# Thread: Twice the speed of light?

1. Hi,

I'm trying to understand a few fundamental scientific principles and I have a problem:

If nothing can apparently travel faster than the speed of light relative to another object, how do you explain the following:

2 particles (for arguments sake let's say Muons) start off adjacent to each other. An event occurs which causes them both to separate from each other, each travelling in opposite directions at almost the speed of light.

Mathematically, relative to Muon A, Muon B would surely be travelling at almost twice the speed of light. Is this possible? I was under the impression that "nothing could travel faster than the speed of light"

I understand that an observer on Muon A would see Muon B travelling away from him at the speed of light. However is this not just an optical illusion due to the speed which light travels and the medium through which the said observer chooses to obtain information?

In an experiment, lets say you fired the two muons in opposite directions down a long tunnel. You place lasers or some sort of detector at regular intervals within the tunnel. Each detector has it's own internal clock and are therefore able to calculate the speed at which each Muon is travelling. Say a computer is linked to all the detectors and after the experiment the computer produces a report on the relative speeds.

In relative terms, surely the computer would say that Muon A travelled at almost twice the speed of light away from Muon B or visa versa.

What is wrong with nominating the computer as the observer and Muon A and Muon B as the two subjects.

2.

3. Originally Posted by Mr. Monkey
Hi,

I'm trying to understand a few fundamental scientific principles and I have a problem:

If nothing can apparently travel faster than the speed of light relative to another object, how do you explain the following:

2 particles (for arguments sake let's say Muons) start off adjacent to each other. An event occurs which causes them both to separate from each other, each travelling in opposite directions at almost the speed of light.

Mathematically, relative to Muon A, Muon B would surely be travelling at almost twice the speed of light. Is this possible? I was under the impression that "nothing could travel faster than the speed of light"

I understand that an observer on Muon A would see Muon B travelling away from him at the speed of light.
Not the speed of light but at just a little closer to c than the individual muons move relative to the starting point. The exact formula is

However is this not just an optical illusion due to the speed which light travels and the medium through which the said observer chooses to obtain information?

In an experiment, lets say you fired the two muons in opposite directions down a long tunnel. You place lasers or some sort of detector at regular intervals within the tunnel. Each detector has it's own internal clock and are therefore able to calculate the speed at which each Muon is travelling. Say a computer is linked to all the detectors and after the experiment the computer produces a report on the relative speeds.

In relative terms, surely the computer would say that Muon A travelled at almost twice the speed of light away from Muon B or visa versa.
It is perfectly allowable for the computer to determine that the difference in speed between muon 1 and muon 2 to be greater than c. What Relativity says is that no one can measure anything as moving greater than c relative to itself.

Assuming muon A is moving at .99c to the left and muon B 0.99c to the right. The computer will measure the difference between their speed as 1.98c. Each muon, however, will measure the other muon as moving at 0.99497c relative to itself.

What is wrong with nominating the computer as the observer and Muon A and Muon B as the two subjects.

4. Originally Posted by Mr. Monkey
Hi,

I'm trying to understand a few fundamental scientific principles and I have a problem:

If nothing can apparently travel faster than the speed of light relative to another object, how do you explain the following:.....
What Janus said is correct.

It is not true that special relativity says that nothing can travel faster than the speed of light, depending on what you mean by "nothing".

What special relativity really does is provide a theory whereby measurement of space and time (and things derived from it, including velocity and acceleration) in one inertial reference frame can be related to measurement of those same quantities in another inertial reference frame. It assumes that the laws of physics are the same in all inertial reference frames and that the speed of light is constant in all such frames. A consequence is that no massive object can travel faster than c, the speed of light in a vacuum. If you also assume causality, then it also says that no information-bearing signal can travel faster than c.

But there are phenomena involving non-material things and non-information-bearing signals that can propagate superluminally. One that you brought up is the recessional velocity between two objects. Another is the closiing velocity. The limit on those is 2c. Another thing is the movement of a spot of light on a distant screen, something like the illuminated circle that results from a spotlight on clouds. Given sufficient distance there is no limit to that speed -- but nothing physical is moving and no signal is being sent.

5. Just out of curiosity,

given a "snail universe" where nothing travels faster than snails, including observations that relay only at the pace of blind snails,

would it be possible to snip the speed of light out of special relativity, by replacing every instance of c with speed of snail..? Would special snail relativity work fine in snail universe? Or would the loss of light speed break it?

6. Originally Posted by Pong
Just out of curiosity,

given a "snail universe" where nothing travels faster than snails, including observations that relay only at the pace of blind snails,

would it be possible to snip the speed of light out of special relativity, by replacing every instance of c with speed of snail..? Would special snail relativity work fine in snail universe? Or would the loss of light speed break it?
I am not sure precisely what you are asking but maybe this will help.

Special relativity is summarized via the Lorentz transformation that tells you how to relate distance and time in one inertial reference frame to distance and time in another. The derivation is based on the assumption that the laws of physics are the same in all inertial reference frames and that there is a phenomena that propagates at a fixed speed, call it "x" in all inertial frames. It does not matter what the phenomena is or what the actual speed "x" is so long as it is the same in all inertial reference frames. That gives you the Lorentz transformation with "x" in place of "c". Then you note the experimental fact that light propagates at "c" in all inertial reference frames and you get the usual Lorentz transformation with "c" as the defining parameter. It also follows that there is only one such speed that is invariant with respect to inertial reference frames.

So, in some hypothetical universe if snails traveled at some speed "x" in all inertial reference frames that you would have special relativity with "x" as the defining parameter. It would also follow that light would travel at "x" since only one invariant speed is possible.

7. That answered my questions. Thank you.

Further question: No massive object can travel faster than x?

8. Thanks for the replies.

Would you not say then that in this example due to the restriction of the speed at which light travels, the observed measurements from an observer on Muon A and Muon B are false and not a true indication of the location or speed of the other Muon?

I think I know what Pong means about the snail universe as I've had similar thoughts myself.. It's all dependent on the medium which an observer chooses to measure speed and time and the restrictions imposed by that medium.

If a blind observer with echolocation chooses to use sound to measure the speed at which he is travelling away from an object by releasing a loud clap every second, lets say the rate at which the loud claps bounced off the object and returned to the observer were one every two seconds, then the observer knows that he is travelling at half of the speed of sound relative to that object. Yet we wouldn't say that time had dilated in order to account for the rate decreasing, because a "preferred observer" blessed with optical vision such as ourselves would be there to correct him and reassure him that it's an illusion based on the restrictions imposed by the medium which he chose to measure time.

One can repeat this imaginary experiment at millions of different speeds using millions of different mediums (including snails) and in each case, so long as there is a "preferred observer" to correct the individual, we would be happy to call it an illusion based on the restrictions imposed by the medium chosen to calculate speed and time.

Why should this "illusion rule" change when we get to the speed of light when it seems that the only thing that changes, is the impossibility of a "preferred observer" being present to correct us. This is why I would prefer to go by the computers calculations in my initial thought experiment as it seems to be in a better position to describe the relative speeds and current locations of the two objects, than an observer on either of the objects measuring speed restricted by the speed which light travels.

9. Originally Posted by Mr. Monkey
Thanks for the replies.

Would you not say then that in this example due to the restriction of the speed at which light travels, the observed measurements from an observer on Muon A and Muon B are false and not a true indication of the location or speed of the other Muon?
No. Absolutely not.

It is important to recognize that the effects described in special relativity, such as length contraction and time dilation are NOT any sort of illusion. They are very real, and have been confirmed by experiment -- daily in particle accelerators.

Special relativity is nothing less than a theory of the nature of space and time. It was revolutionary in its day, and still presents us with a picture that is contrary to everyday experience.

The effect of length contraction is NOT due to the optical effects imposed by the speed of light. In fact, what one might "see" or photograph in a relativistic situation is quite different from what actually is, and that is due to the optical effect of the speed of light.

For instance, if one were to observe a circular hoop (circular in a frame at rest with respect to the hoop) passing by at relativistic speeds, the length contraction of the axis parallel to the motion vector would result in a oval. But if you took a photograph it would appear to be circular -- an insight provided by analysis by Roger Penrose and due to the nature of the actual propagation of light rays. So in this case the circularity itself is an optical illusion.

10. No massive object can travel faster than x?

11. Originally Posted by Pong
No massive object can travel faster than x?
Correct, and if you preserve causality neither does information.

12. Pong wrote:
No massive object can travel faster than x?
Correct, and if you preserve causality neither does information.
Doesn't this contradict Janus's initial reply? My understanding from these replies is that a massive object can travel up to almost 2c relative to another massive object, however an observer placed on either of the objects would measure the difference to be less than c.

13. Originally Posted by Mr. Monkey
Pong wrote:
No massive object can travel faster than x?
Correct, and if you preserve causality neither does information.
Doesn't this contradict Janus's initial reply? My understanding from these replies is that a massive object can travel up to almost 2c relative to another massive object, however an observer placed on either of the objects would measure the difference to be less than c.
From the observer, they are moving apart at almost 2c. From one, looking at the other, they are moving apart at less than 1c.

14. Originally Posted by Mr. Monkey
Pong wrote:
No massive object can travel faster than x?
Correct, and if you preserve causality neither does information.
Doesn't this contradict Janus's initial reply? My understanding from these replies is that a massive object can travel up to almost 2c relative to another massive object, however an observer placed on either of the objects would measure the difference to be less than c.
No it does not contradict Janus's initial reply. Neither object is seen as moving at any speed greater than c in any inertial reference frame.

One observer can see each of two massive objects traveling at nearly c in opposite directions. That means that their separation velocity is nearly 2c, but it does not mean that either object is exceediing c or that an observer moving with either object sees the other object as moving at a speed greater than c.

In special relativity, velocities do not simply add or subtract as they do in non-relativistic mechanics.

15. Originally Posted by DrRocket
Originally Posted by Pong
No massive object can travel faster than x?
Correct, and if you preserve causality neither does information.
Yeah, the relay race of snails. To snails observing their universe by touch, nothing travels faster than snail.

And x could be faster than light?

16. Nothing can apparently travel faster than the speed of light relative to another object.If any please let me know.

17. Originally Posted by Lombard
Nothing can apparently travel faster than the speed of light relative to another object.If any please let me know.
Nothing can travel faster than light as mesured in an inertial reference frame.

18. Originally Posted by Pong
Originally Posted by DrRocket
Originally Posted by Pong
No massive object can travel faster than x?
Correct, and if you preserve causality neither does information.
Yeah, the relay race of snails. To snails observing their universe by touch, nothing travels faster than snail.

And x could be faster than light?
it's more, x will just happen to be the speed of light, regardless of what that speed may be.

19. Originally Posted by Pong
No massive object can travel faster than x?
Actually, if "x" is the invariant speed of your universe (speed limit of your universe), then nothing massive can travel at even "x".

20. I forget the name of the book but it gives an example of a relativistic phenomena which i'll try to summarise more concisely:

Observer A and Observer B are sat on a moving train, opposite and facing each other.

Observer A is facing the front of the train while observer B is facing the rear of the train.

Directly between the two observers is a light bulb. When the light bulb is switched on, both observers raise their hands instantly to confirm that they saw the light. Both observers agree that no matter what speed the train is going they raise their hand at the same time.

However, Observer C is on the platform watching the event through the window and sees Observer A raise his hand before Observer B. (because he is travelling towards the light by the time it reaches him it has travelled a shorter distance)

If all observers are "right" in this occasion then does that not mean that there is no universally accepted truth to any event involving electromagnetic waves? Also, and most importantly, does time dilation play a role in this at all? It seems that the lorentz factor is present as the closer we get to the speed of light the greater the "effect". But in trying to understand what the "effect" is, I can't see how it is any more than just the strength of difference in opinion between observers.

21. The basic point is, there is no universally accepted "at the same time." All three observers are correct within their reference frame. Time dilation and length contraction will matter if you're trying to work out the details.

22. Originally Posted by Mr. Monkey

If all observers are "right" in this occasion then does that not mean that there is no universally accepted truth to any event involving electromagnetic waves? Also, and most importantly, does time dilation play a role in this at all? It seems that the lorentz factor is present as the closer we get to the speed of light the greater the "effect". But in trying to understand what the "effect" is, I can't see how it is any more than just the strength of difference in opinion between observers.
It is more than that. There is no universal "truth" in any sense. There is no universal "time" and there is no universal "space". Different observers will disagree on what events are "simultaneous". They will agree on the order in which events occur.

The only things are agreed upon by different observers are those few things that are preserved by Lorentz transformations. And that only applies in special relativity. Things become even more unsettled in general relativity.

What you need to get your head around is that relativity changes the very notions of time and space. Your intuition is based on the Newtonian model of a single fixed space and a constantly flowing "river" of universal time. Einstein showed that to be just plain wrong. There is no universal time and there is no universal space. GR takes that further. There even a single observer has no global notion of either time or space. Those concepts are local, even for one observer. So, there are no reference frames, except local approximations.

The "effect" of the Lorentz transformations is to alter the very notions of time and space as they relate to observers in different inertial reference frames. These differences are not an illusion. They are quite real. Time really does change. Rulers really are different lengths. Yes it is "strange". But it is true.

You won't understand this by limiting your study to what you get on the internet. I suggest that you read the book Essential Relativity, Special, General and Cosmological by Wolfgang Rindler. It is not overly demanding from a mathematical perspective.

23. I'll see if I can get a copy of these books, if you had to pick one of the two which would you pick? Thanks DrRocket.

The basic point is, there is no universally accepted "at the same time." All three observers are correct within their reference frame. Time dilation and length contraction will matter if you're trying to work out the details.

I don't see how time dilation can play a role in this. From Observer C's perspective, why would he prefer time to dilate differently for Observer A, as opposed to Observer B. As they are both undergoing the same amount of acceleration or velocity, but the only difference is its relation to a particular light source and the consequences would be different if we held the same event with a different light source.

Is the concept of a light source essential in explaining any example of time dilation? In the twins paradox for example is it important to nominate a light source at the location where the twins departed?

24. Originally Posted by Mr. Monkey
I'll see if I can get a copy of these books, if you had to pick one of the two which would you pick? Thanks DrRocket.

The basic point is, there is no universally accepted "at the same time." All three observers are correct within their reference frame. Time dilation and length contraction will matter if you're trying to work out the details.

I don't see how time dilation can play a role in this. From Observer C's perspective, why would he prefer time to dilate differently for Observer A, as opposed to Observer B. As they are both undergoing the same amount of acceleration or velocity, but the only difference is its relation to a particular light source and the consequences would be different if we held the same event with a different light source.
The positioning of a light source has no effect on how C determines the time dilation for A or B. For example, in the light-clock experiment, it doesn't matter where anybody is located wth respect to the light clocks, only their relative velocity to them.

Is the concept of a light source essential in explaining any example of time dilation? In the twins paradox for example is it important to nominate a light source at the location where the twins departed?
No, light position is irrelevant.

25. Originally Posted by Mr. Monkey
I'll see if I can get a copy of these books, if you had to pick one of the two which would you pick? Thanks DrRocket.
I only mentioned one book in that post. The title is Essential Relativity, Special, General and Cosmological. The author is Wolfgang Rindler.

There are lots of other books on relativity, but most require a lot more sophisticated mathematics and few cover both special and general relativity. This is a good one at a relatively accessible level.

Originally Posted by magimaster
The basic point is, there is no universally accepted "at the same time." All three observers are correct within their reference frame. Time dilation and length contraction will matter if you're trying to work out the details.

Originally Posted by MrMonkey
I don't see how time dilation can play a role in this. From Observer C's perspective, why would he prefer time to dilate differently for Observer A, as opposed to Observer B. As they are both undergoing the same amount of acceleration or velocity, but the only difference is its relation to a particular light source and the consequences would be different if we held the same event with a different light source.

Is the concept of a light source essential in explaining any example of time dilation? In the twins paradox for example is it important to nominate a light source at the location where the twins departed?
Forget about light sources. You are chasing a red herring. Relativity is a theory of space and time. Light is a bit player.

I think your problem is that you are trying to understand relativity in the context of your experience with space and time. That won't work.

You have to think rather abstractly. There is no such thing as absolute time. There is no such thing as absolute space. Different observers with see time and space differently. One observer's time will be another observer's space.

It is not space and time. It is one thing, space-time. The problem is that to make this clear and precise you need the abstract mathematics of Minkowski space. Rindler's book will get you on the way to understanding this.

26. Originally Posted by DrRocket

I only mentioned one book in that post. The title is Essential Relativity, Special, General and Cosmological. The author is Wolfgang Rindler.

There are lots of other books on relativity, but most require a lot more sophisticated mathematics and few cover both special and general relativity. This is a good one at a relatively accessible level.
Can I ask what you mean by a "relatively accessible level"?
For example, a book that was at "a relatively accessible level" for a maths undergraduate might not be suitable for many another individuals.
I studied maths up to A-level standard at secondary school (12 to 18 years) in the UK, but that was 30 years ago and I was only "reasonable" at the subject then.
Altho' I am interested in this book, and have heard it mentioned by others, I would probably be reluctant to buy if I thought I had to attempt some kind of crash course in university standard maths in order to understand some of the more technical parts.

27. Originally Posted by Halliday
Originally Posted by DrRocket

I only mentioned one book in that post. The title is Essential Relativity, Special, General and Cosmological. The author is Wolfgang Rindler.

There are lots of other books on relativity, but most require a lot more sophisticated mathematics and few cover both special and general relativity. This is a good one at a relatively accessible level.
Can I ask what you mean by a "relatively accessible level"?
For example, a book that was at "a relatively accessible level" for a maths undergraduate might not be suitable for many another individuals.
I studied maths up to A-level standard at secondary school (12 to 18 years) in the UK, but that was 30 years ago and I was only "reasonable" at the subject then.
Altho' I am interested in this book, and have heard it mentioned by others, I would probably be reluctant to buy if I thought I had to attempt some kind of crash course in university standard maths in order to understand some of the more technical parts.
I certainly requires basic undergraduat mathematics and it explains and requires you learn some more mathematics from time to time.

But any serious treatment of relativity will require similar mathematics.

You will have to understand university level mathematics in order to follow any meaningful treatment of relativity, particularly general relativity. There is simply no way of avoiding mathematics, It is the language of physics.

28. Originally Posted by Mr. Monkey
Is the concept of a light source essential in explaining any example of time dilation?
No, For example, let's take the following analogy:

Take a group of people facing in random directions. Ask them to point North. Assuming that they all know which direction North is, they will all point the same direction. If you ask them how far North Minneapolis is of Miami, they will all give the same answer. This is how time was considered before Relativity. It was an absolute everyone could agree on.

Now ask this same group of people to point left. They will all point in different directions. Not only that, but if you ask them how far left is Minneapolis of Miami, they will all give different answers depending on how they are facing. This is how Relativity treats time: comparative measurements of it depend on which "direction"you are facing.

Now let's use this to examine the Twin paradox. Imagine two men on a featureless plane, these are our twins They start at the same point but walk in different directions. the length of each of their paces is equal to the other's. Each judges "time" to advance in the direction they themselves are walking. (each twin can assume that he is stationary while the other is moving.)

After 30 paces, they compare each other's progress. Since each man judges time to advance in the direction he is walking he will note that the other man has not progressed as far in time as he has.(The other twin will have aged less), as he is "behind" him. As long as the men keep walking in the same directions, they will continue to note the other as aging slower. (Each twin sees the other as undergoing time dilation)

Now consider what happens when one of the men changes direction so that he is now walking in a direction that will cause him to intersect the other man's path. (one of the twins changes velocity to head back towards the other)
As he turns, his direction of time turns with him. As a result the other man's position in time changes. (stand in a your room so that a selected object if to the left and slightly behind you. What happens as you turn to your left? The object shifts from being behind you to being in front of you.)

The other man will now be in front. (The other twin will have aged very rapidly to now be older.)

He continues to walk in this direction until he reaches the other man's path. (the traveling twin returns home.)

He turns to walk in the same direction as the other man. ( the traveling twin comes to rest relative to his twin.)

He will note that the other man is still ahead of him, and the other twin will note that he is behind. (both twins agree that the traveling twin aged less. )

So what distinguishes the traveling twin from the stay at home twin is that he made a change in his velocity in order for them to meet up again while his brother did not.

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