirely without basis, but it requires a little more to work through. I’ll get back to this later.

2. The energy required to speed you up more increases (that’s a necessary consequence of #1)

Let’s do a thought experiment.

Let’s suppose that you’re in a spaceship in outer space. You are at rest, aka not accelerating. (You can tell if you are accelerating by using an accelerometer.)

You drop a rock outside the spaceship, so that the rock is not moving relative to your spaceship. You then accelerate for a while, then stop accelerating. You measure how much internal energy reserves you expended. You measure the speed of that rock (such as with a laser range finder and speed meter), and suppose the laser range finder reports a speed of 50% c.

Now, suppose you restock on fuel somehow (such as by a magically super-efficient solar cell, and your engine uses very, very little reaction mass compared to the mass of the spaceship, in order that I can ignore the whole rocket equation when discussing this problem).

Now, you drop a second rock outside of your spaceship. This rock is at rest relative to your spaceship, and this rock #2 is moving at 50% c when measured from rock #1, and vice versa.

Now, you accelerate again for a while, then stop accelerating. You measure how much internal energy reserves you expended for the second jump. You measure the speed of rock #2, and suppose the laser range finder reports a speed of 50% c. You use the laser range finger again, but on the first rock, rock #1. In normal Earth contexts, speeds like this add, but that’s only an approximation. In the real world, speeds do not add. That laser range finder will not report 100% c. Instead, it will report a value in between 50% and 100% c. (You can calculate it exactly, but I’m too lazy to look up the formula.)

So, the other question is: According to my internal instruments, how much energy did you expend for the first acceleration phase compared to the second acceleration phase? The answer is that you expended the same amount of energy in both acceleration phases. Again, this is the naive answer that one expects. According to your internal instruments, nothing strange is happening. Your spaceship still has the same mass, and it required the same amount of energy in both acceleration phases to change your speed from your initial speed, to your initial speed + 50% c. The only weird thing thus far is that speeds don’t add like they do in naive Newtonian physics.

Still, what Russell says is not entirely without merit, but it’s phrased very badly. I’ll get back to it.

3. Your localized time slows down.

Simply false. This is a common misunderstanding of general relativity, and the twin paradox, which Russell kindly cited.

Wikipedia IIRC does a fairly good job for the twin paradox. I’ll also explain it myself here.
https://en.wikipedia.org/wiki/Twin_paradox
Before I go fully into it, this is the short version of the resolution of the twin paradox: The question “Am I moving, and how fast am I moving?” cannot be answered in reference to some absolute or standard way. The only way to answer that is question is relative to some point of reference. For example “I am moving at 50 miles per hour relative to the road”. However, the question “Am I accelerating, and how fast am I accelerating?” can be answered in an absolute and unrelative way. There are simple devices that can simply and unequivocably report how fast oneself is accelerating without regard to any point of reference.

The resolution of the twin paradox is to note that the situation for the two twins is not equal. One twin stayed on Earth, in a relatively stationary and constant frame of reference. The second twin underwent massive acceleration (several actually, one to go away from Earth, and the second to slow, stop, turn around, and speed up back to Earth, and a third to slow down and stop once reaching Earth). This difference of “who accelerated, and how much” is the resolution to the paradox. If you do the math of special relativity, this is a quite easy conclusion to make. When you plug into the equations and model that one twin accelerated in this manner, and the other twin did not, then you reach the conclusion that when the twins meet up back on Earth, the twin from space looks younger than the twin from Earth.

Now, I must emphasize that for the twin in space, if they have a simple clock with them, such as a pendulum clock, they will notice absolutely nothing unusual. The twin in space will perceive the pendulum clock ticking at the normal rate. The twin in space will measure its own mass as the normal Earth value. Nothing will be amiss. Similarly, the twin on Earth will not notice anything amiss regarding their own pendulum clock right next to them, and will notice nothing amiss regarding their own mass as they measure it on Earth.

However, if one of the twins uses a powerful telescope to look at the other twin, they will notice something amiss. They will notice that the clock is ticking at a “wrong rate”. Further, suppose they performed indirect measurements and calculations to determine each other’s mass. They would each measure and calculate that the apparent mass of the other twin as “wrong”! This is why you will sometimes read online that mass increases when speed increases. However, this is a very confused and confusing way of stating it. Also, the language of “increasing mass” has fallen out of vogue. Nowadays, when talking about the mass of an object, we are only talking about its rest mass, or the mass of the object when we measure the object when the object is stationary relative to us the observer.

So, what is relativity? This video does a great explanation. I’ll also give my own explanation, echoing much of the video.

> The Speed of Light is NOT About Light | Space Time | PBS Digital Studios
https://www.youtube.com/watch?v=msVuCEs8Ydo

Special relativity is based on a few very basic principles that could have been calculated literally thousands of years ago. (Ok, ok, maybe only hundreds. You need calculus to do it, and Maxwell’s equations.) Just no one thought to do it. These simple calculations were made only when the scientific community was faced with very puzzling and confounding experimental results. Even then, relativity was controversial in the physics community for decades after being published (in part because a test of the theory was so difficult to do at that time, and in part because of how much his model violated common sense). What – did you think that Einstein won his Nobel prize in physics for general relativity? Hell no. Einstein won his Nobel prize in physics for his work in quantum theory!

Special relativity is based on the following principles:

* Speed is relative. There is no such thing as an absolute measure of speed.

* The Galilean principle of relativity: All experiments should give the same results no matter how fast the whole experimental apparatus is moving. An experiment in a lab should give the same results when run inside of a train car, and inside of a spaceship in outer space.

* There should be a consistent way for the math of the model to “translate” from one point of reference at rest (e.g. not accelerating) to another point of reference at rest (e.g. not accelerating). The two points of reference may be moving very fast relative to each other, but they’re not accelerating! Remember, speeds are all relative, but undergoing acceleration and being at rest can be measured absolutely without regard to some point of reference.

* The rule for changing from one point of reference to another point of reference should not break Maxwell’s equations of magnetism and electricity.

What do I mean by “a consistent way for the math of the model to translate from one system at rest to another system at rest”? Very loosely, go back to my thought experiment involving the space ship and the two rocks. According to Galileo, speeds should add, but in the real world, they don’t. We need to develop a different formula for this kind of conversion.

It happens that there is only one formula that satisfies our criteria: the Lorentz transformation. The Lorentz transformation was known well before Einstein published his paper, but no one actually took its consequences seriously. Relativity in large part was just taking the pre-existing math and its consequences seriously, and explaining that “no, it’s not a mathematical artifact or glitch – that’s actually how the real world works”.

So, we’re stuck in a world where two observers, who are moving at different speeds, they can see the world in different ways, such as:

No simultaneity: There is no such thing as “simultaneous”. Two events that are simultaneous to one observer might happen at different times according to another observer.

Length contraction: Two observers can see the same object as having different lengths. One might report 1.5 meters, and one might report 1 meter.

Time dilation: Observers who see a pendulum clock ticking might report that the clock tick speed is different. One might report 1 tick per 1 second, and one might report 2 ticks per 1 second, and a third observer might report 0.5 ticks per 1 second.

Mass and energy equivalence: Two observers can observe a different mass value and different energy value for an object.

However, with relativity and the Lorentz transformation, all of the observers are able to calculate what every other observer happens to sees. While they cannot agree on what is the right and wrong answer in many of these cases (and there is no right and wrong absolute answer in many of these cases), they can all calculate what each other sees. The world is consistent in that manner. In relativity, there is still a real world out there. The observers can all agree about the properties of the system and what every individual observer does and should observe. It’s simply that some properties that we thought were absolute and unchanging, such as the apparent tick rate of a pendulum clock, or the apparent length of a stick, depend on the frame of reference of the observer.

PS: Just like we can talk about the rest mass of an object, which is an absolute measure that does not depend on a frame of reference, we can also talk about the rest length of an object, which is an absolute measure that does not depend on a frame of reference.

fin

12. Rob Grigjanis says

Enlightenment Liberal @11:

However, the question “Am I accelerating, and how fast am I accelerating?” can be answered in an absolute and unrelative way. There are simple devices that can simply and unequivocably report how fast oneself is accelerating without regard to any point of reference.

No! You can measure your acceleration with respect to your instantaneous rest frame. The acceleration you measure, like your velocity, will be different in other frames of reference, so it most certainly isn’t “absolute”. I can give you equations if you like.

13. EnlightenmentLiberal says

To Rob Grigjanis
I stand corrected. Thank you.

14. Oh, the many, many discussions on this that I’ve had with science fiction geeks over the years.

You mention causality as an absolute prohibition against time travel. It is my understanding that causality matters only if you define “time” as the chain of cause and effect. But when you define time as a dimension co-existing with the three macro spacial dimensions — spacetime — there is no reason time cannot be be a bi-directional T-axis, not essentially different from the X-, Y- and Z-axes. The question is whether the cause-and-effect and the T-axis definitions actually describe the same phenomenon.

For what it is worth, my own “fake physics” I’ve used in a number of writing projects holds that the T-axis is micro, one of the curled up dimensions described in various superstring theories. At a quantum scale, electrons, neutrinos and quarks pop around time as much as they pop around space, a property called temporality. But like uncertainty and superposition, temporality averages out in larger structures to give the illusion of absoluteness. This way, both definitions of time are absolutely correct: T-axis at the quantum level, cause-and-effect at the macro level.

15. Rob Grigjanis says

Gregory @14:

…T-axis, not essentially different from the X-, Y- and Z-axes.

They are essentially different in the following sense. If two events are separated by the differences Δt, Δx, Δy, Δz in some coordinate system*, the following quantity has the same value for the two events in any coordinate system;

(cΔt)² – (Δx)² – (Δy)² – (Δz)²

Notice the negative signs going with the spatial coordinates. So, this value could be positive, negative or zero. And it will remain so from any point of view (reference frame). Causality (in the physics sense) says that, if this value is negative (spacelike separation), the two events cannot affect each other. There’s nothing really there about the direction of time. That’s a dodgy question which is usually answered by invoking the second law of thermodynamics.

*Assuming flat spacetime, and Cartesian space coordinates for simplicity.

16. EnlightenmentLiberal says

To Rob Grigjanis
I again want to thank you for coming by and offering your knowledgeable corrections. It’s a better thread because of you.

17. I’m currently working on a BS degree in Actuarial Science: lot’s of math, but not really in this direction. I’ll have to give this some study.

But from what I do know, a string of operations and operands has little meaning without it reaching a conclusion. So shouldn’t we have an equation, (cΔt)² – (Δx)² – (Δy)² – (Δz)² = S? That can be generalized to (aΔt)² + (bΔx)² + (cΔy)² + (dΔz)² = S. Assuming the equation is true, it has at least one solution, up to an infinite number of solutions. Is there any restriction holding that a must be non-negative? With only one equation, and assuming that the commutative property applies in this set, I’m not seeing how cause-and-effect come into play.

I finished a Calculus 3 class last quarter, and will start Calculus 4 next month, so I’m still a bit shaky on multivariable manifolds, and will probably never take a class in topology or quantum physics. So I’m not sure where my reasoning is incorrect.

18. EnlightenmentLiberal says

To Gregory in Seattle
What you say makes little sense. It’s not an equation that is being solved.

In relativity, there is the idea of a “light cone”. A light cone is a proper mathematical cone, extending in both directions from a single point. Every point in space time has its own unique light cone. For a given point X, all points inside of the light cone of X are either in the past or future of X. For points Y in the future light cone of X, it is possible to send a signal from X to Y. For points Y outside the light cone of X, it is not possible to send a signal from X to Y. Remember, these points X and Y have spatial coordinates and a time coordinate.

It’s called a light cone because if I shined a light in all directions for a brief moment, then the (future) light cone describes the location in time and space of that pulse of light.

To put this in another way. Let’s suppose that I am an observer, and I define a coordinate system so that I am at (0, 0, 0, 0) and my velocity is 0, and I happen to not be accelerating. Then, suppose I consider another point of space time, call it P. It’s a simple matter to observe and calculate the delta X, delta Y, delta Z, and delta T to that point P. Then, I can plug those into the formula
(cΔt)² – (Δx)² – (Δy)² – (Δz)²
and calculate the single Real-value result. If that result is negative, this means that the point P is outside of my light cone. If the point P is outside of my light cone, then it is not possible for me to send a signal from my current position in time and space to the point P in time and space. If that result is positive, then the point is inside my light cone, and assuming the point is in my future light cone, then it is possible to send a signal from my point in space and time to the point P in space and time.

In other words, there is a special kind of distance in special relativity that is invariant under coordinate transformations. Remember the problem I laid out above regarding naive Galilean coordinate transformations?

According to Galileo, going from one inertial (e.g. at rest) coordinate system to another inertial coordinate system is just a simple matter of adding some offsets. However, this breaks Maxwell’s equations and observation of actual magnetic and electric fields, and it also doesn’t work for a finite speed of light that is the same for all coordinate systems.

So, we can talk about the normal Euclidean distance between two objects. That distance is given by Pythagoras:
sqrt( (Δx)² + (Δy)² + (Δz)² )

However, consider what happens to that distance when we change coordinate system for a new inertial frame of reference. That Euclidean distance changes. Euclidean distance is not invariant under coordinate system changes.

In special relativity, the following “distance” is invariant under Lorentz transformations:
sqrt( 0 + (Δt)² – (Δx)² – (Δy)² – (Δz)² )

That different sign is significant. For all pairs of points of spacetime P and Q, For all inertial coordinate systems, if you calculate this “distance” value for points of spacetime P and Q in that coordinate system, you will always get the same number. In other words, this “distance” is invariant, unlike Euclidean distance.

This only works because the sign on the time term is different than the sign on the spatial terms.

I’ve often heard it said that this is a deep and fundamental insight and fact. This difference in sign in this equation (and similar equations) is the “difference” between time dimensions and spatial dimensions.

19. EnlightenmentLiberal says

PS:
What I said applies only to special relativity, aka where there is no gravity. Gravity makes it more complex, but roughly the same ideas are right. (I think.)

Also, it’s probably more appropriate to present the special relativity invariant “distance” formula as such:
sqrt( 0 + (Δx)² + (Δy)² + (Δz)² – c²(Δt)² )

Because then I can easily contrast it with the Pythagorean distance formula:
sqrt( 0 + (Δx)² + (Δy)² + (Δz)² )

And show that the special relativity distance formula is just an extension, or improvement, on the Pythagorean distance formula. Or, in equivalent wordage, the Pythagorean distance formula is just a limiting case of the special relativity distance formula: when the time coordinate delta is 0.

So, if the distance between two spacetime points is positive according to this formula, then it’s a space-like separation. That means that the first spacetime point is outside the lightcone of the second spacetime point. In very crude language, the two points in space and time are separated by space, not time. In other words, it’s like my home and my place of work, right now, in this instant of time, according to my particular coordinate frame. They are separated by space, not time, which means it’s not possible to send a signal from my place of work at this moment of time to my home in this moment of time. That would require instantaneous communication, which is impossible.

If the distance according to this formula is an Imaginary number, then the distance is time-like. This means that one spacetime point is in the lightcone of the other spacetime point, and vice versa. This means that it’s possible to send a signal from one to the other (but only one way, because no signaling backwards in time).

And for emphasis, when two events, each at their own point in spacetime, have space-like separation, it is not meaningful to talk about which happens first or second. There is no absolute first or second. Only when two spacetime points have time-like (or light-like) separation can one meaningfully talk about the temporal order that two events at the spacetime points happened. For two spacetime points with space-like separation, there is one observer who says that P happens before Q, and another observer who says that Q happens before P, and a third observer who says that P and Q happen at the same time. And for emphasis, all observers will calculate correctly what all other observers will see. And for emphasis, all observers will calculate that the two spacetime points do not exist in each other’s light cones, and all observers will calculate for all other observers, the two spacetime points do not exist in each other’s light cones.

PPS:
And this is also why naive faster-than-light travel machines are also go-back-in-time machines. If you can send a signal to some spacetime point outside of your light cone, then there is at least one observer who observes the signal arriving before being sent, and who can send another faster-than-light signal back to your spatial location before you sent the signal in the first place!

20. Rob Grigjanis says

So shouldn’t we have an equation, (cΔt)² – (Δx)² – (Δy)² – (Δz)² = S?

Yes, and S (or -S) are usually called the proper (or invariant) time (or length) interval squared, depending on whether you’re using S or -S. Conventions in physics can be confusing, and particle physicists tend (or tended) to use a sign opposite to that use by cosmologists.

Apart from choosing an overall sign, and using different units (e.g. in which c=1), you can’t generalize this equation. It describes the geometry of spacetime, in this case a flat static one.

With only one equation, and assuming that the commutative property applies in this set, I’m not seeing how cause-and-effect come into play.

It’s a principle. The version I gave in #15 is minimal; it simply says events A and B with a spacelike separation (S less than zero) can’t affect each other. In particular then, A can’t cause B or vice versa. A stronger version says A can only cause B (necessarily but not sufficiently) if B is in the future light cone of A. In other words, if their separation is timelike (S greater than zero), and B’s time coordinate is greater than A’s.

I suspect I’m not seeing what you’re getting at. But in sci-fi, you’re free to make up whatever loopholes you want 😉

21. Rob Grigjanis says

Sorry. My #20 was addressed to Gregory @17.

22. It sounds like I was making assumptions from “spacetime consists of four dimensions” and not understanding that the phrase is a very basic simplification. Interesting.

Being a hard science fiction geek is fun, but doing it right means having to actually learn stuff. I will have to see if the school I’m starting has any classes I can take, this would be fun to explore. Thanks for the corrections.

23. ptaswist says

@Russell Glasser

Do you have a plan for actually finding him? I mean, we only have a vague general location for the events mentioned in the Bible, no idea what he was up to for most of his life. The dates are not precise, and the dude has a common name and not much else in terms of some unique identifiers. Sounds like a lot of ground to cover for just one time traveller. And I’m guessing you don’t speak aramaic or koine greek either.

Maybe it would be easier skip forward some years after the crucifiction, find a large-ish group of early christians, and work your way back, asking people where did they get their stories from? Seems like it would be super hard anyway without our modern ways of tracking people.

24. Mobius says

“At normal speeds it’s not likely to be noticeable at all, but as you get close to the speed of light a few things happen:”

Just to point out, velocity is relative. There is no absolute frame of reference, so no one ever sees themselves as traveling near the speed of light. Instead, they always see themselves as standing still and everything else moving in relation to them. For example, we are moving at 19 miles per second relative to the Sun, yet we see ourselves standing still.

So, no, you won’t see the effects of relativity on yourself when you are traveling fast. You will just see the effects of relativity on other things.

25. Mobius says

@22 Gregory in Seattle

Actually, topologically spacetime IS four dimensional. However, it is not a Eucliean four dimensional space. In Einsteinian spacetime, there are points which can not be connected by a “straight line”, or geodesic. It has a different metric, and that different metric is what probably accounts for the greater complexity you are mentioning.

26. StevoR says

@8 L.Long :

Let’s say time travel is do-able. So what!? what would you do with it?

Travel through it!

Backwards and forwards and seeing lots of cool stuff and learning what really happened and what dinosaurs and megafauna really looked like. 😉

Of course, a lot would depend on the nature of that temporal travel and the answer to the temporal equivalent of the
Fermi paradox -if there is time travel where are the time travellers? Perhaps they can only observe not interfere? Perhaps there are time laws and lords and when knows what?

Varify jesus is real? Why? true believers would deny what ever you don’t find and say you made it up! .

Yeah maybe but if you have video or other proof then it might convince a lot of, shall we say not so true believers or people who can be persuaded? Ditto Mohammad, Abraham, Buddha etc .. Could be kinda interesting to find out some truths behind some of the myths. And what if it turns out the Flying Sphaghetti Monster really existed!

Seriously, does the fact that people deny we landed on the Moon now mean it wasn’t worth doing?

Change the past? Why?

To improve it and save lives and make things better for more people maybe? Like say preventing genocides and preserving the bets whilst removing the worst of old cultures so that human lives all got better faster?

One could argue there’s actually a moral utilitarian case for there being an ethical obligation to alter history for the greatest good of the greatest number? How you still exist as you from this time created by what led to us whilst doing so is natch, another story again.

Killing Hitler? Well would that change anything for the better? How do you know? .

Because you read history books, maybe visit a Holocaust museum or Shoah memorial or three? Six million dead human individuals that were killed for no good reason that would have a chance to live again instead? That H-word hasn’t become an icon of the worst evil for nothing you know. Oh & there might be non-leathal ways of stopping Hitler too -suppose a benefactor got him into art school after all or onto Prozac as an art festival campaign in Adelaide South Oz controversially once suggested and a friend of mine wrote a short story about respectively.

Plus there are other historical villainies you can also hypothetically abort too – say Columbus and the extermination of so-many Indigenous Peoples. Go back and vaccinate the Incas and First Australians and Amerindians against smallpox, stop slavery at its source, just small things like that ..

Go back an live in a better time? ANd when is that?

Well, that’s what you have a time machine for isn’t it? Finding out! 😉

It may be fun as a discussion point for physicists & philosophers to masturbate with.

Plus science fiction writers and ,well, blog commenters and most people really. Fun to imagine and discuss generally I find albeit not necessarily productive – but sometimes quite thought-provoking. So thanks.

(& sorry if too snarky / flip , late at night /early morn here and I’m tired. Fun thought experiment or two though. Seriously.)

27. Devocate says

“Six million dead human individuals that were killed for no good reason that would have a chance to live again instead?”

How could you possibly know that? What happens if you kill Hitler, return to your time and discover that Stalin overran Europe instead, and he killed 10 million people? Or what if Hitler (being dead) failed to drive out the scientists who enabled the making of the atomic bomb, and Germany got on first, and used it to forward the racist agenda that many there had? I am willing to bet that Hitler never killed a single one of those people personally.

If you think you can easily direct the course of history to a utopia, PLEASE demonstrate by explaining hot to make the future perfect.

28. StevoR says

@ ^ Devocate : “How could you possibly know that?”

Because we know what happened in our history as it happened and thus we know that those six million were killed in the Shoah. What positive things could those six million lives have added to the world had they lived? I don’t know -they never had the chance to show us and that’s part of the tragedy of it. Do you really not think so?

What happens if you kill Hitler, return to your time and discover that Stalin overran Europe instead, and he killed 10 million people?

Then you go back and kill or otherwise stop Stalin in that first place second time. Ditto Chairman Mao, Franco, etc .. Come to think of it, given the chance I’d do that anyhow as Stalin, Mao, Franco were intrinsically evil and murderous enough to warrant stopping on their own accounts too. In fact I’d prevent Lenin and the bolsheviks taking power earlier preceding Stalin – and maybe most of the Tsars as well.

If you think you can easily direct the course of history to a utopia, PLEASE demonstrate by explaining hot to make the future perfect.

Well, I didn’t say it’d necessarily be easy or that we’ll ever get things perfect and I haven’t actually got a time machine to demonstrate with but I’m sure you and I can think of a hell of a lot of ways we can change history for the better starting with removing fascist dictators and intervening to prevent historical atrocities and injustices and so on.