# Virtual particles

#### DevilsAvocado

Gold Member
i'm sorry, i don't understand what the question is, nor what the difficulty is

can you spell it out, please?

Okay, your own words, my bolding:

if we regard something as moving north at speed v faster than light, then an observer moving at speed slower than light but faster than c2/v will regard the same thing as moving south at a speed faster than light …

Problem: I’m aware of Relativity of Simultaneity, but I have never heard of "Relativity of Direction".

Question: If "something" is moving north, let’s say from the South Pole to the North Pole, and another observer is experiencing this "something" as if moving south, i.e. from the North Pole to the South Pole. Where will this "something" finally end up, the South Pole or the North Pole?

Or to keep it simple: One object can’t be in two places at once.

#### Constantin

Problem: I’m aware of Relativity of Simultaneity, but I have never heard of "Relativity of Direction".
If you start moving faster than a certain object, it will appear reversing direction.
I'm not saying it's about moving faster than Alice in this case though, just that your problem is very simple.

One object can’t be in two places at once.
"Two places at once" is wrong. It will be in two different places for two different observers. Or for the same observer after he changes his motion. That's normal and very simple as well.

#### tiny-tim

Science Advisor
Homework Helper
Question: If "something" is moving north, let’s say from the South Pole to the North Pole, and another observer is experiencing this "something" as if moving south, i.e. from the North Pole to the South Pole. Where will this "something" finally end up, the South Pole or the North Pole?
yes!

one observer says it ends up at the South Pole, another observer says it ends up at the North Pole …

where's the difficulty?
Or to keep it simple: One object can’t be in two places at once.
nobody's saying it is

#### DevilsAvocado

Gold Member
one observer says it ends up at the South Pole, another observer says it ends up at the North Pole
Great, now we’re almost there. Instead of "saying" that it ends up at the South Pole and the North Pole, both observers travels to "their Pole" to check their measurement apparatus.

What will they find?

#### tiny-tim

Science Advisor
Homework Helper
Great, now we’re almost there. Instead of "saying" that it ends up at the South Pole and the North Pole, both observers travels to "their Pole" to check their measurement apparatus.

What will they find?
you mean one observer (with the given velocity) times his start so as to reach A when the spot of light does, and the other observer (with the other given velocity) times his start so as to reach B when the spot of light does?

then the first one will find he's just in time to catch the spotlight before it turns off, and so will the second one!

#### DevilsAvocado

Gold Member
you mean one observer (with the given velocity) times his start so as to reach A when the spot of light does, and the other observer (with the other given velocity) times his start so as to reach B when the spot of light does?

then the first one will find he's just in time to catch the spotlight before it turns off, and so will the second one!
ehhhhh "catch the spotlight"...

Look, I don’t know what’s going here... but it’s clearly a waste of time...

Take care and I wish you luck as Science Advisor.

#### Constantin

I agree such thought experiments are not easy to understand. I didn't understand it either at the beginning. But the explanations were quite good and helpful.

#### Fredrik

Staff Emeritus
Science Advisor
Gold Member
It's interesting to examine some of the details of a version of the laser pointer thought experiment that tiny-tim suggested. Suppose that a laser pointer shines at a fixed point on the moon for a while, and is then rotated so that the red dot on the moon moves faster than light to a new location. Suppose that the laser pointer is then constrained to keep shining at that point for some time. Let's call the event where the red dot begins to move A, and the event where it stops moving B. How would these things be described in an inertial system in which B occurs before A?

At first there's one dot, at the location on the moon where event A will occur at a later time. After a while, a new dot appears at event B, and immediately splits in two. So now there are three dots. One of the two new ones stays at the location on the moon where event B occured. The other one moves at a superluminal speed toward the other location. When it merges with the red dot that's already there, both of them disappear. So now there's only one red dot again.

This is all easy to see in a spacetime diagram.

#### tiny-tim

Science Advisor
Homework Helper
… So now there are three dots. One of the two new ones stays at the location on the moon where event B occured. The other one moves at a superluminal speed toward the other location. When it merges with the red dot that's already there, both of them disappear. So now there's only one red dot again.
oooh, nice, Fredrik!

#### byron178

hmm … how about i ask you a question instead …

i shine a laser beam at the the moon, so that the spot travels across the moon's surface faster than light (that's very easy! ) …

i say it travels from A to B faster than light, another observer says it travels from B to A faster than light …

where's the difficulty?
so the laser "time traveled backwards in time".and is it really time travel?doesn't this also violate causality? i also got this off of wiki.If a laser beam is swept quickly across a distant object, the spot of light can move faster than c, although the initial movement of the spot is delayed because of the time it takes light to get to the distant object at the speed c. However, the only physical entities that are moving are the laser and its emitted light, which travels at the speed c from the laser to the various positions of the spot. Similarly, a shadow projected onto a distant object can be made to move faster than c, after a delay in time.[38] In neither case does any matter, energy, or information travel faster than light.[39]

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#### DevilsAvocado

Gold Member
It's interesting to examine some of the details of a version of the laser pointer thought experiment that tiny-tim suggested. Suppose that a laser pointer shines at a fixed point on the moon for a while, and is then rotated so that the red dot on the moon moves faster than light to a new location. Suppose that the laser pointer is then constrained to keep shining at that point for some time. Let's call the event where the red dot begins to move A, and the event where it stops moving B. How would these things be described in an inertial system in which B occurs before A?

At first there's one dot, at the location on the moon where event A will occur at a later time. After a while, a new dot appears at event B, and immediately splits in two. So now there are three dots. One of the two new ones stays at the location on the moon where event B occured. The other one moves at a superluminal speed toward the other location. When it merges with the red dot that's already there, both of them disappear. So now there's only one red dot again.

This is all easy to see in a spacetime diagram.

But Fredrik, moving laser dots and shadows don’t qualify for FTL, they are not physical objects and you cannot use it to send information FTL. If it was, any freak with a laser pointer would qualify for an instant Nobel Prize in Physics (probably why tiny-tim is so fond of it :rofl:).

My 'reaction' is due to the fact that the 'casual reader' could easily get the impression this "superluminal-dual-reversed-direction" is some form of empirical fact, at the same level as the very real consequences of Relativity of Simultaneity and other effects in SR & GR. All you have to do is "think again" and "do the maths".

This is wrong.

And I think anyone following these latest posts understands that the one calling out for others to "think again", hasn’t done so himself.

The problem, as I see it, is that we are talking about purely hypothetical features as some form of "no-brainer-every-day-experience". And as we have seen from latest posts – you run into hilarious paradoxes when trying to 'implement' this in a real world with real physical objects, in exactly the same way as you run into the unsolvable http://en.wikipedia.org/wiki/Grandfather_paradox" [Broken] when claiming that Special and General Relativity might allow time travel.

I have 'reconstructed' my Gedankenexperiment to close all "spotlight-loopholes" and any other "time-consuming-uncertainties" into a bulletproof and somewhat 'brutal' version...
Superluminal Gedankenexperiment II

Adolf is very a cruel dictator that hates science, and most of all he hates the famous physicists Albert & Niels.

Adolf has stolen a brand new weapon from the defeated enemy; the so-called Titanium Tachyon Bullet (TTB) which is superluminal and very lethal, and always hits its target. Adolf has planned the execution to be as degrading as possible for Albert & Niels, and for the other captured physicists who are forced to inspect the event in different frame of reference.

This is what Adolf has set up:
• Albert is placed to the north, and Niels is placed to the south.
• The inspecting physicists are moving between Albert & Niels, in different frame of reference.
• Adolf is now firing the Titanium Tachyon Bullet in secret, from either north or south.
• When the TTB has traveled halfway, it’s spotted by the physicists.
• Some of them will see the TTB going north to kill Albert.
• Some of them will see the TTB going south to kill Niels.

One Titanium Tachyon Bullet going in two directions north/south

At this point we have 4 possible future options, which could happen in this kind of hypothetical superluminal reality:
• Albert is hit and killed, Niels survives.
• Niels is hit and killed, Albert survives.
• Both Albert and Niels is hit and killed.
• Both Albert and Niels survives.
And as we all can see, none of these options are logical satisfying – it’s a superluminal paradox!

(Personally I would love if both Albert & Niels were still alive, of course!)

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#### tiny-tim

Science Advisor
Homework Helper
But Fredrik, moving laser dots and shadows , they are not physical objects and you cannot use it to send information FTL.
correct
… don’t qualify for FTL …
of course they qualify for FTL!

any tachyon (your bullet, for example) follows a curve in space-time, and a moving laser dot can be made to follow the same curve

so we can unambiguously (and beyond criticism) study the laser dot, and be sure that any description of its course in any frame applies also to the tachyon!

you agree?
My 'reaction' is due to the fact that the 'casual reader' could easily get the impression this "superluminal-dual-reversed-direction" is some form of empirical fact, at the same level as the very real consequences of Relativity of Simultaneity and other effects in SR & GR.
dunno what you mean by "empirical"

but Frederik and I are simply pointing out the easy-to-calculate description of particular superluminal paths in the frames of different observers

have you checked the maths??​
This is what Adolf has set up:
• Albert is placed to the north, and Niels is placed to the south.
• The inspecting physicists are moving between Albert & Niels, in different frame of reference.
• Adolf is now firing the Titanium Tachyon Bullet in secret, from either north or south.
• When the TTB has traveled halfway, it’s spotted by the physicists.
• Some of them will see the TTB going north to kill Albert.
• Some of them will see the TTB going south to kill Niels.
is Adolf between them?

if so, you're wrong …
• Some of them will see the TTB going north to kill Albert.
• Some of them will see the TTB going south to kill Adolf.

and if the physicists had spotted it earlier, they would have seen it kill all three of them!

where's the difficulty?

#### Fredrik

Staff Emeritus
Science Advisor
Gold Member
But Fredrik, moving laser dots and shadows don’t qualify for FTL, they are not physical objects and you cannot use it to send information FTL.
Of course you can't use them to send information, but a) they're still moving faster than light, so it's certainly FTL, and b) we haven't been talking about sending information; we have only been talking about "objects" moving FTL.

My 'reaction' is due to the fact that the 'casual reader' could easily get the impression this "superluminal-dual-reversed-direction" is some form of empirical fact, at the same level as the very real consequences of Relativity of Simultaneity and other effects in SR & GR. All you have to do is "think again" and "do the maths".

This is wrong.
What do you mean it's wrong? It's predicted by the same part of the same theory that predicts time dilation, and it is relativity of simultaneity.

The problem, as I see it, is that we are talking about purely hypothetical features as some form of "no-brainer-every-day-experience".
We're just talking about what the theory predicts, so there's no problem. From a theorist's point of view, we're just talking about straight lines in $\mathbb R^4$.

And as we have seen from latest posts – you run into hilarious paradoxes when trying to 'implement' this in a real world with real physical objects, in exactly the same way as you run into the unsolvable http://en.wikipedia.org/wiki/Grandfather_paradox" [Broken] when claiming that Special and General Relativity might allow time travel.
Real physical objects moving FTL? What does that mean? SR associates positive mass only with timelike curves. Particles moving as described by spacelike curves would by definition have m2<0. So if your definition of "real physical object" includes a mass that isn't an imaginary number, then your real physical FTL objects immediately contradict SR.

the so-called Titanium Tachyon Bullet (TTB) which is superluminal and very lethal,
Titanium consists of atoms with mass m>0, so if you want to discuss titanium moving FTL, you will have to invent a new theory in which m>0 particles can move FTL. But for the sake of the discussion, I'll pretend that you said "unobtainium" rather than titanium, so that we can at least try to figure out what SR says about your scenario.

• Adolf is now firing the Titanium Tachyon Bullet in secret, from either north or south.
• When the TTB has traveled halfway, it’s spotted by the physicists.
• Some of them will see the TTB going north to kill Albert.
• Some of them will see the TTB going south to kill Niels.
First of all, you can't "fire" this bullet. It's either moving >c at all times or <c at all times. But we can imagine a gun that produces a TTB, so I'll do that. If some of the observers see this TTB going north to kill Albert, the others will see it going south to enter the barrel of the gun and be destroyed there, right after Adolf pulls the trigger.

And as we all can see, none of these options are logical satisfying – it’s a superluminal paradox!
Actually, it's just a poorly specified scenario (sorry). But the picture of the bullets was nice. I suggest that you draw a spacetime diagram for the next scenario you want to think about. If the diagram can't be drawn, the scenario doesn't make sense (in SR).

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#### byron178

Of course you can't use them to send information, but a) they're still moving faster than light, so it's certainly FTL, and b) we haven't been talking about sending information; we have only been talking about "objects" moving FTL.

What do you mean it's wrong? It's predicted by the same part of the same theory that predicts time dilation, and it is relativity of simultaneity.

We're just talking about what the theory predicts, so there's no problem. From a theorist's point of view, we're just talking about straight lines in $\mathbb R^4$.

Real physical objects moving FTL? What does that mean? SR associates positive mass only with timelike curves. Particles moving as described by spacelike curves would by definition have m2<0. So if your definition of "real physical object" includes a mass that isn't an imaginary number, then your real physical FTL objects moving FTL immediately contradict SR.

Titanium consists of atoms with mass m>0, so if you want to discuss titanium moving FTL, you will have to invent a new theory in which m>0 particles can move FTL. But for the sake of the discussion, I'll pretend that you said "unobtainium" rather than titanium, so that we can at least try to figure out what SR says about your scenario.

First of all, you can't "fire" this bullet. It's either moving >c at all times or <c at all times. But we can imagine a gun that produces a TTB, so I'll do that. If some of the observers see this TTB going north to kill Albert, the others will see it going south to enter the barrel of the gun and be destroyed there, right after Adolf pulls the trigger.

Actually, it's just a poorly specified scenario (sorry). But the picture of the bullets was nice. I suggest that you draw a spacetime diagram for the next scenario you want to think about. If the diagram can't be drawn, the scenario doesn't make sense (in SR).
can someone help me with why a group or phase velocity can exceed the speed of light?

#### DevilsAvocado

Gold Member
But we can imagine a gun that produces a TTB, so I'll do that.
Thankee, I was about to give up...

If some of the observers see this TTB going north to kill Albert, the others will see it going south to enter the barrel of the gun and be destroyed there, right after Adolf pulls the trigger.
Aha! Gotcha!!

Serious Fredrik, I’m not running for someone’s "scalp" here, I’m just here to learn and hopefully others will do the same, in the 'process'.

Now to the point, as we can see from your 'acknowledgement' above; there’s one TTB performing two tasks at two separate locations in space... it doesn’t matter that the experiment 'goofed'. This was the main point I wanted to draw attention to.

And I hope you admit there’s something 'strange' going on here... to say at least...

AFAICT, this doesn’t work according to current knowledge.

So, AFAICT, the only way to have an "object" moving at FTL in two different directions, at once, is to treat "it" as 'unreal' or virtual, and then we’re back to the OP question, thank god! :rofl:

Thanks for taking the time; (I think) I learned something new today!

#### DevilsAvocado

Gold Member
where's the difficulty?
No worries mate, everything is cleared up.

#### Fredrik

Staff Emeritus
Science Advisor
Gold Member
Now to the point, as we can see from your 'acknowledgement' above; there’s one TTB performing two tasks at two separate locations in space... it doesn’t matter that the experiment 'goofed'. This was the main point I wanted to draw attention to.
If the TTB is created when the gun fires and destroyed when it interacts with Albert's body, its world line is a single spacelike straight line segment. In no coordinate system is it in two places at once. On the other hand, if we use the kind of setup I described earlier, where the TTB is kept bouncing between two tachyon mirrors and then released to travel to a different location where it's trapped bouncing between two tachyon mirrors again, then in some coordinate systems, the number of TTBs changes from 1 to 3 and then back to 1 again. (Very easy to see in a spacetime diagram). And...hehe...I just realized something cool when I visualized that spacetime diagram in my head. We can change that to "the number of TTBs changes from 1 to N and then back to 1 again", for any odd integer N≥3 by making the TTB and the observer fast enough. (Speed →∞ for the TTB and speed →c for the observer).

And I hope you admit there’s something 'strange' going on here... to say at least...
Yes, but these are still just easily derived consequences on SR. If you want to see some really strange (self-contradictory) consequences of FTL messages in SR, check out this post. (It contains a typo that's corrected in #138).

This thought experiment looks like proof by contradiction that FTL messages can't exist in a SR universe, but the argument actually has loopholes. For example, if the time it takes to emit and/or detect a tachyon grows at least linearly with the distance it travels, there's nothing self-contradictory about this setup. OK, but it still rules out the possibility of tachyons that can be emitted and detected quickly, right? Wrong. The correct conclusion (a long discussion with JesseM in another thread helped me see this) is that there's no theory of matter in Minkowski spacetime such that its equations of motion have solutions that describe experiments similar to this one. There can still be a theory of tachyonic matter interacting with normal matter in Minkowski spacetime, but if it has a solution where someone begins to build this setup, something will happen that prevents the experiment from being carried out. The possibilities include such things as equipment malfunction, the Earth getting destroyed by a comet that's been on a collision course with us since it was formed billions of years ago, or the experimenter simply choosing not to go through with it.

I'm not sure what to make of this counterargument. I have a feeling that it's possible to come up with some good counter-counterarguments, but I haven't found one that really works.

#### byron178

If the TTB is created when the gun fires and destroyed when it interacts with Albert's body, its world line is a single spacelike straight line segment. In no coordinate system is it in two places at once. On the other hand, if we use the kind of setup I described earlier, where the TTB is kept bouncing between two tachyon mirrors and then released to travel to a different location where it's trapped bouncing between two tachyon mirrors again, then in some coordinate systems, the number of TTBs changes from 1 to 3 and then back to 1 again. (Very easy to see in a spacetime diagram). And...hehe...I just realized something cool when I visualized that spacetime diagram in my head. We can change that to "the number of TTBs changes from 1 to N and then back to 1 again", for any odd integer N≥3 by making the TTB and the observer fast enough. (Speed →∞ for the TTB and speed →c for the observer).

Yes, but these are still just easily derived consequences on SR. If you want to see some really strange (self-contradictory) consequences of FTL messages in SR, check out this post. (It contains a typo that's corrected in #138).

This thought experiment looks like proof by contradiction that FTL messages can't exist in a SR universe, but the argument actually has loopholes. For example, if the time it takes to emit and/or detect a tachyon grows at least linearly with the distance it travels, there's nothing self-contradictory about this setup. OK, but it still rules out the possibility of tachyons that can be emitted and detected quickly, right? Wrong. The correct conclusion (a long discussion with JesseM in another thread helped me see this) is that there's no theory of matter in Minkowski spacetime such that its equations of motion have solutions that describe experiments similar to this one. There can still be a theory of tachyonic matter interacting with normal matter in Minkowski spacetime, but if it has a solution where someone begins to build this setup, something will happen that prevents the experiment from being carried out. The possibilities include such things as equipment malfunction, the Earth getting destroyed by a comet that's been on a collision course with us since it was formed billions of years ago, or the experimenter simply choosing not to go through with it.

I'm not sure what to make of this counterargument. I have a feeling that it's possible to come up with some good counter-counterarguments, but I haven't found one that really works.
Fredrik,What moves backwards in time with the group velocity?

#### DevilsAvocado

Gold Member
... I'm not sure what to make of this counterargument. I have a feeling that it's possible to come up with some good counter-counterarguments, but I haven't found one that really works.
Thanks a lot Fredrik for your ideas and comments, very interesting. I must read every post in the thread you provided.

*So little time so much to do*

My first thought regarding "counterarguments" is the http://en.wikipedia.org/wiki/Novikov_self-consistency_principle" [Broken] to solve the problem of paradoxes in time travel. Maybe it’s possible to impose this on the TTB... (my feeling is that you had a track along these lines).

My natural feeling (for what it’s worth) is that it just feels 'unnatural'... Ockham's razor'ish...

[And now I take one step back]

I woke up with an 'epiphany' this morning! Now I know what went 'wrong' when we discussed moving laser dots, shadows and FTL "objects". I hope I can explain it easily:

The main 'epiphany point' is that moving laser dots and shadows are events happening in spacetime, not "objects" moving in spacetime. And suddenly everything makes perfect sense, and we can even use RoS (at ≤ c) to explain it all. Heck! We can even use Einstein's old train thought experiment from 1917 to visualize it, and it works like a dream!

"[URL [Broken] for large 1024x1577 picture
[/URL]

In this experiment, lightning simultaneous strikes both train ends a "time 0", i.e. if we were to implement this with a laser pointer, it would mean 'infinite' speed... But we could 'easily' () move this experiment to the surface of the moon, and at first put the laser spot at one end of the train, and then move it to the other end. This will cause just a slight difference to Einstein's 1917 experiment (time of events), but otherwise – it’s exactly the same thing!

... I hope you agree ... :shy:

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#### byron178

I need some clairafacation,do virtual particles time travel backwards in time when they travel faster than light,because relativity says that if a particle were to travel faster than light then in one frame it will travel backwards in time,but ive been some research and have not heard of virtual particles going backwards in time or coming from future to present.

#### tiny-tim

Science Advisor
Homework Helper
I need some clairafacation,do virtual particles time travel backwards in time when they travel faster than light,because relativity says that if a particle were to travel faster than light then in one frame it will travel backwards in time,but ive been some research and have not heard of virtual particles going backwards in time or coming from future to present.
hi byron178!

(i'm sorry no-one's answered you for some time )

only some virtual particles (in the momentum representation only) travel faster than light (virtual particles have all possible speeds, both slower and faster than light)

a virtual particle has no "time of its own" (unlike us, say), so we prefer to say that a virtual particle is exchanged between A and B (rather than going from A to B or vice versa)

anything travelling faster than light breaks causality, in that some observers say it moves from A to B, while others say it moves from B to A

if it had a well-defined "direction of ageing" (a human for example starts looking like a baby, and finishes looking like an old person), then some observers would say it was ageing backwards, ie it was going backwards in its own time while of course going forward in the observer's time

but no material can travel faster than light, so there isn't a well-defined "direction of ageing", and every observer simply says "it's going forward in my time, and it doesn't appear to have any time of its own"

(of course, virtual particles are just mathematical artefacts that help in the calculations, so this is a bit like discussing how many angels can dance on the head of a pin )

#### byron178

hi byron178!

(i'm sorry no-one's answered you for some time )

only some virtual particles (in the momentum representation only) travel faster than light (virtual particles have all possible speeds, both slower and faster than light)

a virtual particle has no "time of its own" (unlike us, say), so we prefer to say that a virtual particle is exchanged between A and B (rather than going from A to B or vice versa)

anything travelling faster than light breaks causality, in that some observers say it moves from A to B, while others say it moves from B to A

if it had a well-defined "direction of ageing" (a human for example starts looking like a baby, and finishes looking like an old person), then some observers would say it was ageing backwards, ie it was going backwards in its own time while of course going forward in the observer's time

but no material can travel faster than light, so there isn't a well-defined "direction of ageing", and every observer simply says "it's going forward in my time, and it doesn't appear to have any time of its own"

(of course, virtual particles are just mathematical artefacts that help in the calculations, so this is a bit like discussing how many angels can dance on the head of a pin )
Tiny-Tim,So what your saying is that virtual particles travel faster than light but don't travel backwards in time to the past,is this what your saying?

#### Drakkith

Staff Emeritus
Science Advisor
2018 Award
Tiny-Tim,So what your saying is that virtual particles travel faster than light but don't travel backwards in time to the past,is this what your saying?
I'm not sure, but it sounds to me like he's saying they don't actually travel through space.

#### tiny-tim

Science Advisor
Homework Helper
Tiny-Tim,So what your saying is that virtual particles travel faster than light but don't travel backwards in time to the past,is this what your saying?
in each observer's time, everything travels toward the future

if it had its "own time" (like a human), it could travel toward the past in its own time while travelling toward the future in the observer's time, in other words the observer would say it was getting younger

but it doesn't have its "own time"
I'm not sure, but it sounds to me like he's saying they don't actually travel through space.
hi Drakkith!

it depends what you mean by "travel" …

(eg in general relativity, do we say that an object travels along its world-line, or merely that it has a world-line? )

each observer certainly regards it as travelling (from A to B or from B to A), but since different observers can't agree (for faster-than-light travel) on the direction, is it really travelling (or is it really only "being exchanged")?

(of course, i repeat: virtual particles aren't real, they're just mathematical artefacts that help in the calculations )

#### Drakkith

Staff Emeritus
Science Advisor
2018 Award
As your tiny sized text at the bottom says, they aren't real(which I agree with), so why is this even an issue? More variations in interpretations?

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