Faster than the speed of light

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If time slows down as you approach the speed of light then does this mean that it stops when you reach the speed of light and/or runs backwards above the speed of light?
 

chroot

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If those velocities were possible, yes, that's what would happen. If you were to go faster than light, you would be performal 'acausal' motion, and could go backwards in time and kill your father and so on.

It is true that there is a viable theory of particles called 'tachyons,' which always travel faster than light. The speed of light is a barrier -- anything travelling < c will always travel < c, and anything travelling > c will always travel > c. It's a brick wall in both directions.

Some number of experiments were designed, built, and run to detect such tachyons -- but none were ever found.

- Warren
 

jeff

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Jack,

The speeds of objects with non-zero rest mass can approach but never equal light speed since then their relativistic mass would become infinite, violating conservation of energy.
 
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Originally posted by chroot
It is true that there is a viable theory of particles called 'tachyons,' which always travel faster than light. The speed of light is a barrier -- anything travelling < c will always travel < c, and anything travelling > c will always travel > c. It's a brick wall in both directions.
- Warren
Tachyons were going to be the subject of my next question actually. Everything you said about them was correct although I don't know much more about them than that, in fact I don't think anyone knows much more about them. Does this mean that they travel backwards in time and what are the implications of this?

And stenitz, I was going to add that I realised faster than the speed of light travel was possible because I just knew that someone would say that.
 
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Originally posted by Jack
Tachyons were going to be the subject of my next question actually. Everything you said about them was correct although I don't know much more about them than that, in fact I don't think anyone knows much more about them. Does this mean that they travel backwards in time and what are the implications of this?
The implications of traveling backward in time (according to GR), is that one is conducting negative travel through space. This makes no sense, of course, as there is no such thing as negative movement through all three of the spacial dimensions, at the same time (at least not that I can concieve of).
 
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Its impssible to go faster than the spped of light
 

marcus

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Originally posted by Viper
Its impssible to go faster than the spped of light
Viper, you and I are receding at twice the speed of light from the people (if there are any) living in a certain galaxy which was observed only last year.

Superluminal speeds of recession are part of General Relativity and routine in cosmology.

When you say no speeds can be faster than light be sure to specify that it is in the context of Special Relativity. It is true in that context and not true in the universe at large of General Relativity.

It causes terrible confusion when people say "no speeds faster than light" without being clear about the context. Physicists do the public a great dis-service when they fail to point that out.

People get the absurd notion that it is an absolute truth about nature and it interferes with their understanding of basic facts like the Hubble law and expansion.

This is also a remonstrance with some of the other posts in this thread which were insufficiently qualified as well.
 
Originally posted by marcus
Viper, you and I are receding at twice the speed of light from the people (if there are any) living in a certain galaxy which was observed only last year.
ALERT! CONTRADICTION DETECTED! :)
How could we have observed something that is receeding twice the speed of light?
 

Hurkyl

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How could we have observed something that is receeding twice the speed of light?
Might I ask what by reason you think we shouldn't be able to see such a thing?
 

marcus

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Originally posted by AndersHermansson
ALERT! CONTRADICTION DETECTED! :)
How could we have observed something that is receeding twice the speed of light?
Yes, Anders, please tell us why you think this is contradictory!
Hurkyl wants to know why you think this too.
The object was a quasar observed in 2002 at z = 6.4
The current estimated distance to the thing is 28 billion LY and the
current speed of recession is 2c.

http://www.sdss.org/news/releases/20030109.quasar.html

One does not observe the quasar as it is today, of course, since its light took over 12 billion years to get here. Because of the expansion that occurred during that time, its present distance is calculated to be, as I said, 28 billion LY. And its distance is increasing at the rate 2c.

Even though you think this is at odds with Special Relativity, it is not-----special relativity, with its speed limit, simply does not apply in this case so there is no logical contradiction.

But if you think there is, please explain it to us :wink:
 
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marcus, perhaps it would be appropriate to explain to Anders why this is possible.

Anders, there are a few reasons that something could be observed as moving faster than c. One is redshift, which you are probably already familiar with. Another is the fact that the expansion of space is taking place at a rate greater than c.
 
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Also, marcus and Hurkyl, Anders' questions appears to be slightly different than might be assumed. You see he was asking how we could observe something, if it were moving at a speed greater than c. He wasn't (IMO) asking how we could observe something as moving faster than c (even though that's what I initially assumed, also).

Perhaps AndersHermansson should explain it himself though, as the above is just the result of a "twice-over" by me.
 

marcus

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Originally posted by Mentat
marcus, perhaps it would be appropriate to explain to Anders why this is possible.

Anders, there are a few reasons that something could be observed as moving faster than c. One is redshift, which you are probably already familiar with. Another is the fact that the expansion of space is taking place at a rate greater than c.
Mentat, I just got back to the computer and saw your post.
This is a helpful comment and clarifies things. Also what you said after that is relevant. I will respond momentarily.
 

marcus

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Originally posted by Mentat
Also, marcus and Hurkyl, Anders' questions appears to be slightly different than might be assumed. You see he was asking how we could observe something, if it were moving at a speed greater than c. He wasn't (IMO) asking how we could observe something as moving faster than c (even though that's what I initially assumed, also).
Perhaps there are two separate questions, one that you just posed and one that Anders asked.

If you ask "how can we observe something in the act of moving at > c?"

then the answer is that we can't. Once something is receding at over the speed of light it can never send a signal that reaches us. Light from that object will never get here.

[self editing: sorry erase this. we can sometimes observe things receding at > c. Please disregard what I said which was not sufficiently thought out. See Hurkyl's immediately following comment.]

But I believe Anders was responding to an example I gave of an object which we can see today (as it was 13 billion years ago) and which is now calculated to be 28 billion LY away and receding at 2c-----this is this redshift 6.4 quasar observed last year.

I said:
--------------------------------------------------------------------------------
Viper, you and I are receding at twice the speed of light from the people (if there are any) living in a certain galaxy which was observed only last year.
--------------------------------------------------------------------------------


Anders said:
--------------------------------------------------------------------------------

ALERT! CONTRADICTION DETECTED! :)
How could we have observed something that is receeding twice the speed of light?
--------------------------------------------------------------------------------

Indeed we have observed something, the quasar (as it was 13 billion years ago), which we believe is currently receding at twice c, and there is no contradiction.

I may have misunderstood Anders comment yet again!!! But I hope not. Maybe we will hear from him directly :smile:, which would be a definite plus.
 
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Hurkyl

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Once something is receding at over the speed of light it can never send a signal that reaches us. Light from that object will never get here.
You sure on that? If, for instance, we start with an object receding special relativistically at a speed of 0.7 c, and then add in a 0.5 c recession due to the expansion of space, the light from the object should have no problem reaching us, although the object is receeding at 1.2 c.
 
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Originally posted by Hurkyl
You sure on that? If, for instance, we start with an object receding special relativistically at a speed of 0.7 c, and then add in a 0.5 c recession due to the expansion of space, the light from the object should have no problem reaching us, although the object is receeding at 1.2 c.
This is very interesting, though I have to wonder if Relativity really allows one to make such a distinction about the movement of an object.
 

marcus

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Originally posted by Hurkyl
You sure on that? If, for instance, we start with an object receding special relativistically at a speed of 0.7 c, and then add in a 0.5 c recession due to the expansion of space, the light from the object should have no problem reaching us, although the object is receeding at 1.2 c.
just saw your post. no I am not sure what happens in that situation.

I was considering only objects at rest w/rt Hubble flow.
[edit: I must revise what I think even in this case]

But you have posed a much more interesting problem.
there is some expansion and some special relativistic speed.
will consider at soonest possible. why didnt it occur to me? duh.
 
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marcus

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Hurkyl

yeah, for sure it reaches us

duh squared
 

Hurkyl

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Oh, the expansion of space between us and the theorized current position of that distant quasar is at a 2c rate? How would one compute that?
 

marcus

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Originally posted by Hurkyl
Oh, the expansion of space between us and the theorized current position of that distant quasar is at a 2c rate? How would one compute that?
1. they have an idea of being at rest w/rt CMB---same as being
at rest w/rt "hubble flow" the expansion of space.

2. this lets them split the manifold into &Sigma; x R---a space part and a time part

3. the Robertson Walker metric is applied. Also nowadaysow it is assumed (because of CMB observations) that the space part is flat, the RW metric is extremely simple
just has a scale factor a(t) and

ds^2 = -dt^2 + a^2(t)[ euclidean thing]

the scale factor a(t) shows the expansion and it is a solution of
the Friedmann equations, it determines the redshift, and
a t/a is by definition = H0

4. the hubble law v = H0 D is true at all distances
if D is measured in the present moment ( by the RW metric) and v is the rate of change in that distance.

5. HOW TO CALCULATE starting from z.

there are messy formulas which find the current distance to the quasar from z----these involve the prevailing assumptions
that cosmological const is 0.73 of rho crit. Spatial flatness.
Hubble parameter is 71 km/s per Mpc. I resort to Wrights
online calculator, which has these as default settings but allows
you to put in a different Hubble parameter and different cosmological constant if you want. I use the default settings.

You put in z = 6.4 (which was observed) and it does the messy
part and gives you that the distance to put in the Hubble law is 28 billion LY. this is the present distance also called "comoving" distance---basically just the RW metric in presentday space.

It also tells you how long the light has been traveling---how old the universe was when the light was emitted---and so on.

Then you take the distance D of 28 billion LY and apply the Hubble law and get v = H0 D = 2c

that part is easy because H0 reciprocal is 14 billion Y
so just divide 28 billion LY by 14 billion Y and get 2c.

You might be interested in the formulas and calculating it yourself instead of resorting to the Javascript online calculator.
they are hairy because the redshift was acquired at different epochs of time during different regimes of expansion, what with
cosmological constant egging on the expansion and matter slowing it down and these things being in changing proportions thru time. It is basically a bunch of integrals which people have solved in closed form but there are a lot of terms. I have only rarely tried to compute this myself and am always forgetting terms
So I have come to rely on the calculator.

Would you like me to dig up the formulas though? You may wish to try them. Cant promise that I can lay hands on them but could also look on web.

You also may wish to use the calculator to explore dependence on
parameters so here is the URL for it

http://www.astro.ucla.edu/~wright/CosmoCalc.html
 

schwarzchildradius

4. the hubble law v = H0 D is true at all distances
Do they say that this is instantaneously true? What about C = a/t?
 
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I thought that when recession reaches 1c, distant object is 'switched off' for us. That we can observe only objects that at the time when they emitted their light were receding from us < 1c.

Now you people tell that for expansion, this doesn't count. This is very interesting, because (paraphrasing Hurkyl) IF, for instance, we start with an object receding special relativistically at a speed of 0.0 c, and then add in a infinite c recession due to the expansion of space, the light from the object should have no problem reaching us, although the object is receeding at infinite c.

If objects are stationary in relation to each other relativistically, then they actually can be receeding due to expansion at infinite speed, and we could see them?! wow.

Then what, redshift drops frequency down towards 0Hz, or, static field?

So, emitted photons are not lost, only redshifted and perceived as having reduced energy. As BB is only 14Gyr, before that photons were not free. But, in future, we then should 'see' more and more relict photons building up, coming from areas of space that were far away from us at moment of BB? Jesus, then we should be able to 'watch a movie' of BB occuring just by selecting frequency of relict radiation reaching us.
 

marcus

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the zero subscript on H0 refers to the present moment, which is called t = 0.
The Hubble law applies precisely to distances and velocities measured at the present moment in time.

More generally the definition of H is a-dot/a (cant type a with dot over it)
that is time-derivative of scalefactor a(t) divided by scalefactor itself
that is at divided by a.

a-sub-tee is another way to write the time-deriv or rate of change of the scalefactor a

both a and its time-derivative change with time, so the
ratio at / a also changes with time

evaluating this at time zero gives us H0 the present value of the hubble parameter


Originally posted by wimms
I thought that when recession reaches 1c, distant object is 'switched off' for us. That we can observe only objects that at the time when they emitted their light were receding from us < 1c.
Wimms, I have been thinking about how to answer and have erased my original answer. I just have to think some more about what you say. What I orig. said was too hasty. Sorry. will get back to this as soon as time permits
 
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Originally posted by marcus
I do not understand this. can't figure out where you got this idea. It sounds quite wrong.
I was confused by Hurkyl's example that you agreed with. I did read it as: if we have object that was relativistically receeding at 0.7c, and it was in point of space that receeded from us at 0.5c due to expansion, back then, then we'll be able to see that light although in total it was receeding at 1.2c. I just exagerated that to infinity, duh. How about 0.99c + 0.99c?

I got impression that if object was receeding at <1c relative to 'intermediate' frame, space, then its light 'escapes' it and further on travels at 'c' towards us. And although space itself expands, in shorter distance expansion speed is <<c, and because any inertial frame is equal, light speed is not 'reduced' over that distance, only redshift occurs.

Anyway, if recessioon of 1c is max we can see, then it must be that in future we'll be seeing limit of U where distant objects are being 'switched off' as we look at them, due to crossing critical limit of 1c recession? Hard to imagine that exact crossover point, one day you receive light at 'c' from it, next day you receive nothing at all.
 
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OK, now for my next stupid question-

If time slows down to a stop as you approach the speed of light then how can light travel?
 

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