Question about time travel to the past

[JohnnyGui]

Good day to you all,

I have been reading Stephen Hawking's book "A Briefer History of Time" (yes, I'm a novice ;)) and I need some verification on if my understanding is correct regarding his theory/conclusion saying that if one travels faster-than-light, he would be able to travel into the past and that the order of events would differ for 2 observers with different velocities.

Here's what he says:
- Event A occurs on Earth
- Event B occurs on Proxima Centauri (PC) one year later Earth's time after event A
- Earth and PC are 4 light-years apart
- In order for an observer on Earth to experience both events, he'd have to travel faster than light to PC after event A occurs

If my understanding is correct, does this mean that the observer, while going faster-than-light during his travel to PC, he would "pass" the lightbeams of event A going to PC along with him? He'd then reach PC, experience event B and then receive the lightbeams of event A afterwards? Wouldn't he be experiencing the events in the order [A (when he was on Earth)] - B - [A (receiving the lightbeams while standing on PC)]? Is my statement correct as to what he meant with traveling to the past by going faster-than-light?

The part after that makes less sense to me, it's about an observer standing on PC and moving away from Earth at light speed:
"This observer would say it is possible, if you could move faster than light, to get from event B to event A. In fact, if you went really fast, you could also get back from A to PC before that event."

How is it possible for that observer standing on PC, who already experienced event B on PC, to experience event A on Earth after B while event A already happened 1 year Earth's time before event B? Or does he mean that, by going faster-than-light away from PC, he'd "pass" the lightbeams of Event B, then he'd meet during his travel to Earth the lightbeams of event A that approaches him and then receive the lightbeams of event B afterwards?

Are my statements correct? If not, could one please explain to me in layman terms what he really meant?

 

[jerromyjon]

Seems to me all that is being stated is that "if" anything could exceed the speed of light, which nothing can, then causality would be defeated and that is the example. It might be close to 15 years since I read that book so I don't recall it clearly, but it appears to me to be correct.

 

[Nugatory]

If you google for "tachyonic antitelephone" you'll find some more discussion, "closed timelike curves" will get you even more. However, you have to remember that all of this weirdness and paradoxical behavior comes from assuming that you can travel faster than light - and you can't, so that's a bad assumption. If you start with a bad assumption, the conclusions you will draw from that assumption may also be false, and that tells you nothing except that you made a bad assumption.

Get hold of something like Taylor and Wheeler's "Spacetime Physics" if you want to get started on understanding relativity. People here can help you through the hard spots if you're working at learning the real thing, but you can't learn from the popularizations.

 

[JohnnyGui]

Thanks for your responses. I'm very aware that nothing can travel faster than light. Aside from that, I merely wanted verificiation on if my understanding is correct as to what Stephen Hawking meant in his explanation.

 

[JohnnyGui]

Are there any other insights on the quote that I might have missed or have misunderstood? Not that I doubt your judgement jerromyjon :)

 

[PeroK]

Are there any other insights on the quote that I might have missed or have misunderstood? Not that I doubt your judgement jerromyjon :)

Thinking about the time it takes light to travel from an event to an observer is not relevant in terms of understanding relativity. If I set up a mirror, then I can observe an event twice: once when the light travels directly to me and again, later, when I observe the reflected light. But, that doesn't mean I think the event happened at two different times.

You need to calculate out the travel time of light from an event in order to establish when the event happened.

The key is to understand "reference frames". Two observers at rest with respect to each other, one on PC and one on Earth, will agree about the time and place of an event. Even though an event that takes place on Earth will only be observed on PC four years later.

An observer who is traveling at high speed between the two will not agree with them about the time and place of an event. Or, to be more precise, they will be different in his reference frame. Not because of anything to do with the delay in receiving light signals, but because of the relativity of space and time for observers moving with respect to each other. That is the basis of Special Relativity (SR).

The problem then is that the equations governing SR do not admit faster than light speed. In classical physics there would be no problem in traveling to PC in one year. But, in SR there is the overwhelming problem that it is not physically possible. Trying to resolve, using SR, what might or might not happen for someone hypothetically traveling faster than light is problematic and, in my opinion, harder than understanding SR in the first place!

Personally, I would forget about faster than light travel and if you're really interested get an introductory book on SR, which is fascinating and marvellous - not least because it's how the universe actually works!

 

[HAL9000]

Thinking about the time it takes light to travel from an event to an observer is not relevant in terms of understanding relativity. If I set up a mirror, then I can observe an event twice: once when the light travels directly to me and again, later, when I observe the reflected light. But, that doesn't mean I think the event happened at two different times.

You need to calculate out the travel time of light from an event in order to establish when the event happened.

The key is to understand "reference frames". Two observers at rest with respect to each other, one on PC and one on Earth, will agree about the time and place of an event. Even though an event that takes place on Earth will only be observed on PC four years later.

An observer who is traveling at high speed between the two will not agree with them about the time and place of an event. Or, to be more precise, they will be different in his reference frame. Not because of anything to do with the delay in receiving light signals, but because of the relativity of space and time for observers moving with respect to each other. That is the basis of Special Relativity (SR).

The problem then is that the equations governing SR do not admit faster than light speed. In classical physics there would be no problem in traveling to PC in one year. But, in SR there is the overwhelming problem that it is not physically possible. Trying to resolve, using SR, what might or might not happen for someone hypothetically traveling faster than light is problematic and, in my opinion, harder than understanding SR in the first place!

Personally, I would forget about faster than light travel and if you're really interested get an introductory book on SR, which is fascinating and marvellous - not least because it's how the universe actually works!

This is a great post liable to make someone actually go and study SR.

 

[JohnnyGui]

Thinking about the time it takes light to travel from an event to an observer is not relevant in terms of understanding relativity. If I set up a mirror, then I can observe an event twice: once when the light travels directly to me and again, later, when I observe the reflected light. But, that doesn't mean I think the event happened at two different times.

You need to calculate out the travel time of light from an event in order to establish when the event happened.

The key is to understand "reference frames". Two observers at rest with respect to each other, one on PC and one on Earth, will agree about the time and place of an event. Even though an event that takes place on Earth will only be observed on PC four years later.

An observer who is traveling at high speed between the two will not agree with them about the time and place of an event. Or, to be more precise, they will be different in his reference frame. Not because of anything to do with the delay in receiving light signals, but because of the relativity of space and time for observers moving with respect to each other. That is the basis of Special Relativity (SR).

The problem then is that the equations governing SR do not admit faster than light speed. In classical physics there would be no problem in traveling to PC in one year. But, in SR there is the overwhelming problem that it is not physically possible. Trying to resolve, using SR, what might or might not happen for someone hypothetically traveling faster than light is problematic and, in my opinion, harder than understanding SR in the first place!

Personally, I would forget about faster than light travel and if you're really interested get an introductory book on SR, which is fascinating and marvellous - not least because it's how the universe actually works!

I thank you for this very insightful post. Just before reading your reply, it indeed came to my mind that merely a delay in receiving light signals doesn't bring you to the past at all. What I can't wrap my head around after realising that though, is how one traveling at high speed (not necessarily faster-than-light) could be able to disagree with the time of an event to such an extent that it finds that the order of events are reversed, based on the scenario that I quoted in my opening post.

I definitely should go read more on SR.

 

[Nugatory]

What I can't wrap my head around after realising that though, is how one traveling at high speed (not necessarily faster-than-light) could be able to disagree with the time of an event to such an extent that it finds that the order of events are reversed, based on the scenario that I quoted in my opening post.

Google for "Einstein train simultaneity" to see how one observer can find that events A and B happen at the same time while another finds that A happened before B. From there it's a straightforward exercise (all you need is another train moving in the opposite direction) to find a third observer who finds that B happened before A.
As long as no faster-than-light travel is involved, such reversal can only happen for events that cannot have any causal relationship (they are "spacelike-separated", another google-worthy term) so no paradoxes result.

 

[JohnnyGui]

Google for "Einstein train simultaneity" to see how one observer can find that events A and B happen at the same time while another finds that A happened before B. From there it's a straightforward exercise (all you need is another train moving in the opposite direction) to find a third observer who finds that B happened before A.
As long as no faster-than-light travel is involved, such reversal can only happen for events that cannot have any causal relationship (they are "spacelike-separated", another google-worthy term) so no paradoxes result.

Thanks, that made sense to me. Regarding the causal relationship, are you saying that for example you can travel to the past only up until the moment that you have discovered time travel?

I'm reading on wormholes at the moment and I can't seem to get how wormholes could make you travel into the past just because you're traveling to a destination in a shorter time than light. Could someone please elaborate on this?

 

[Mister T]

Are there any other insights on the quote that I might have missed or have misunderstood?

It's like saying "A person would have to be invisible to have made it through that entry way without having been caught on the video cameras".

The point is that it can't be done.

 

[Nugatory]

Thanks, that made sense to me. Regarding the causal relationship, are you saying that for example you can travel to the past only up until the moment that you have discovered time travel?

No. I am saying that there is no such thing as time travel as the phrase is generally understood: a person or object being able to return to their own past so that they can be present at an event that they've already been present at. The relative ordering in Einstein's train thought experiment can happen only for events that are separated (have you googled for "spacelike-separated" yet?) in such a way that no person or object could be present at both of them, so they cannot be things like "bullet fired at A; bullet hit target at B" or "Strapped myself into time machine at A; opened door and stepped out at B"; "something happened at A; this caused an effect at B".

I'm reading on wormholes at the moment and I can't seem to get how wormholes could make you travel into the past just because you're traveling to a destination in a shorter time than light. Could someone please elaborate on this?

You'll hear "faster than light" tossed around in non-serious discussions of wormholes, but it's sort of cheating. Imagine two cities on the Earth's equator; city B is 39000 kilometers to the east of city A. My airplane flies at 500 km/hr, so you'd expect that it takes me more than three days to fly from A from to B... But somehow I do it in a mere two hours. That doesn't mean that I've somehow managed to get my dinky little airplane to fly at 20000 km/hr (serious spaceship speeds!), it means that I decided to fly west instead of east.

A spacetime geometry that includes wormholes will have more than one path between some points. If the paths have different lengths, it might be possible to move from one point to the other along the shorter path in less time than it would take a light signal to get there along the longer path. Calling that "faster than light" is very misleading - it is not possible to beat a light signal that takes the same path that I do, and no one will be able to beat a light signal that takes the shortest path.

Spacetime geometries that have multiple paths like this can also have paths that allow an object to return to its own past (called "closed timelike curves" - did you google for that yet?). However, there is every reason to believe that such spacetimes do not exist - they appear as solutions to the Einstein Field Equations only if you make impossible assumptions about the distribution of energy and matter.

 

[JohnnyGui]

You'll hear "faster than light" tossed around in non-serious discussions of wormholes, but it's sort of cheating. Imagine two cities on the Earth's equator; city B is 39000 kilometers to the east of city A. My airplane flies at 500 km/hr, so you'd expect that it takes me more than three days to fly from A from to B... But somehow I do it in a mere two hours. That doesn't mean that I've somehow managed to get my dinky little airplane to fly at 20000 km/hr (serious spaceship speeds!), it means that I decided to fly west instead of east.

A spacetime geometry that includes wormholes will have more than one path between some points. If the paths have different lengths, it might be possible to move from one point to the other along the shorter path in less time than it would take a light signal to get there along the longer path. Calling that "faster than light" is very misleading - it is not possible to beat a light signal that takes the same path that I do, and no one will be able to beat a light signal that takes the shortest path.

Spacetime geometries that have multiple paths like this can also have paths that allow an object to return to its own past (called "closed timelike curves" - did you google for that yet?). However, there is every reason to believe that such spacetimes do not exist - they appear as solutions to the Einstein Field Equations only if you make impossible assumptions about the distribution of energy and matter.

Thank you so much for your response. I was indeed aware of the fact that wormholes don't make you go faster-than-light since that's not the local movement what a traveller undergoes in there.
I did go as far as closed timelike curves, them being closed loops of spacetime, but I'm struggling at the way it would work out that a wormhole could spit you out into the past with the following example that I found on the wiki page:

"This would be accomplished by accelerating one end of the wormhole to a high velocity relative to the other, and then sometime later bringing it back; relativistic time dilation would result in the accelerated wormhole mouth aging less than the stationary one as seen by an external observer, similar to what is seen in the twin paradox. However, time connects differently through the wormhole than outside it, so that synchronized clocks at each mouth will remain synchronized to someone traveling through the wormhole itself, no matter how the mouths move around

For example, consider two clocks at both mouths both showing the date as 2000. After being taken on a trip at relativistic velocities, the accelerated mouth is brought back to the same region as the stationary mouth with the accelerated mouth's clock reading 2004 while the stationary mouth's clock read 2012. A traveler who entered the accelerated mouth at this moment would exit the stationary mouth when its clock also read 2004, in the same region but now eight years in the past. Such a configuration of wormholes would allow for a particle's world line to form a closed loop in spacetime, known as a closed timelike curve".

I do understand that accelerating an object or the wormhole mouth in that case would make its time go slower. What I don't get is how time connects differently through a the wormhole than outside of it in such a way that synchronized clocks at each mouth would remain synchronized to someone traveling through the wormhole, even if one mouth has a slower going time with respect to the other. Why would the traveler, who entered the accelerated mouth which its clock shows 2004 exit the stationary mouth at the same year while the stationary mouth says that its 2012?

 

[peety]

I notice that our present never seems to get interfered with by future events.

 

[PeterDonis]

Why would the traveler, who entered the accelerated mouth which its clock shows 2004 exit the stationary mouth at the same year while the stationary mouth says that its 2012?

He wouldn't. He would exit the stationary mouth when the stationary mouth said it was 2004.

In other words: suppose the traveler starts out with his spaceship, with one mouth of the wormhole inside it, parked outside a house, and the other mouth of the wormhole is inside the house, with the traveler's twin standing next to it. Both twins' clocks read 2000 at this point, and time is hooked up through the wormhole the same way as it is outside it at this point, so if either twin steps through the wormhole, he will be standing next to the other twin with the other clock reading the same as his own that he just left. (It will be no different, except for a slight difference in travel time, than if the twin had taken the ordinary path, walking out of the spaceship/house and then walking into the house/spaceship.)

Now the traveler flies out, comes back, and lands his spaceship next to the house. His clock reads 2004, and if he looks through the wormhole, he sees his twin's clock also reading 2004 (because that's how time is hooked up through the wormhole, so that both clocks show the same reading if you look through the wormhole from one to the other). But if he looks out the window of his spaceship, through the window of the house, he sees his twin's clock reading 2012.

So if the traveler, just after he lands, steps through the wormhole, he will be standing next to his twin when his twin's clock reads 2004. If he then looks out the window of the house, he won't see the spaceship parked there; it will be flying away at relativistic speed. He would have to wait eight years for the spaceship to come back--until the clock inside the house reads 2012; then, if he walked out of the house and into the spaceship that had just landed, he would see the clock inside the spaceship reading 2004, and the previous version of himself, eight years younger, just stepping through the wormhole.

 

[JohnnyGui]

He wouldn't. He would exit the stationary mouth when the stationary mouth said it was 2004.

In other words: suppose the traveler starts out with his spaceship, with one mouth of the wormhole inside it, parked outside a house, and the other mouth of the wormhole is inside the house, with the traveler's twin standing next to it. Both twins' clocks read 2000 at this point, and time is hooked up through the wormhole the same way as it is outside it at this point, so if either twin steps through the wormhole, he will be standing next to the other twin with the other clock reading the same as his own that he just left. (It will be no different, except for a slight difference in travel time, than if the twin had taken the ordinary path, walking out of the spaceship/house and then walking into the house/spaceship.)

Now the traveler flies out, comes back, and lands his spaceship next to the house. His clock reads 2004, and if he looks through the wormhole, he sees his twin's clock also reading 2004 (because that's how time is hooked up through the wormhole, so that both clocks show the same reading if you look through the wormhole from one to the other). But if he looks out the window of his spaceship, through the window of the house, he sees his twin's clock reading 2012.

So if the traveler, just after he lands, steps through the wormhole, he will be standing next to his twin when his twin's clock reads 2004. If he then looks out the window of the house, he won't see the spaceship parked there; it will be flying away at relativistic speed. He would have to wait eight years for the spaceship to come back--until the clock inside the house reads 2012; then, if he walked out of the house and into the spaceship that had just landed, he would see the clock inside the spaceship reading 2004, and the previous version of himself, eight years younger, just stepping through the wormhole.

Your great example really helped me understand the mechanics of wormholes way better. I have 2 questions regarding this example:

1. If the traveler, after he lands his spaceship in 2004 (his clock), would look through his window at the house of his twin, would he see the 2012 version of his twin? And if he looked through the wormhole the 2004 of the twin?

2. I'm sorry if this is what you tried to explain as well but why exactly do wormholes have a synchronous clock on both sides regardless of one accelerating? From what I understand, acceleration should result in an absolute time difference among the two.

 

[PeterDonis]

If the traveler, after he lands his spaceship in 2004 (his clock), would look through his window at the house of his twin, would he see the 2012 version of his twin?

Yes; as I said:

if he looks out the window of his spaceship, through the window of the house, he sees his twin's clock reading 2012.

And if he looked through the wormhole the 2004 of the twin?

Yes:

His clock reads 2004, and if he looks through the wormhole, he sees his twin's clock also reading 2004

why exactly do wormholes have a synchronous clock on both sides regardless of one accelerating?

Because that's how time is hooked up through the wormhole. At least, that's how it would be hooked up through the wormhole in the simple model of a wormhole that is being used in this example. See below.

From what I understand, acceleration should result in an absolute time difference among the two.

No; acceleration results in a time difference between the twins (it's actually more complicated than that, but I don't think we need to go into a detailed discussion of the usual twin paradox here) if we look at the way time is hooked up in ordinary spacetime, not through the wormhole. That's the point; once the wormhole mouths are separated and have different states of motion, time is hooked up differently through the wormhole than it is outside the wormhole. (At least, that's one way of trying to describe what's going on in ordinary language.)

Here's another way of looking at it: if we look at things outside the wormhole, the two twins are in relative motion during the trip. But if we look at things through the wormhole, the twins are at rest relative to each other during the entire trip! (Kip Thorne, in his discussion of this scenario in Black Holes and Time Warps, emphasizes this point by having the two people hold hands through the wormhole during the entire trip.) So if we look at things through the wormhole, we don't expect the "time rates" of the twins to be any different, because they're not moving relative to each other.

Of course such a thing would be impossible in ordinary flat spacetime, or even in ordinary curved spacetime without wormholes. A main point of this whole scenario is to emphasize the sorts of strange things that could happen if wormholes existed.

 

[JohnnyGui]

Here's another way of looking at it: if we look at things outside the wormhole, the two twins are in relative motion during the trip. But if we look at things through the wormhole, the twins are at rest relative to each other during the entire trip! (Kip Thorne, in his discussion of this scenario in Black Holes and Time Warps, emphasizes this point by having the two people hold hands through the wormhole during the entire trip.) So if we look at things through the wormhole, we don't expect the "time rates" of the twins to be any different, because they're not moving relative to each other.

Ah, now THAT'S what I wanted to know to understand why the clocks are synchronous! I'm now trying to picture how they're not moving with respect to each other through the wormhole and why this results in the clocks being the same at both mouths and I have an explanation for this in my head. I'd like to know if my explanation would be the correct way to look at it:

If the spaceship moves through ordinary spacetime with the mouth of the wormhole inside of it, that mouth should move through spacetime with the spaceship as well. Since the other mouth in the twin's house remains still in space-time, this would result in a "stretch" of the tunnel between the two mouths of the wormhole. This tunnel stretching also stretches the space-time fabric inside of it that forms the walls of the tunnel and therefore making the whole tunnel's clock go slower (just like space-time stretches around large gravity sources).
Thus, the spaceship's contribution of slowing down its own time, would be transferred through the whole tunnel of the wormhole all up to the other mouth resulting in the same slowed down clock at the mouth in the twin's house.
Ofcourse, this is only the case if every bit of space-time in the tunnel would be equally stretched with respect to the accelerating mouth in the spaceship.

Sorry if I'm asking too much, but I tend to take things a step further as soon as I understand it.

 

[SlowThinker]

I'm now trying to picture how they're not moving with respect to each other through the wormhole and why this results in the clocks being the same at both mouths

You're looking for something complex but the idea is really simple. If you put clock next to each wormhole, one ticks 4 years while the other ticks 12 years, but looking through the wormhole, they are running with the same speed. It can't be any other way.
If you want a wormhole that connects different parts of space but not time, I think it's against the principle of relativity.

this would result in a "stretch" of the tunnel between the two mouths of the wormhole. This tunnel stretching also stretches the space-time fabric inside of it that forms the walls of the tunnel and therefore making the whole tunnel's clock go slower

I'd say OK until the "tunnel clock". The two mouth are simply connecting 2 parts of spacetime, one in the traveling ship, the other in the house. No funny things happen when you go through.
I'm not familiar with E-R wormholes but I'm pretty sure the "tunnel" can be just a few nanometers long, when looking through. Perhaps this is the source of your confusion? The path through the wormhole stays the same, no matter what the other end is doing.

Anyway since there are many reasons wormholes cannot exist, this is just an exercise in imagination.

 

[PeterDonis]

I'm now trying to picture how they're not moving with respect to each other through the wormhole and why this results in the clocks being the same at both mouths

Because the distance between the two ends of the wormhole, as viewed through the interior of the wormhole, is constant (see below). That means the clocks at both mouths run at the same rate, as viewed through the interior of the wormhole--they're a constant distance apart.

If the spaceship moves through ordinary spacetime with the mouth of the wormhole inside of it, that mouth should move through spacetime with the spaceship as well.

Ok so far.

Since the other mouth in the twin's house remains still in space-time, this would result in a "stretch" of the tunnel between the two mouths of the wormhole.

No. At least, not with the simple model of a wormhole being used in this example. In that model, the "length" of the wormhole--the distance you would perceive yourself to travel if you passed through it--is constant. The interior of the wormhole doesn't have to stretch just because its mouths are moving apart, as viewed from outside.

the spaceship's contribution of slowing down its own time, would be transferred through the whole tunnel of the wormhole all up to the other mouth resulting in the same slowed down clock at the mouth in the twin's house.

No, that won't work. Slowing down time can't get "transferred", and anyway you're not thinking about it from a spacetime viewpoint.

My advice: draw a spacetime diagram of the scenario. First draw the usual "twin paradox" diagram, where the traveler goes out in the spaceship and comes back, and 4 years elapse along his worldline while 12 years elapse on the stay-at-home twin's worldline.

Then draw in a dotted line representing the interior of the wormhole (dotted because it doesn't pass through the spacetime you're drawing; the interior of the wormhole is just a different piece of spacetime that doesn't appear on the diagram, only the mouths do). At the start, both mouths are at year 2000; then one mouth moves along the traveler's worldline, while the other mouth moves along the stay-at-home worldline. But through the interior of the wormhole, there is now a path between a given event on the traveler's worldline, and the event on the stay-at-home worldline that has the same clock reading.

So when the traveler returns, the dotted line is now vertical--it connects the point where the twins meet up again (where the traveler's clock reads 2004 and the stay-at-home clock reads 2012) and the point on the stay-at-home worldline where that clock reads 2004. Nothing got "transferred" anywhere; it's just that there is an extra piece of spacetime (the interior of the wormhole) that connects two events in ordinary spacetime by a much shorter path than their connection in ordinary spacetime (which is eight years long).