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# Relativity and Cosmology

This is a Blog on relativity and cosmology for engineers and the like. You are welcome to comment upon or question anything said on my website (relativity-4-engineers), in the eBook or in the snippets I post here.

Comments/questions of a general nature should preferably be posted to the FAQ section of this Blog (http://cr4.globalspec.com/blogentry/316/Relativity-Cosmology-FAQ).

A complete index to the Relativity and Cosmology Blog can be viewed here: http://cr4.globalspec.com/blog/browse/22/Relativity-and-Cosmology"

Regards, Jorrie

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# Faster than Light Puzzle

Posted September 05, 2007 9:38 AM by Jorrie
Pathfinder Tags: Faster than light Tachyons

In relativity theory, tachyons are hypothetical particles that can only move faster than light (FTL) in every inertial frame of reference. It is also said (quite correctly) that such FTL particles can "arrive 'there' before they leave 'here' and can hence send information back in time, violating cause-before-effect (causality) principles".

Without just quoting the Wikipedia tachyon article, which says that tachyons can't violate causality, what do you think?

Jorrie

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#1

### Re: Faster than Light Puzzle

09/05/2007 11:37 PM

Hi Jorrie, I'm new to this subject and not well informed. I would like to make an observation on TFL particles, particularly the statement that " particles can arrive there before they leave here". As relativity is a problem of observation, I would like to advance the following explanation, or question. This is inspired by the train analogy, where by the train drops off a carriage as it advances, so if you apply this in reverse and say that some particles advance piece at a time waiting to assemble as the others catch up before again advancing. Then to the observer the particle would appear to arrive before leaving, but would in fact be the same particle, advancing piece by piece?

Regards JD

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#2

### Re: Faster than Light Puzzle

09/06/2007 12:56 AM

Hi JD.

What you described is more or less the difference between phase velocity and group velocity. Group velocity ('the center of mass of that train') can exceed c ('the front of the train'), but then, can the center of mass arrive before it even left?

What I'm referring to in the puzzle is 'real' tachyons - hypothetical particles that can do nothing else but move faster than light - and the whole particle or 'train of particles' exceed c.

The puzzle is this: if a tachyon moves at say 2c, then it will take half the time that a photon would take to travel from A to B. Why can one say that it may arrive at B before it leaves A?

Jorrie

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#8

### Re: Faster than Light Puzzle

09/06/2007 9:53 PM

Without getting into specifics of tachyons, let's just consider the general principle of something traveling in excess of the speed of light. Then anyone observing from approximately the direction in which the tachyon was traveling would observe it as though it had arrived before it left its origin. This is because the means of observation would depend on signals traveling at the speed of light or slower.

But wouldn't someone observing from a point at or behind the point of origin observe such a particle as having started at the point of origin and traveled very quickly to the point of destination? Are the suggestions about seeming to travel backward in time supposed to be based in actual observation? Or are such suggestions based on abstract mathematics derived from the theory of special relativity?

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#9

### Re: Faster than Light Puzzle

09/06/2007 10:13 PM

Guest, you asked: "Are the suggestions about seeming to travel backward in time supposed to be based in actual observation?"

Yep, actual observation as defined in Reply #6 above.

"Or are such suggestions based on abstract mathematics derived from the theory of special relativity?"

In order to explain the actual observations, one needs special relativity...

Jorrie

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#11

### Re: Faster than Light Puzzle

09/07/2007 1:37 AM

To enhance understanding of the issue:

Pictured below is a light cone[1] on a Minkowski space-time diagram, with the z-axis suppressed. The red arrow is the 'world line' of a tachyon, lying outside of the future light cone of the observer, meaning it exceeds the speed of light in the observer's frame of reference. It marks two events: event A when the tachyon's coordinates coincide with the origin and event B when the tachyon is detected at coordinates x, y, z, t.

Light-cone1

It is clear that the observer will obtain a positive cΔt for any tachyon measured, even if its velocity approaches infinity. The issue of this thread is: can another inertial observer, moving at sub-luminal speed relative to this reference frame, measure cΔt' as negative in her/his inertial reference frame?

Jorrie

[1] Basic light cone from: http://en.wikipedia.org/wiki/Light_cone

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#13

### Re: Faster than Light Puzzle

09/08/2007 11:55 AM

Jorrie wrote: "The issue of this thread is: can another inertial observer, moving at sub-luminal speed relative to this reference frame, measure cΔt' as negative in her/his inertial reference frame?"

In order to visualize the situation in two different inertial frames, one must plot them on one Minkowski graph. The blue orthogonal axes indicate the reference coordinate frame and the green skewed axes indicate a frame moving at a constant speed relative to the reference frame.

Figure 2:

The red bullets represent two events (A and B) with Δx and cΔt the space and time separations between the events in the blue reference frame. Likewise Δx' and cΔt' are the space and time separations in the green moving frame. It is immediately obvious that in the blue coordinate system, event B happens later than event A, while in the green coordinates, event B happens before event A. This is Einstein's 'relativity of simultaneity' at work and there is nothing contentious about that.

To relate the above to the puzzle of tachyons, let's say event A is the emission of a tachyon and event B is the detection of that tachyon. It is perfectly acceptable in the blue coordinate system, because by definition tachyons travel faster than light, but it still takes a positive time to travel from A to B.

In the green moving coordinate system however, the tachyon detection time is before its emission time.[1] How can this be? Even more puzzling, does this not violate causality? If tachyons exist, could they be used to send information into the past of 'green' observers?

Jorrie

[1] Note that emission and detection times are as recorded on the spot by suitably placed observers who have clocks synchronized in their respective inertial frames by the Einstein synchronization method.

[2] You can read more on clock synchronization in a download from Inertial Movement, a free chapter from Relativity 4 Engineers.

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#14

### Re: Faster than Light Puzzle

09/09/2007 12:29 AM

"In the green moving coordinate system however, the tachyon detection time is before its emission time.[1]"

Sorry Jorrie, but this sounds like so much BS to me! Even if these particles existed, it makes no sense that they could travel backwards in time. Can u show a reference or a test result?

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#15

### Re: Faster than Light Puzzle

09/09/2007 1:39 AM

Guest, you asked: "Can u show a reference or a test result?"

There are some complex treatments in the formal literature, but interesting discussions can be found on the physics forums, e.g. this one on tachyons, esp. post #6. There are no experimental results (yet?), simply because nobody has detected a tachyon so far. Maybe they do not exist in practice...

My questions "How can this be? Even more puzzling, does this not violate causality? If tachyons exist, could they be used to send information into the past of 'green' observers?" point to an apparent paradox and the purpose of this thread is to try and unravel the paradox.

Jorrie

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#18

### Re: Faster than Light Puzzle

09/10/2007 2:06 AM

Jorrie, you said your questions "point to an apparent paradox and the purpose of this thread is to try and unravel the paradox."

I do not think it is an apparent paradox, but a real paradox that proves that tachyons cannot exist, so why bother?

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#19

### Re: Faster than Light Puzzle

09/10/2007 2:25 AM

Guest, you may be right that tachyons cannot exist, but it is possible to show that the idea that tachyons can send information into the past is a 'solvable apparent paradox'.

I have given some clues in post 11 on clock synchronization. Also think about the time zones on Earth and how we synchronize our clocks. If I send a radio signal from London to New York, does it arrive before I send it?

Jorrie

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#20

### Re: Faster than Light Puzzle

09/10/2007 4:39 AM

I wrote: "I have given some clues in post 11 on clock synchronization."

It was actually post 13 that contained the clues on clock synchronization.

"I send a radio signal from London to New York, does it arrive before I send it?"

This does not try to say the situation in inertial frames are the same as time zones, it's just another 'prompt'.

Jorrie

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#21

### Re: Faster than Light Puzzle

09/10/2007 1:42 PM

"...but it is possible to show that the idea that tachyons can send information into the past is a 'solvable apparent paradox'."

OK Jorrie, I take this to mean that tachyons cannot send information into the past.

But how am I to read your original statement: "It is also said (quite correctly) that such FTL particles can "arrive 'there' before they leave 'here' and can hence send information back in time, violating cause-before-effect (causality) principles"."

Together, your two statements highlighted above make no sense. Can you explain?

I also see no connection with the times zones on earth. What was that all about?

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#23

### Re: Faster than Light Puzzle

09/11/2007 1:23 AM

Hi again Guest (if you are the same one!)

"OK Jorrie, I take this to mean that tachyons cannot send information into the past."

This depends how you define 'past'. Every inertial reference frame has a clear past and future with a set temporal order of events. Let's choose any one as the reference frame. Every inertial frame that moves relative to the reference frame has its own past and future definition and its own temporal order of events. Events in the future in the reference frame can be in the past in another frame. Look at Figure 2 again.

Figure 2:

If we believe Einstein and Minkowski, it looks like information could be sent into the past of the green (moving) frame at least. The issue is, could observers in the green frame make use of this information coming from their future?

Take into account that the same observer (of either frame) cannot be present at both events A and B (the sending and the detection of the hypothetical tachyon), because they cannot travel faster than light.

"I also see no connection with the times zones on earth. What was that all about?"

I used this 'foot in the mouth' to make readers think about how different observers can have different times on their clocks. It is clear from the figure that there are differences between the clock readings of the two frame along their respective x-axes.

Say we set the clocks at the coinciding origins to momentarily read the same time in both frames. If the relative speed of the two frames is 0.6c, then at a reference frame x-coordinate of 5 light-seconds the green frame clock momentarily in that same spot will be set 5 x 0.6 = 3 seconds ahead of the blue clock in that position. This is due to the Einstein clock synchronization method.[1]

Jorrie

PS: I hope you can tolerate me for not giving my full reasoning, but just clues. I would like to see a few more ideas...

[1] As referenced before, it is available from Inertial Movement.

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#24

### Re: Faster than Light Puzzle

09/11/2007 2:00 AM

Ok, to sum it up, it seems that there is no practical objective achieveable here in sending information into the past, only theoretical.

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#25

### Re: Faster than Light Puzzle - Solution?

09/11/2007 10:40 PM

Hi David.

You wrote: "... it seems that there is no practical objective achievable here in sending information into the past, only theoretical."

Yea maybe, but consider this, especially the closing paragraph.

In the puzzle it was stated about tachyons: "It is also said (quite correctly) that such FTL particles can "arrive 'there' before they leave 'here' and can hence send information back in time, violating cause-before-effect (causality) principles."

The "(quite correctly)" qualifier is not quite valid for the last part of the statement, i.e. "violating cause-before-effect (causality) principles. It has been shown that "arrive 'there' before they leave 'here'" is possible simply due to the way clock are synchronized in frames moving relative to one another, as was shown in figure 2, repeated here for ease of reference (for the 2nd time in this thread!):

Figure 2:

The figure shows a green coordinate system (x',ct') moving at v=0.6c relative to a reference coordinate system x,t. The blue and green x-axes are the lines of simultaneity for each coordinate system. Clocks along each axis are synchronized by sending a light signal from the origin at time zero and each clock is set to read a time equal to the clock's x-coordinate divided by the speed of light.

It is clear that, apart from at the origin, the clocks along the green x'-axis will not agree with the readings of the clocks along the blue x-axis when they pass each other. If the spatial distance A to B is 5 light-seconds, the green clocks passing event B at any time will be set 0.6 x 5 = 3 seconds behind the blue clock at that instant (the equation of the x' axis is: ct= vx/c). This is in line with Einstein's synchronization of clocks principle.[1]

A tachyon is 'fired' at the joint origin of the two coordinates systems (event A) and travels at a speed vt=4c relative to the reference frame, until it is detected at event B. In the blue (reference) system, the tachyon will take 5/4 = 1.25 seconds to travel the 5 light-seconds to reach event B. The green observer that passes event B will read 1.25–3 = -1.75 seconds. Conferring with the green observer at A, they conclude that the tachyon arrived at B 1.75 seconds before it was fired at A, as read off their respective clocks.

Does this mean that something 'from the future of the green observer' has arrived at B? Not quite. It was simply a matter of clocks synchronized using the speed of light, which means that if a tachyon travels faster than light, it will appear as if the detection happened before the transmission of the tachyon.

Further, the transmission and the detection happened at different observers in different places. Violations of cause-before-effect (causality) can only happen when a single observer can receive signals that it has not yet sent. This is not demonstrated in this thought experiment.

With 'real' causality violations ruled out (I hope) it leaves another question: if tachyons exist, can they be used for transmitting information faster than light?

Jorrie

[1] As before, the Einstein method of clock synchronization is discussed fully in Relativity 4 Engineers. The relevant chapter can be downloaded from Inertial Movement.

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#26

### Re: Faster than Light Puzzle - Solution?

09/11/2007 11:04 PM

Jorrie, this was smooth, but perhaps too smooth. Consider this change to your figure 2:

Let the tachyon travel at infinite speed - this is allowed, not so? Event B will now sit on your blue x-axis, meaning no time has passed in the blue frame. Let the tachyon be sent back towards the origin, but this time by the green frame, also at infinite speed. The tachyon will now move from the blue x-axis left-down at the same slope as your green dotted line.

According to your equation for the x'-axis, the line will cut the blue time axis at -3 seconds. Does this mean that the blue observer can detect the tachyon 3 seconds before sending it?

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#27

### Re: Faster than Light Puzzle - Solution?

09/12/2007 1:08 AM

Hi Guest.

"According to your equation for the x'-axis, the line will cut the blue time axis at -3 seconds. Does this mean that the blue observer can detect the tachyon 3 seconds before sending it?"

Do you mean like this?

Figure 3:

If there was a green observer at event C (the detection of the return tachyon), she would have recorded the arrival time as -3 seconds. However, if she took a simultaneous peek at the blue clock, she would have noted that it read 0 seconds when the tachyon arrived. Can you work out why?

Jorrie

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#28

### Re: Faster than Light Puzzle - Solution?

09/12/2007 5:39 AM

Jorie, your "However, if she took a simultaneous peek at the blue clock, she would have noted that it read 0 seconds when the tachyon arrived." just don't want to gel with me.

As I understood your figure 2, the blue and the green frames' clocks were set to agree at the origin, so how can they now differ there? If the blue clock at A reads zero, then the green clock must also read zero.

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#29

### Re: Faster than Light Puzzle - Solution?

09/12/2007 6:56 AM

Guest, you stated: "If the blue clock at A reads zero, then the green clock must also read zero."

I assume you mean the green clock at event C, right?

Figure 3:

First check what a green clock that passes event B of figure 3 will read. It must read -3 seconds, similarly to the green clock of figure 2 that read 1.75 seconds in reply #25 above. Now, all the green clocks on the returning tachyon's arrow must read the same, because it's a line of simultaneity, so the green clock at event C reads –3 seconds.

Similarly, the blue clock at event B reads zero and so does the blue clock at event A, because they are on blue's line of simultaneity. This is to be expected - after all, you said the tachyon is infinitely fast, which is apparently possible...

Got it?

Jorrie

PS: this whole tachyon business tends to bend one's brain a bit. It's however good exercise in using Minkowski space-time diagrams.

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#30

### Re: Faster than Light Puzzle - Solution?

09/12/2007 7:41 AM

OK, I see, thanks Jorrie.

I suppose the blue event C in your figure 3 represents a green clock then?

I agree with the brain-bending bit. One may ask: what practical use may this have? I see you started a new thread on FTL communication with tachyons. That sounds more promising.

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#31

### Re: Faster than Light Puzzle - Solution?

09/13/2007 2:50 AM

"I suppose the blue event C in your figure 3 represents a green clock then?"

Oops, yea, it may be confusing - should have made those labels at C green.

One must remember that the way it is drawn, with blue as the reference frame, it is the blue observer at A that takes a peek at the green clock at C, just as the tachyon arrives at blue's spatial location.

"I see you started a new thread on FTL communication with tachyons"

Some guest (yourself?) has pointed there to a Wikipedia article that says the detection of tachyons may be impossible due to spurious emissions of tachyons. If correct, it would make the thought experiment of this thread pretty meaningless...

Jorrie

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#3

### Re: Faster than Light Puzzle

09/06/2007 6:40 AM

And, good Friar Jorrie, how many angels can dance on the head of a pin?

bobguz

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#4

### Re: Faster than Light Puzzle

09/06/2007 7:16 AM

is it by observation? one is still receiving the light (photons) indicating that the tachyon is still in its starting position of A, even though it has already traveled to B and the light indicating its arrival at B has yet to be received?

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#6

### Re: Faster than Light Puzzle

09/06/2007 8:28 AM

Architect3451 wrote: "is it by observation?"

Yes, but the most straightforward way is to have a hypothetical "tachyon transmitter" at the start point and a "tachyon detector" at the arrival point, with clocks that are synchronized in your inertial frame of reference. The clocks record the departure and arrival times of a tachyon bundle. Then one can check if the arrival event occurred before the departure event.

Jorrie

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#5

### Re: Faster than Light Puzzle

09/06/2007 7:51 AM

Hi Jorrie, Then we are saying that a train travelling along a rail line as a group represents a centre of particles or photon moving linearly at the speed of light, and the phase is the passing of any group monitored from a single point such as trains passing through a station at a frequent interval, but a hypothetical tachyon is a train or object that arrives at the next station before its left the previous one? And is clearly identifiable as the same train or object. So I would like your opinion on a further observation. As photons move through space from their point of origin, and referring to the train analogy, we consider each carriage as moving under its own power and at a slightly different angles, then over a period of time they would disperse sideways while becoming less dense from front to back. The question is do the photons evenly space themselves, is there a force of distribution that regulates the density, so any observation at a station would see trains of the same length passing, the hypothetical question then is, if such a force exists are tachyons accelerated to the front of the queue?

JD

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#7

### Re: Faster than Light Puzzle

09/06/2007 8:38 AM

Hi again JD.

I'm not sure I understand your question and how it relates to tachyons (which are not related to photons). They have imaginary rest mass, where photons have zero rest mass.

By their definition, tachyons will always 'outrun' photons. The puzzling question is: can they appear to be moving backwards in time?

Jorrie

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#10

### Re: Faster than Light Puzzle

09/07/2007 1:32 AM

If I were watching a tachyon take off from a distant location with a telescope, I would feel the tachyon hit me before I "SAW" it reach me. Yes, it would "appear" to move backward in time compared to what my eyes and body perceive, but only because my eyes can't see past the speed of light. Without light, it would be dark from my point of view.

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#12

### Re: Faster than Light Puzzle

09/07/2007 6:50 AM

Hi David

"... I would feel the tachyon hit me before I "SAW" it reach me."

True, but remember that observing and seeing are not equivalent in science. To know the speed of a tachyon, one must time its travel over a certain distance. If light is used to announce the passing by of the tachyon to a distant observer, the travel time of light must be subtracted to get the coordinate times of the events.

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#16

### Re: Faster than Light Puzzle

09/09/2007 1:47 PM

I'm in unfamiliar territory with this, but how can you see a tachyon take off using a telescope when a tachyon travels faster than a photon.

In an experiment, the measurement can not be done visually.

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#17

### Re: Faster than Light Puzzle

09/10/2007 1:11 AM

In reality, it can't be done at all. tachyons do not exist. They are theoretical particles. The statement I made was correct, but hypothetical. I made it to show a point.

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#22

### Re: Faster than Light Puzzle

09/10/2007 3:29 PM

Jorrie -

Your blogs and posts are SO interesting! I could spend all day reading them. One of these days you're gonna get me fired. (Of course, that WOULD give me more time to read!)

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#32

### Re: Faster than Light Puzzle

09/26/2007 4:19 PM

Trick question.

-you are observing a departure at the speed of light

-You are observing the arrival at the speed of light

Regardless of how fast the tachyon travels it will always take time to travel.

If the observer is somewhere in between the visual line of sight to the start and finish will always be farther then the direct line of travel taken by the tachyon.

The observer will always see the event after it happened. (both the start and completion) By injecting the observer (Operating at the speed of light) and a reference speed of light from the start to the finish into the math, you are only creating a circular math equation

The circular math compares the speed of light travelling from both the start and finish to the speed of the tachyon. Since your reference is the speed of light . The math truly only proves the tachyon is travelling faster than the reference (speed of light) which is what you started with.

Reality check!

A more realistic analogy of faster then light travel times is as follows:

It takes 10 minutes for light to travel from the sun to the earth at the speed of light.

If the sun radiated a tachyon at 2X the speed of light it would take half the time (5 minutes) If the tachyon was 1000 X faster then the speed of light it would take 3.6 seconds. Even approaching infinity it never reaches instantaneous or negative.

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#33

### Re: Faster than Light Puzzle

09/26/2007 9:45 PM

Hi Techno.

You are right, as I also pointed out in post #25 above. It is only the way clocks are set and synchronized in relatively moving frames that creates the illusion of tachyons arriving before they left.

Jorrie

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#34

### Re: Faster than Light Puzzle

03/23/2008 4:02 PM

I want to know how you intend to measure real tachyons? It seems fairly problematic to me since they are imaginary (in our slower than light universe) and may pass through most known energy detectors without effecting them. It seems that detecting them may be a problem related to positionality. Is there a way to detect them without having to know that they might be arriving, a way of randomly detecting them? How would you go about building such a detector?

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#35

### Re: Faster than Light Puzzle

03/28/2008 10:26 AM

Hi guest. Since tachyons are hypothetical, I suppose the detector is also hypothetical!

If tachyons exist, they must have finite mass/energy and I suppose if one can make them interact with ordinary matter, one can detect them that way. They cannot be stopped though, since for them to stop they must pass the speed of light from the other side and that will release infinite energy - hence impossible.

More than that I do not know.

Jorrie

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#36

### Re: Faster than Light Puzzle

03/29/2008 6:55 PM

Okay then Jorrie, is was just wondering if tachyons might have different influence on different types of matter or conventional energy, for that matter, regarding the passage of time? Do you think this might be possible? If so, can a device be built that could take advantage of the differences to measure the presence of tachyons? How might such a device be built?

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#37

### Re: Faster than Light Puzzle

08/24/2008 11:05 AM

You don't need to introduce hypothetical tachyons into this puzzle, use the real phenomenon of quantum entanglement. The speed of information between entangled particles is infinite and instantaneous. This fact can be used in any of the clock synchronization paradoxes to yield real results.

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#38

### Re: Faster than Light Puzzle

08/25/2008 7:22 AM

Hi ralfcis, welcome to the Forum!

You wrote: "You don't need to introduce hypothetical tachyons into this puzzle, use the real phenomenon of quantum entanglement. "

Only problem is that no information can be sent by entangled pairs. The very act of reading the information destroys it.

Jorrie

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#39

### Re: Faster than Light Puzzle

08/25/2008 11:45 AM

You are correct but bear with me while I try to work quantum cryptography into this. Say you synchronize two clocks. They each produce a data stream which contains their time info. You then encrypt the data stream with an XOR gate with the random sequence from two entangled particles. The random sequence is instantaneous no matter how far apart the clocks are. You perform your relativity experiment and then analyze the results. Since you know the data stream from each clock should be identical because you synchronized them, and since quantum entanglement is independent of the speed of light, any differences you see when you decrypt and compare the two data streams later on should produce results which are independent of the effect of observation and the limit of the speed of light to transfer information. No?

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