Speeds greater than the speed of light

[yuiop]

When you used both “Bob's point of view” and “Alice's point of view” as reliable to judge distant event synchronizations (causality) you did not just define a preferred frame, you used two of them!

It is not a case of defining a preferred frame. That is sort of the whole point of relativity. there is no preferred frame. I used two frames to describe the situation from different view points and I could have used an infinite number of different frames. Being able to describe a situation from any number of arbitary reference frames is the same as having no preferred frame.

When
As I said before; You need to be much more detailed:
Care to explain exactly when and where in the Alice's frame Bob was when the 2c FTL message was sent and recieved?
And exactly where and when was Alice in Bob’s frame when she sent it and when he received it to return a #C FTL reply?
How fast are Alice and Bob moving wrt each other and is that towards each other or apart?

I mantioned in the first post with the diagram that Bob and Alice are moving away from each other at 0.9c. The rest of your questions are answered in this updated diagram.

http://img383.imageshack.us/img383/4903/superluminal2zn9.th.gif

Note that observers in Alice's frame do not agree with a lot of things that observers in Bob's frame measure and vice versa. That is the failure of simultaneity of space-like events.

Only “c” appears to be the same in all frames; how fast is the c2 signal measured in Bob's frame and how fast is the 3c signal when measured in Alice’s frame?

In Bob's frame Alice is moving at -0.9c (right to left) and by the velocity addition formula her query signal of +2c (left to right) as measured in her frame, is 1.235c (left to right) according to observers in Bob's frame.

Note that the sign of the velocity does not tell you whether the signal is going forward or backwards in time but only tells you whether it is going left or right.

In Alice's frame, Bob is moving at +0.9c (left to right) and by the velocity addition formula his reply signal of -3c (right to left) as measured in his frame, is -1.375c (right to left) according to observers in Alice's frame.

Note once again the negative signal velocity in itself does not imply backwards in time but only give direction (right to left).

To determine the order of events, the time intervals have to be calculated using the Lorentz transformations as demonstrated in https://www.physicsforums.com/showpost.php?p=1947893&postcount=17".

Exactly what established the foreword and backward time changes you are plotting if not some frames of reference?

The Lorentz transformations establish the forword and backward time changes.

What do you change that would have caused Bob’s replies to have come further in the future than of all Alice’s questions and responses to his replies.

If Bob is at rest with respect to Alice or if Bob is going towards rather than away from Alice, then Alice would receive the replies after the queries (normal time order) even with superluminal signal speeds.

However, I don't think that is exactly what you are asking and it hard to interpret what you mean. Could you rephrase it using normal syntax?

Also, "Bob's replies" is a vague. There are two events involved in a reply, namely, Bob sending a reply and Alice receiving Bob's reply. If you mean that Bob sending a reply is in the future of Alice receiving the reply then that is entirely subjective. There is no way to determine if one event is in the future or past of another event in any absolute sense, if those two events are space-like separated.

 

[RandallB]

It is not a case of defining a preferred frame. That is sort of the whole point of relativity. there is no preferred frame.

But you diagramed two frames with causality lines over a distance. And then selectively used both of them for different parts of a single solution to create time travel as you pleased – a double error as I said before.

I used two frames to describe the situation from different view points and I could have used an infinite number of different frames.

Fine use the velocity addition formula to create a third frame in the middle with A and B frames moving away from it at the same speed in different directions.

Being able to describe a situation from any number of arbitary reference frames is the same as having no preferred frame.

That does not mean you get to generate multiple frames, use one some of the time and another for another time interval to assume whatever you want about how time at a distance is behaving.
The requirement is to solve the entire problem IN COMPLETE DETAIL as in real numbers not just lines. From beginning to end in just one reference frame (not using two frames at the together as you are doing); including using Lorentz transformations to define Where and When each event happened in the location and time coordinates of the other two frames.
Then pick another frame and do the same again.
And since you claim you can do it with any number of arbitrary reference frames do it for a third as well.

Only if all three frame views each give the same results for all three frame coordinate times and locations for each event can you claim to have a solution that all frames agree on.

That means real numbers, not just a line that says “time goes backwards here”.

If you can show that a “reply” arrives at Alice before Alice sent it; Then you have to be able to show When and Where Bob was in each Ref Frame: 1) When Bob received it and replied [One event] 2) When Alice sent it. 3) And when Alice received the reply

You have not offered anything like that.

And the simultaneity rule makes it clear you cannot. If there is a preferred frame there can only be one, you cannot use two frames at the same time as if they were both preferred. You don’t need FTL signals to establish synchronized clocks in one frame and have SR show a second frame synchronized clocks out of sync indicating forward or backward time events. Any Twins problem will do that.
Simultaneity does not say you can pick the one you like; Simultaneity says you cannot trust anyone of the time lines as correct for defining causality.

Uses real numbers and do the math, you will get stuck soon enough.

 

[gdsandkes]

Is that not exactly what is postulated in inflationary theory in cosmology, in an attempt to explain the observable universe?

 

[yuiop]

And the simultaneity rule makes it clear you cannot. If there is a preferred frame there can only be one, you cannot use two frames at the same time as if they were both preferred.

Yes, IF there is a preferred frame... , but the first postulate of relativity clearly states there is NO preferred frame.

Uses real numbers and do the math...

I did, in post#17 and I note that you have not done any.


Look at it another way.

Let's assume, a priori for the sake of argument, that Alice sends a superluminal signal to Bob and Bob sends a reply traveling backwards it time to Alice. This is all in Alice's frame. Now switch to Bob's frame. We now see that what was a superluminal signal in Alice's frame has become a backwards in time signal in Bob's frame. The reply that was a signal going backwards in time in Alice's frame becomes a superluminal signal going forward in time in Bob's frame.

It should become clear to you that superluminal signalling and signalling backwards in time are two sides of one coin. They go hand in hand. If you have one then you have the other. If you don't have one then you don't have either. The most likely option is the latter because superluminal signalling and time travel have never been observed and if they did exist, the paradoxes are unresolvable.

 

[RandallB]

Is that not exactly what is postulated in inflationary theory in cosmology, in an attempt to explain the observable universe?

?
Explain what you mean by “that”
And what is “what is postulated in inflationary theory”
I have no clue what you are talking about,
This is a SR issue AFAIK not a Big Bang one.

 

[gdsandkes]

I am responding to the original question in this thread "speeds greater than the speed of light"

 

[DrGreg]

RandallB, there's nothing wrong with kev's argument. You cannot insist on considering a single frame only; we have to consider multiple frames in order to use the principle that all frames are equally valid. An argument that relied on a single frame could not be a relativistic argument.

You demanded some real numbers, so here goes (and let's hope I haven't made an arithmetical error!).

Let's consider Alice and Bob moving apart at speed v=4/5 (in units where c=1), so that $\gamma = 5/3$ and $\gamma v = 4/3$.

In Alice's frame consider the three events E, F, G given by

$$(t_E, x_E) = (0, 0)$$
$$(t_F, x_F) = (12, 48)$$
$$(t_G, x_G) = (-21, 0)$$​

Note that events E and G both occur at distance zero from Alice; Alice experiences both events directly and the elapsed time of 21 seconds between them is Alice's proper time, measured by a single clock. Therefore all observers unambiguously agree that event G occurs before event E.

Bob moves at speed 4/5 in the positive x direction, synchronising his clocks and distances to zero at event E. So, applying the Lorentz transform

$$t' = \gamma(t - vx) = \frac{5t - 4x}{3}$$
$$x' = \gamma(x - vt) = \frac{5x - 4t}{3}$$​

we measure the 3 events in Bob's frame as

$$(t'_E, x'_E) = (0, 0)$$
$$(t'_F, x'_F) = (-44, 64)$$
$$(t'_G, x'_G) = (-35, 28)$$​

So far so good. No mention of signalling or velocities, just a slightly painful* exercise in the Lorentz transform for 3 events.

Now, in Alice's frame, if a signal were to travel from E to F, it would travel forwards in time (according to Alice) at a speed of 48/12 = 4c, faster than light. And in Bob's frame, if a signal were to travel from F to G, it would travel forwards in time (according to Bob) at a speed of (28 - 64) / (-35 + 44) = -4c, faster than light. (The minus indicates the direction of travel.) But now we have sent a message from E to F to G, and G occurs unambiguously (absolutely) before E.

What did we assume above?
(a) that a signal could travel at 4c relative to Alice in the + direction
(b) that a signal could travel at 4c relative to Bob in the - direction
(c) that the Lorentz transform is valid.

If you accept all the above assumptions are true, then I have shown how to send a message backwards in time. If you think that's impossible then at least one of the assumptions above must be wrong. (And I could have picked different numbers for any speed greater than c instead of 4c.)

If you think (a) could be true but (b) could be false, that would be to deny the principle of relativity: the laws of physics should be the same for both Alice and Bob. If you believe in relativity and also believe in causality, then both (a) and (b) must be false.

_______
*More painful for me than for you, because I had to work backwards from my objective of getting 4c for the answer!

 

[RandallB]

RandallB, there's nothing wrong with kev's argument. You cannot insist on considering a single frame only; we have to consider multiple frames in order to use the principle that all frames are equally valid. An argument that relied on a single frame could not be a relativistic argument.

What is “the principle that all frames are equally valid”.
I’ve never seen, or used it. Who declared it? how did they justify it? and
when did the science community acknowledge it in peer reviewed publication?

I do not “considering a single frame only” at all.
I reject relying on even one frame as correct in SR.
Because SR simultaneity is clear that you can not declare synchronized clocks as simultaneous. In SR synchronized and simultaneous are two different things and no one (or Two) reference frames can resolve that in SR.

" ... I had to work backwards from my objective of getting 4c for the answer! "
And yes I can see you worked backwards from only the detailed answers that support you objective without giving any of the details I asked for.
IF “all frames are equally valid” then pick any two additional frames and see if you can them to give same amount of time causality error. Since kev was already indentifying how to pick frames that would show a forward rather than backward time causality error, how could they be “equally valid”?

 

[yuiop]

What is “the principle that all frames are equally valid”.

It is usually know as the 1st postulate of relativity that is usually paraphrased in casual terms as "the laws of physics are the same in all inertial reference frames".

I’ve never seen, or used it. Who declared it?

Einstein.

how did they justify it?

By showing that the implications (predictions) of making that assumption (postulate) agreed with actual experimental results better than Newtonian predictions.

and when did the science community acknowledge it in peer reviewed publication?

.. I can not give it an exact date, but the world at large accepted Einstein's Relativity Theories in 1919 when Eddington's observations of an eclipse confirmed Einstein's predictions over Newton's. The scientific community accepted his theries much earlier when it explained the null MMX result and the "anomalous" precession of the perihelion of Mercury.

 

[gdsandkes]

Then according to E=Mc2, if you increase the speed of light then you violate the equation, (unless you alter the total mass and/or energy)

Thus my question about inflation in Cosmology.

 

[RandallB]

What is “the principle that all frames are equally valid”.

It is usually know as the 1st postulate of relativity that is usually paraphrased in casual terms as "the laws of physics are the same in all inertial reference frames".

Einstein.

kev this is old ground. Just repeating old errors is not helpful.
We already covered the “special principle of relativity” by Galileo from 1639 and that it became part of SR.
That has nothing to do with how you are applying “all frames are equally valid” in defining events based on their synchronized clocks – regardless of what other frames say.

Fact is Einstein showed that this is not true with SR! That is the whole point here.

Sure that could mean SR is “incompatible with the first postulate” (oh no what to do?)
Except the first postulate does not mean all inertial frame have the same “classical laws” it says they all use the same laws of physics; And SR comes with an addition Law, Rule, whatever you want call it.

And that is the Simultaneity Rule where NO FRAME CAN BE TRUSTED to define any from of absolute measure of simultaneous only synchronized clocks that can give the appearance of distant simultaneous events but only in the view of that frame no others.

Is that the same in all frames,
YES because no frame is allowed to define simultaneous events as real!

And you cannot define Backwards time without picking using a frame or two or three or four all defining their own version simultaneous events in synchronized clocks giving multiple versions of different absolute times.
Which you keep doing demanding to do in violation of SR Simultaneity, so whatever your doing it is not based on relativity.

Down side of Simultaneity;
since the rule says no frame can be trusted to absolutely define separate events as simultaneous, then a the Newton idea of absolute time, cannot be supported.

Physics is currently based on not using Newton absolute time. Other than appling Simultaneity as I've discribed it, just how did science come to abandon Newton absolute time?

gdsandkes
This issue here has nothing to do with GR, BigBang, inflation e=mc2 or Cosmology. It is just a matter of correctly using the SR Simultaneity Rule.

 

[rbj]

The trouble is that if you change the the c in the Lorentz factor to to 1/2c then the Lorentz gamma factor becomes:

$$\gamma = \frac{1}{\sqrt{1 - 4\frac{v^2}{c^2}}}$$

rather than the usual

$$\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$$and time dilation and momentum measurements made in particle accelerators every day would not agree with the equations, so that new equation would not represent the physical laws of the universe we live in.

kev, keep in mind that any physical measuring instruments in any particle accelerators or anything anywhere/anytime, that in all of these measurements, what is essentially being measured are dimensionless quantities. you never measure a length or a time by itself apart from some other reference (tick marks on your meter stick or ticks on your clock). no measurement of c is made without reference to some other velocity. it is only the dimensionless ratios of these like-dimensioned physical quantities that matter, in the final analysis. this, plus the fact that the speed of light (or some other EM radiation) can be so handily used in a lab along with a good (cesium) clock to define the meter as a unit length such that c is defined to be 299792458 m/s.

so what you're saying about changing c to c/2 is just non-sensical. even if you were a some kinda god-like being with access to the control knobs of nature and changed it (in some manner so that you would know the difference), it would still be c to us mortals that are governed by physical reality and we would not know the difference (unless some dimensionless "constant" like $\alpha$ changed, and then the net essential issue is that $\alpha = \frac{e^2}{\hbar c (4 \pi \epsilon_0)}$ changed and which of the dimensionful factors inside of it that changed ($e \ \hbar \ c \ \epsilon_0$) is only a matter of how your units of measure are defined. and nature doesn't care which units we use. so the it doesn't matter and a changing c is meaningless. could just as well be a changing $\hbar$.

may i suggest looking at:

Comment on time-variation of fundamental constants

Trialogue on the number of fundamental constants

 

[DrGreg]

What is “the principle that all frames are equally valid”.
I’ve never seen, or used it. Who declared it? how did they justify it? and
when did the science community acknowledge it in peer reviewed publication?

kev has already answered that.

I do not “considering a single frame only” at all.
I reject relying on even one frame as correct in SR.
Because SR simultaneity is clear that you can not declare synchronized clocks as simultaneous. In SR synchronized and simultaneous are two different things and no one (or Two) reference frames can resolve that in SR.

" ... I had to work backwards from my objective of getting 4c for the answer! "
And yes I can see you worked backwards from only the detailed answers that support you objective without giving any of the details I asked for.
IF “all frames are equally valid” then pick any two additional frames and see if you can them to give same amount of time causality error. Since kev was already indentifying how to pick frames that would show a forward rather than backward time causality error, how could they be “equally valid”?

To clarify what your position is:

Do you accept the logic that if (a) (b) and (c) were all true in post #42, then a message could be sent, unambiguously and absolutely, backwards in time?

- If no, which part of the logic do you not understand?

(i) Do you accept that all observers agree that G occurs absolutely before E? If not, what criterion would you accept to prove one event occurs absolutely before another?
(ii) Do you accept that if a signal can travel at 4c relative to Alice it can travel from E to F?
(iii) Do you accept that if a signal can travel at 4c relative to Bob it can travel from F to G?​

- If yes, is the sticking point that you think (a) could be true while (b) is false?

What are the "the details you asked for" that I haven't provided?

 

[Kopachris]

I don't know if this has already been said or not:

Nothing with mass can travel faster than the speed of light. Einstein postulated that as the velocity of an object increases, so does its mass. As said object approaches the speed of light, the mass approaches infinity. At the speed of light, any object with any positive non-zero rest mass would have infinite mass and so it would require infinite energy to accelerate it. There are many phenomena that appear to "break" this rule, but no particles are actually traveling faster than local c.

There is a loophole, however. Objects cannot travel faster than light, but spacetime can. Theoretically, if one could create a pocket of spacetime around a spaceship and get it moving faster than light, it would carry the spaceship with it without breaking any laws. There wouldn't even be any problems with time-dilation or the crushing effects of accelerational g-forces. Lookup "Alcubierre Drive" on Wikipedia for more info.

 

[RandallB]

Oh Good Grief!

kev has already answered that.

Not with a valid or logical answer.

Do you accept the logic that if (a) (b) and (c) were all true in post #42, then a message could be sent, unambiguously and absolutely, backwards in time?

Of course not – to borrow a coined phrase post #42 is just silly, much more so than von Neumann's silly mistake (ref: J Bell)

Do you accept that all observers agree that G occurs absolutely before E?
If not, what criterion would you accept to prove one event occurs absolutely before another?

With the rather obvious flawed logic in #42, of course not.

Since SR simultaneity makes it clear that no ref frame of synchronized clocks can be trusted to define its “simultaneous” clock times as an accurate reference of simultaneity with which to define causality, within the limits of SR I am willing to accept the “apparent simultaneity” (and resulting causality standard) defined by A REFERANCE FRAME.

But unlike you and kev, because I accept the simultaneity rule, I will only accept an analysis based on a standard built only within a single reference frame.

What are the "the details you asked for" that I haven't provided?

I asked details like when and where Bob claimed remote locations were at the event times for “E” and “F”.

You set the time standard as the Alice frame where Alice0 and Bob0 both have the time as t=t’=0 (Alice0 kind of likes Bob0).
- And far ahead you have Alice48 waiting for Bob0 to be coming her way at the “simultaneous” time of t=0 and reports that Bob80a (‘a’head of Bob0) is with her NOW.
- Also, both Alice48 & Bob80a can confirm that t’=-64 is on Bob80a’s clock.
Alice48 is waiting on Bob48a for a date, but he seems to be late, he must have a slow clock just as Bob80 does!
But Bob0 backs up his guy and tells Alice0 that Alice48 just cannot read her own clock and doesn’t know what real time is. (Alice0 frowns at his comment about one of her girls)

Still on your standard:
At t=12 for Alice0 and Alice48 with the 4c FTL signal reaching Alice48 (and returned at some new FTL speed) she is being visited by Bob64a who shows a time of t’= -44 claiming it’s the correct ‘real’ time.
- - Simultaneously Alice0 is visited by BOB16b (‘b’hind Bob0) claiming the correct time is t’=20 and saying her view of Time being defined by t not t’ is flawed.
Alice0 protests and puts a call out for “Where is Bob0”
– Alice9.6 (also at t=12) reports that Bob0 is with her and he claims that the real time is t’=7.2 and "we girls are all nuts" for thinking our time t is a standard for causality and simultaneity!
“Laired” declares Alice0, “kick them all to the curb girls - tell them to move on.”
(no wonder all the Bob’s are ‘moving on’ at 0.8c, bad news for Bob48 & that date)

But after you set the standard of using Alice0 and her girls t time as correct for "real" time;
you and kev decide to “ditch the witch” and switch to side with the boys!
- But only after establishing as “real” the time 12 for event F, and also including to use as "real" the boys claim of a "real" time of -44!
That is using two times as "real" for one event!

You have yet to rationally justify doing that!
- This is not just some twin moving from one frame to another frame; but continue to analyze both twins from the view of just one ref frame.
You are changing the frame by which you claim to analyze reality; from t & x to t’ & x’!

Nowhere in SR is there a rule that allows you to make such a change of view, and use two frames of reference to set two standards for what is "real"!

Depending on how the return speed of the FTL signal is defined – I am willing to continue with you in this problem:
but only in the Alice frame you started with.
There you could find the return signal reaching Alice0 at t=21 with her being visited by Bob28b at t’=35.

So unless you can provide a justification for arbitrarily changing the “real” time standard from t to t’ you are not following the SR rules.
To be sure, I am not implying that Alice is using the correct frame to define “real”; only that SR simultaneity will permit and tolerate the use of a single frame as defining the standard for “real” to work though a problem; but never can two frames as you use them by applied as if both could define a standard for real. The conflict between the boy and the girls here is why and how the SR simultaneity rule was established by Einstein in the first place!

You should redo the problem in only the t’ frame with Bob0 chasing after the signal.
If you do all the math with the extra detail you should be able to demonstrate for us how the when and where the FTL signal will return passing Bob0 to reach Bob28b.
By showing the simultaneous clocks in the Bob frame setting the standard for “real” the various Alice reading will become unrealistic and Bob and his guys will show a forward in time causality.
– that is if you willing to do the math with the extra details without making a faulty assumption just to reach a preplanned result.

[Take your time, so you can check your work; I’ll be out of touch for awhile until likely after Thanksgiving]

 

[Austin0]

Hi Jake ( and welcome to PF )

I am using coordinate notation such that (x,t) is (distance,time)

Alice's frame (S)

Event A: Alice sends a superluminal signal at (0,0)
Event B: Bob receives the superluminal signal at (10,5)

The signal travels 10 lightseconds in 5 seconds (2c) in Alice's frame.

Bob's frame (S')

Event A' = (0,0)
Event B' = (x',t')

Using the Lorentz transformation

$$x^{\prime} = \gamma (x - vt)$$

$$t^{\prime} = \gamma \left( t - \frac{vx}{c^2} \right)$$

where $$\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$$

Assume Bob is moving at 0.8c relative to Alice and units such that c=1.

$$\gamma = \frac{1}{\sqrt{1 - \frac{0.8^2}{1^2}}} = 1.666$$

$$x^{\prime} = 1.666 ( 10 - 0.8*5) = 10$$

$$t^{\prime} = 1.666 \left( 5 - \frac{0.8*10}{1^2} \right)= -5$$

________________________________________________________________________
Hi I apprecciated the clear cut presentation of the maths but couldn't help note a certain paradoxical self negation in your final derivation.
It appears to me that if the signal actually went back in time it couldn't possibly arrive at x=10 and conversely if it did arrive at x=10, it by definition was traveling forward in time no matter what the maths say.


There is the negative time interval: minus 5 seconds.

 

[DrGreg]

RandallB, re post #50

I'm trying to work out if there is any common ground between us, anything we can both agree on. That was the purpose of my post #48 and your dismissal of my entire post as "obviously flawed" doesn't help me in that objective. (By the way, what is "obvious" to you need not be obvious to anyone else, otherwise we wouldn't be having this discussion.) Let me spell this out in pedantic detail.

Here are some problems and solutions. I'd like to to consider each problem in isolation and tell me if you accept each solution, or, if not, why not. (All times are in seconds, all distance in light-seconds.)

Question 1: Relative to inertial observer Carol, H and K are the events

$$(T_H, X_H) = (0, 0)$$
$$(T_K, X_K) = (12, 48)$$​

Regardless of whether you think this is possible in the real Universe, if information were to travel from H to K, what would its speed be relative to Carol?

Answer 1: 4 (in the + direction).

Question 2: Relative to inertial observer David, L and M are the events

$$(T'_L, X'_L) = (-44, 64)$$
$$(T'_M, X'_M) = (-35, 28)$$​

Regardless of whether you think this is possible in the real Universe, if information were to travel from L to M, what would its speed be relative to David?

Answer 2: -4 (i.e. 4 in the - direction).

Question 3: Relative to inertial observer Elizabeth, P and Q are the events

$$(T''_P, X''_P) = (0, 0)$$
$$(T''_Q, X''_Q) = (-21, 0)$$​

Do you think all inertial observers agree that Q occurs before P? If not, give an example of an observer who disagrees.

Answer 3: Yes, all observers agree, because $T'''_Q = \gamma(T''_Q - vX''_Q) = -21\gamma < 0$, whatever the value of v and $\gamma$.

Question 4: Relative to inertial observer Alice, E, F and G are the events

$$(t_E, x_E) = (0, 0)$$
$$(t_F, x_F) = (12, 48)$$
$$(t_G, x_G) = (-21, 0)$$​

Bob moves at speed 4/5 relative to Alice (in the + direction) with clocks & distances synced such that in Bob's coordinates

$$(t'_E, x'_E) = (0, 0)$$​

What are the coordinates of F and G relative to Bob?

Answer 4:

$$(t'_F, x'_F) = (-44, 64)$$
$$(t'_G, x'_G) = (-35, 28)$$​

I know we are going to disagree at a later stage but can you please restrict yourself to commenting on the above 4 independent problems and let me know if you disagree with any of the solutions?

I've asked these questions so we can avoid wasting time arguing over things we agree on and concentrate on where we disagree.

 

[carstenk]

I'm a noob here and have a related question, or maybe it's the same one: Can the relative speed of two objects exceed the speed of light? I would assume so, for example the diametrically opposing objects on the edges of the observable universe that each move away from Earth at the speed of light. Grateful for you expert advice.

 

[Phrak]

There is a loophole, however...Lookup "Alcubierre Drive" on Wikipedia for more info.

Your loophole requires the existence of exotic matter.

 

[HallsofIvy]

I'm a noob here and have a related question, or maybe it's the same one: Can the relative speed of two objects exceed the speed of light? I would assume so, for example the diametrically opposing objects on the edges of the observable universe that each move away from Earth at the speed of light. Grateful for you expert advice.

No. In relativity speeds don't add like that. If object A is moving away from the Earth with speed .99c relative to the Earth and object B is moving in the opposite direction with speed .99c relative to the eath then the speed of each relative to the other would be
$$\frac{.99c+ .99c}{1+ \frac{(.99c)(.99c)}{c^2}}= \frac{1.98c}{1+.9801}$$
= .99994904975c still slightly less than c.

 

[azzkika]

Assume there is a circular device on the moon. it consists of laser activated propulsion plates that move a ball upon activation. now imagine this to be very big. then you shine a laser from Earth powerful enough to activate the plates. you then rotate it faster and faster until such time the beam that reaches the moon's surface is traveling faster than c across it's surface triggering the plates at greater than c speeds. would the ball travel faster than c??

 

[A.T.]

Assume there is a circular device on the moon. it consists of laser activated propulsion plates that move a ball upon activation. now imagine this to be very big. then you shine a laser from Earth powerful enough to activate the plates. you then rotate it faster and faster until such time the beam that reaches the moon's surface is traveling faster than c across it's surface triggering the plates at greater than c speeds. would the ball travel faster than c??

No. You could just as well ask if the ball would travel at infinite speed, if you trigger the platforms simultaneously.

 

[Mr.Amin]

I think this thread is done.

In nature, no phenomena has been observed to actually propagate faster then EM waves. Special relativity/general relativity, and the post-parameterized Newtonian models model near light speed behaviors quite well. Until superluminal phenomena are observed, this is a debate worthy of a coffee break. Mind you, even the most cooky theorists would not try to cook up things that refute observable nature--that is for mathematicians to explore.

IF there is such a thing, nature will eventually show us. Until then, c is c.

 

[azzkika]

No. You could just as well ask if the ball would travel at infinite speed, if you trigger the platforms simultaneously.

just out of curiosity, what speed would the ball achieve if such an experiment could be conducted?

And when approaching c, how much mass is gained as a ratio of itself of the actual ball?

Sorry to be a pain.

 

[334dave]

wow ..i have gone through a bag of popcorn reading this thread ..
first the org question concerns speed of light ..
it is my understanding that C is verabale .. ie in gravaty field water gas's diamond ect..
thus in "space" which is not empty it will change..
the vacuum speed ref.. should we not be considering the speed of a gamma partial ?
any way my real question of the moment is
a super lumen signal is energy of some kind [[which as we know is that e= mC thingy]]
\IF we assume that supper lumen singling is possible then is not time travel it self possible again due to that mater and energy are two sides of a sea saw?

an another question .. in my small mind as we approach C and mass increases would we not collapses to a micro black hole?

 

[Mr.Amin]

Alll right, I sent e-mails to the previous gent/lady "azzkika".

First, let's use what we know about the physical universe.
1) No signal can be sent at any rate exceeding that of light traversing a vacuum.
2) As you build "speed" (I hate that term), MASS is NOT generated.
3) Gravitational field curve space, they do not slow light trajectories.
4) Mass distributions (i.e. glass, dust, water) transparent to light slow light BECAUSE their electrons interact witht the light. Remember you lessons on polarization and complex susceptibility.

SO
1) Even if you could say get in front of an electromagnetic signal, what use is it since the you have not intercepted the signal. Causality still holds. Superluminal signals have nothing to do with "time travel" unless you are speaking of going forwards.

2) E=mc^2 does not mean that MASS increases when kinetic energy increases. The equation is fully written with a relativistic gamma multiplying the rest mass, m_0. It is the momentum that you are fighting to go faster. The change in momentum is what skyrockets. This is why it takes so much energy to go from 0.99c to 0.999c. Therefore, even if you could get a Ferrari traveling near c, you would not get a black hole. See Schutz's book or Misner Thorne and Wheeler's book. This interpretation took a little longer to understand.

3) Light always travels along null trajectories. This means that electromagnetic waves irrespective of wavelength (power line through hard gamma) travel the SAME route in a vacuum. For those of you who would ask about refractive effects, remember refraction requires charges to be present.

4) This is suitable for another thread or is nicely explained in "Modern Optics" by Fowles.
It is also in Jackson, for those daring enough.

 

[334dave]

first:

No. In relativity speeds don't add like that. If object A is moving away from the Earth with speed .99c relative to the Earth and object B is moving in the opposite direction with speed .99c relative to the eath then the speed of each relative to the other would be
$$\frac{.99c+ .99c}{1+ \frac{(.99c)(.99c)}{c^2}}= \frac{1.98c}{1+.9801}$$
= .99994904975c still slightly less than c.

wow .. you know i kinda thought the question was a good one.
i have never understood that before..
should have gone to collage i guess..

Alll right, I sent e-mails to the previous gent/lady "azzkika".
First, let's use what we know about the physical universe.
1) No signal can be sent at any rate exceeding that of light traversing a vacuum.

oh i agree, in my small mind the only way to seem to excede C would be folding or worm holes

2) As you build "speed" (I hate that term), MASS is NOT generated.
3) Gravitational field curve space, they do not slow light trajectories.

ugh here i agree- i referring to appearance time laps of that light from egality two diff sources one will arrive later due to the apparent effects of the gravity fields between us and sorce and the other source has no gravity wells between us..
ie if space it self is warped then ther is an appearent streching

4) Mass distributions (i.e. glass, dust, water) transparent to light slow light BECAUSE their electrons interact witht the light. Remember you lessons on polarization and complex susceptibility.

SO
1) Even if you could say get in front of an electromagnetic signal, what use is it since the you have not intercepted the signal. Causality still holds. Superluminal signals have nothing to do with "time travel" unless you are speaking of going forwards.

2) E=mc^2 does not mean that MASS increases when kinetic energy increases. The equation is fully written with a relativistic gamma multiplying the rest mass, m_0. It is the momentum that you are fighting to go faster. The change in momentum is what skyrockets. This is why it takes so much energy to go from 0.99c to 0.999c. Therefore, even if you could get a Ferrari traveling near c, you would not get a black hole. See Schutz's book or Misner Thorne and Wheeler's book. This interpretation took a little longer to understand.

humm seems i must have skimped that day.. as i thought that as you neared C yur mass increased.. will have to attempt correcting this miss understanding..
thanks for bringing it to my attention..

3) Light always travels along null trajectories. This means that electromagnetic waves irrespective of wavelength (power line through hard gamma) travel the SAME route in a vacuum. For those of you who would ask about refractive effects, remember refraction requires charges to be present.

4) This is suitable for another thread or is nicely explained in "Modern Optics" by Fowles.
It is also in Jackson, for those daring enough.

 

[carstenk]

No. In relativity speeds don't add like that. If object A is moving away from the Earth with speed .99c relative to the Earth and object B is moving in the opposite direction with speed .99c relative to the eath then the speed of each relative to the other would be
$$\frac{.99c+ .99c}{1+ \frac{(.99c)(.99c)}{c^2}}= \frac{1.98c}{1+.9801}$$
= .99994904975c still slightly less than c.

Thanks for your clear answer, which aligns with other explanations I have seen. I have great difficulties in accepting it though, as it obviously defies logic. I would think that since object A and object B are not interrelated in any way they would simply be invisible to each other once their relative velocities exceed c. One interesting implication of your answer also seems to be that everything in the universe is visible to us, because nothing will ever escape the event horizon due to relative velocities exceeding the speed of light.

But these are obviously just my amateurish speculations, and that's usually put to rest by empirical evidence. It's hard to imagine empirical evidence for something we can't see, but is the inverse may have been proven (that we never loose sight of anything)? grateful for the direction to some such experiment in that case.

 

[A.T.]

I have great difficulties in accepting it though, as it obviously defies logic.

It doesn't defy logic, just intuition and presumptions. Pure logic alone doesn't tell you how nature behaves.

 

[JesseM]

Thanks for your clear answer, which aligns with other explanations I have seen. I have great difficulties in accepting it though, as it obviously defies logic.

It may seem less illogical if you understand that each observer defines "speed" in terms of distance/time on rulers and clocks at rest relative to themselves, and that each observer also measures the rulers and clocks of other observers to be distorted (rulers shrunk, clocks slowed down). So, the fact that a third observer sees A and B separating at faster than the speed of light does not imply that A and B measure each other to be moving away faster than light.

I would think that since object A and object B are not interrelated in any way they would simply be invisible to each other once their relative velocities exceed c. One interesting implication of your answer also seems to be that everything in the universe is visible to us, because nothing will ever escape the event horizon due to relative velocities exceeding the speed of light.

The formula above is only intended to work in special relativity where spacetime itself doesn't behave in a dynamical way--in general relativity where spacetime is curved by mass, there actually can be an event horizon between sufficiently distant galaxies because the space between them is expanding faster than a light beam can bridge the gap (see http://www.scientificamerican.com/article.cfm?id=misconceptions-about-the-2005-03 for some more on this).

 

[Ich]

I would think that since object A and object B are not interrelated in any way they would simply be invisible to each other once their relative velocities exceed c.

Well, the whole point of HallsofIvy's answer is that relative velocities never exceed c. So I don't see where your difficulties come from - except that you maybe hadn't time to read carefully, as you answered hastily.

 

[cyberfish99]

Don't say definitely that no matter can go faster than the speed of light. There is always the theoretical sub-atomic particle, the tachyon. For a quick overview, http://en.wikipedia.org/wiki/Tachyon"

 

[JesseM]

Don't say definitely that no matter can go faster than the speed of light. There is always the theoretical sub-atomic particle, the tachyon. For a quick overview, http://en.wikipedia.org/wiki/Tachyon"

Tachyons can't be ruled out absolutely, but they'd violate either relativity or causality (meaning you could use them to send messages into the past). See the discussion on this thread for example.

 

[carstenk]

The formula above is only intended to work in special relativity where spacetime itself doesn't behave in a dynamical way--in general relativity where spacetime is curved by mass, there actually can be an event horizon between sufficiently distant galaxies because the space between them is expanding faster than a light beam can bridge the gap (see http://www.scientificamerican.com/article.cfm?id=misconceptions-about-the-2005-03 for some more on this).

Thanks for your patient explanations, which is highly appreciated. Unfortunately the article on Scientific American that you refer to requires a paid subscription that I currently can't justify. But your answer is interesting, since it in fact seems to (politely) refute HallsofIvy's original explanation, and in fact say that relative speeds (based on the expanding universe at least) above the speed of light is indeed possible in the scenario I originally described, since the farthest observable objects on diametrically opposite sides of the Earth are indeed escaping at the speed of light because of the expanding universe. I'm just puzzled that this is not advertised more, because I had known I would obviously not have asked my original question, and a lot of the discussion here could instead concentrate on the implications of the cases where c is actually exceeded.

 

[JesseM]

Thanks for your patient explanations, which is highly appreciated. Unfortunately the article on Scientific American that you refer to requires a paid subscription that I currently can't justify.

Sorry, I didn't notice that, it had been free for a long time...anyway I found a free PDF copy on an MIT page here:

http://space.mit.edu/~kcooksey/teaching/AY5/MisconceptionsabouttheBigBang_ScientificAmerican.pdf

But your answer is interesting, since it in fact seems to (politely) refute HallsofIvy's original explanation, and in fact say that relative speeds (based on the expanding universe at least) above the speed of light is indeed possible in the scenario I originally described, since the farthest observable objects on diametrically opposite sides of the Earth are indeed escaping at the speed of light because of the expanding universe. I'm just puzzled that this is not advertised more, because I had known I would obviously not have asked my original question, and a lot of the discussion here could instead concentrate on the implications of the cases where c is actually exceeded.

The problem is that to deal with cosmological scenarios we have to deal with non-inertial coordinate systems, while the restriction that nothing can travel faster than c is only intended to apply in inertial frames, the way that we can define a non-inertial coordinate system in GR is totally arbitrary (you could define a coordinate system where you were moving faster than c relative to some object in your own room, for example, although presumably light itself would move even faster in such a coordinate system). In general relativity all large-scale coordinate systems are non-inertial, one can only define "local" inertial frames in very small neighborhoods around freefalling observers, a consequence of the "equivalence principle" which is discussed in http://www.aei.mpg.de/einsteinOnline/en/spotlights/equivalence_principle/index.html .