Can we travel faster than the speed of light?

[Stephanus]

Dear PF Forum,
Before I get a NO answer, I'd like to ask a few question.
https://en.wikipedia.org/wiki/Hubble's_law#Observed_values
As of 13th July, 2016 Hubble flow is 67.6 km/s per mega parsec.
Or 67km/s per 31 trillion * 1 million km or per 3.26 million light year.
Say a galaxy 11.68 giga light year away from us. This galaxy is traveling at 80% the speed of light away from us.
What I want to know. Is it possible for an object at that galaxy to travels say, 30% the speed of light "away" from us relative to the galaxy?
If it is, then wouldn't the object travel at 1.1c?
And one more thing. Any object as far away as 13.8 giga light year from us can never reach us because it has already traveled more than the speed of light.
And I read somewhere (do I have to make a citation here?) that any object less than 13.8 gly from us can reach us, because it haven't traveled at the speed of light.
So the object at 11.68 gly can reach us. But can an object at that galaxy which travels 30% the speed of light away from us, then stop then travel back to us, say 0.99c reach us?
Thank you very much.

 

[Jorrie]

Say a galaxy 11.68 giga light year away from us. This galaxy is traveling at 80% the speed of light away from us.

Galaxies at that distance do not "travel away from us at at 80% the speed of light". We say they a have a recession rate of 0.8c, because we cannot measure (SR-like) speed over the curved spacetime of those distances. As you probably know, the recession rate is the result of the metric expansion and does not have an upper limit.

Also, I do not think you can generally add recession rates like you did - perhaps at the lower ranges it may be approximately right.

PS: You should read Brian Powell's Insights article about Cosmological Horizons.

 

[Charles Kottler]

Say a galaxy 11.68 giga light year away from us. This galaxy is traveling at 80% the speed of light away from us.
What I want to know. Is it possible for an object at that galaxy to travels say, 30% the speed of light "away" from us relative to the galaxy?
If it is, then wouldn't the object travel at 1.1c?

Look up "Einstein velocity addition".

 

[Jorrie]

Look up "Einstein velocity addition".

No, this is SR and does not work for cosmological distances and also not for any curved spacetime.

 

[vanhees71]

Also have a look here, concerning the interpretation of the gravitational Hubble red shift as Doppler effect:

http://www.edu-observatory.org/physics-faq/Relativity/GR/hubble.html

 

[Charles Kottler]

No, this is SR and does not work for cosmological distances and also not for any curved spacetime.

Sorry, I guess you are correct that it would not apply in the context of this question, where the 'velocity' is a result of the metric expansion. Would it be correct to say that SR would apply locally over every region between the remote galaxy and us, and that we can then think of the expansion as being similar to a long piece of elastic being stretched: the ends can move apart very fast relative to each other while in any small section the expansion is hardly noticeable?
67.6 km/s per mega parsec sounds a lot until you convert it back to more common units - turn it around and see how long it takes for one Km to 'grow' by 1mm. Regardless of the distance (and therefore speed) between the endpoints it will always be possible to get a signal or to travel from one point to another given enough time.

 

[Jorrie]

Also, I do not think you can generally add recession rates like you did - perhaps at the lower ranges it may be approximately right.

Actually, in comoving coordinates, we can add recession speeds normally. It is implied by the way comoving distance is defined: D = H₀ V_rec/c.
As an example, at the Hubble radius (R_H=14.4 Glyr), the recession speed is c. For a comoving observer at our Hubble radius, a galaxy that lies in the same direction, but on that observer's R_H, will also have a recession rate of c to them. That galaxy will be 28.8 Glyr from us, at a recession rate of 2c.

 

[Stephanus]

Look up "Einstein velocity addition".

Thanks for your reply . Some mentor said (in my previous post), you can't use that for Hubble flow

 

[Stephanus]

Look up "Einstein velocity addition".

No, this is SR and does not work for cosmological distances and also not for any curved spacetime.

Yes, I was afraid that we have to you SR velocity addition. Because if I recall correctly some mentor/advisor in PF said that we can't use that.

 

[Jorrie]

Yes, locally SR will apply everywhere.

Regardless of the distance (and therefore speed) between the endpoints it will always be possible to get a signal or to travel from one point to another given enough time.

With the present accelerating expansion, there is actually a cosmological event horizon (at some 16.5 Glyr comoving) from beyond which no present emission can ever reach us. We can observe particles originally from areas that are presently more than 45 Glyr away, due to the fact that accelerated expansion only started "recently" (actually some billions of years ago).

 

[Stephanus]

Yes, locally SR will apply everywhere.

Everywhere?? What about very distant galaxy that travels recedes more than the supposed speed of light?
[Add: Oh, locally]

 

[Jorrie]

Everywhere?? What about very distant galaxy that travels recedes more than the supposed speed of light?

Did you notice the word "locally"? It means in the vicinity of the observer in the galaxy, or wherever...

 

[Stephanus]

Did you notice the word "locally"? It means in the vicinity of the observer in the galaxy, or wherever...

Sorry, I have corrected my post. But thanks anyway. You beat me to it

 

[Jorrie]

Sorry, I have corrected my post. But thanks anyway. You beat me to it

No problem, feel free to ask more clarification.
This has gone into cosmology now, so maybe further questions should be asked in that sub forum.

 

[Lautaro]

http://www.preposterousuniverse.com...never-expands-faster-than-the-speed-of-light/

 

[Jorrie]

http://www.preposterousuniverse.com...never-expands-faster-than-the-speed-of-light/

Naturally, because expansion does not have a speed - but the recession speed of a specific galaxy/cluster is well defined. It is the rate of change of its proper (or physical) distance per unit cosmic time and it can far exceed c. For expansion, we do not have a specific distance that changes over time; we express it as the Hubble parameter, which is a fractional rate of increase per unit distance.

 

[vanhees71]

Everywhere?? What about very distant galaxy that travels recedes more than the supposed speed of light?
[Add: Oh, locally]

Please, read this very well written Usenet FAQ article:

http://www.edu-observatory.org/physics-faq/Relativity/GR/hubble.html

The bottom line: the Hubble redshift is not a Doppler effect in the strict sense, and the recession velocity is not a proper relative velocity between (local!) events!

 

[Chris Miller]

If you were approaching a 100 light year distant (by Earth measurement) star at nearly c, due to length foreshortening, it might be only a short distance away by your measurements. Then, if you were to decelerate very rapidly to 0 v, it would "suddenly" retreat 100 light years, for a relative velocity of many times c.

 

[Ibix]

The star doesn't move in that case. And how rapidly the distance to it "changes" is entirely a matter of definition.

 

[Dale]

it might be only a short distance away by your measurements. Then, if you were to decelerate very rapidly to 0 v, it would "suddenly" retreat 100 light years, for a relative velocity of many times c.

There is no inertial coordinate system in which this statement is true.

You could, of course, make a non-inertial coordinate system where that is true, but speeds are not limited to c in non-inertial coordinate systems.

 

[Andrew Mason]

Actually, in comoving coordinates, we can add recession speeds normally. It is implied by the way comoving distance is defined: D = H₀ V_rec/c.
As an example, at the Hubble radius (R_H=14.4 Glyr), the recession speed is c. For a comoving observer at our Hubble radius, a galaxy that lies in the same direction, but on that observer's R_H, will also have a recession rate of c to them. That galaxy will be 28.8 Glyr from us, at a recession rate of 2c.

The second galaxy that is 28.8 Glyr from us would be unobservable to us. So is there any empirical evidence to support your example?

AM

 

[Jorrie]

The second galaxy that is 28.8 Glyr from us would be unobservable to us. So is there any empirical evidence to support your example?

No, a galaxy presently 28.8 Glyr from us has a redshift of about 7. The redshift record for galaxies has recently been set at around z=11, a distance around 32 Glyr. I'll have to look up to find a specific observation at z=7, but this was not the point.

As an aside, the observed light left such a (z=7) galaxy when it was around 3.6 Glyr from "us" (our region of the universe). We will obviously never see light that leaves it now, because it is way outside our present cosmological horizon. You can use any modern cosmological calculator to find these distances.

 

[Andrew Mason]

No, a galaxy presently 28.8 Glyr from us has a redshift of about 7. The redshift record for galaxies has recently been set at around z=11, a distance around 32 Glyr. I'll have to look up to find a specific observation at z=7, but this was not the point.

As an aside, the observed light left such a (z=7) galaxy when it was around 3.6 Glyr from "us" (our region of the universe). We will obviously never see light that leaves it now, because it is way outside our present cosmological horizon. You can use any modern cosmological calculator to find these distances.

What I meant was that the light from a galaxy that is 28.8 Glyr away and traveling at a speed of 2c relative to us would never reach us. My question is: what evidence do we have that such galaxies exist? In other words, what evidence is your cosmological calculator based on?

AM

 

[Jorrie]

What I meant was that the light from a galaxy that is 28.8 Glyr away and traveling at a speed of 2c relative to us would never reach us. My question is: what evidence do we have that such galaxies exist? In other words, what evidence is your cosmological calculator based on?

I suggest that we start a new thread under the cosmology section if you want in-depth discussion on the cosmological model and evidence in its support. Also check post#2 above: that 2c is not a relative speed (SR-fashion), but is a recession rate to be understood in the sense of metric expansion of the cosmos.

 

[Andrew Mason]

Look up "Einstein velocity addition"

No, this is SR and does not work for cosmological distances and also not for any curved spacetime.

I suggest that we start a new thread under the cosmology section if you want in-depth discussion on the cosmological model and evidence in its support. Also check post#2 above: that 2c is not a relative speed (SR-fashion), but is a recession rate to be understood in the sense of metric expansion of the cosmos.

I am trying to understand, then, why Einstein velocity addition is not essentially the correct answer to the OP's question. He stated that the galaxy in question defined an inertial frame moving at a speed of .8c relative to the earth. He then asked why an object traveling at .3c relative to the galaxy in a direction away from the Earth would not be measured at 1.1c relative to the earth. I appreciate that there are some gravitational effects, but I don't see how they would materially affect an answer based on SR velocity addition. Let's say the galaxy was Andromeda which is about 1 million light years away if that will make it easier.

AM

 

[Jorrie]

I am trying to understand, then, why Einstein velocity addition is not essentially the correct answer to the OP's question.

Because his Glyr implied cosmological distances, where a single inertial frame is not workable. If he used a few Mlyrs, then one can think of a single inertial frame as a reasonable approximation and employ SR's addition of velocities rule.

Again, when we are talking relative speeds, we normally imply SR and inertial coordinates; when we are talking recession rates (or speeds), we normally imply cosmological (comoving) coordinates. So the issue is really about the fact that speed depends on the choice of coordinates system. And we normally choose the coordinate system that fits the scenario best.

PS: a hypothetical galaxy moving away at 0.8c at 1 Mlyr distance, must have a peculiar velocity of that magnitude relative to us. Peculiar velocities essentially means movement in the inertial frame of a comoving observer and can never exceed c.

 

[Nugatory]

I am trying to understand, then, why Einstein velocity addition is not essentially the correct answer to the OP's question. He stated that the galaxy in question defined an inertial frame moving at a speed of .8c relative to the earth.

There is no inertial frame that includes both the Earth and the distant galaxy. If we were working with a flat spacetime we could find such a frame and use special relativity and the velocity addition formula, but we aren't.