Big Bang & Speed of Light: Explained

[disregardthat]

I have heard that nothing can overcome the light in speed, (that will say in vacuum) but when i read abot the big bang, the mass extended itself in a speed that was much faster than light. can someone explain this for me?

And another question, can gravity make an object go faster than the speed of light?

 

[mathman]

The expansion of space is not limited by the speed of light. That is what happened at the big bang and is still happening now.

Gravity cannot make objects go faster than the speed of light.

 

[HMS]

Does this imply that there are certain regions of space that are moving at a speed faster than light ? Is this a hypothesis or has it been verified through observation ?

 

[DaveC426913]

There is evidence that some of the most distant parts of the universe are receding from us at a speed greater than c. But I think there is some contention in that interpretation of the data.

(And in response to the inevitable question 'what do we see?', the answer is: nothing - that is the effective edge of our *visible* universe).

 

[JesseM]

In special relativity, nothing can move faster than light (assuming no tachyons). In general relativity, which deals with curved spacetime, the laws of physics must locally reduce to those of special relativity (ie an observer whose path is not being influenced by any forces besides gravity, when making measurements in his immediate spatial region over a short period of time, should see exactly the same results as he'd predict from special relativity). This means that locally, nothing can ever exceed light speed in GR either. But when dealing with large regions of spacetime, general relativity allows you to use pretty much any coordinate system you like, and some of the coordinate systems that are most natural to use in cosmology do allow galaxies to move apart at faster than light, although I think it would be possible to pick a different coordinate system where they don't (see the 'Many Distances' section on this page of Ned Wright's cosmology tutorial). You might also find some of the sections in the Scientific American article http://www.sciam.com/article.cfm?articleID=0009F0CA-C523-1213-852383414B7F0147 helpful.

 

[disregardthat]

but if the big bang expanded faster than light. that MUST mean that the mass that was being expanded did have a speed that was faster than lightspeed. and is there a special reason for that mass cannot go faster than light? it is possible to get almost in that speed. for example galaxies is going in a speed of ca 200 000 km\s (i think)

 

[pervect]

Given two masses at the same point in space and time, their relative velocity will always be less than 'c' as measured by clocks and rulers at that same point (the point where both objects are at). More specifically, the velocity of body#2, as measured by the clocks and rulers of body 1, will be less than c, and this measured velocity will be the same velocity as the velocity of body #1 measured by the clocks and rulers of body #2.

This is generally true for all coordinate systems (curved and otherwise), i.e. it is true in SR and GR.

In flat-space time (i.e. in SR), one can relax the requirements that the two objects be at the same place. In general, however one cannot omit this requirement.

If two bodies are not at the same place, there is no general way to determine their velocity in GR.

See for instance the longish quote from Baez et al in

https://www.physicsforums.com/showpost.php?p=1008379&postcount=94

One popularly says that the "space between the bodies" can expand faster than light. This gives the right answer, but is a bit of an oversimplificaiton.

 

[reidy]

using the forumula E= mc^2 / sqrt (1 -v^2/c^2)
we can prove that something that has a rest mass of let's say 1kg can not be accelerated to the speed of light as E would have to be infinite.

Isnt the speed of light 3*10^8 m/s

 

[Farsight]

Gravity cannot make objects go faster than the speed of light.

Mathman: If we had a very very large mass a very very long way away, and found ourselves accelerating towards it at an ever increasing rate, is there any limit to the "speed" at which we travel?

 

[pervect]

Mathman: If we had a very very large mass a very very long way away, and found ourselves accelerating towards it at an ever increasing rate, is there any limit to the "speed" at which we travel?

If the object (large mass) is not a black hole, you will be going slower than the speed of light when you hit the surface of the object.

If the object IS a black hole, it will have no surface, per se, but it will have an event horizon.

If you imagine an observer hovering (with a rocket) over the event horizon, your velocity relative to the hoverign observer as you fall into the black hole will increase towards the speed of light as the hovering observer gets closer and closer to the event horizon. In the limit, your velocity at the event horizon will be 'c' relative to a hypothetical observer exactly at the event horizon.

Note however, that such an observer cannot actually occur. No actual observer will actually be able to hover exactly at the event horizon and observe you traveling at c, though a hovering observer can see you travel very close to 'c'. In theory he can see you travel arbitrarily close to 'c', if he (the hovering obsever) has an unlimited (but finite!) acceleraiton capability.All motion is relative, so "speed" can only be measured relative to some observer. At or inside the event horizon of a black hole, no object can remain stationary.

Thus it remains true that if any two objects are at the same place at the same time, their relative velocity will be lower than the speed of light as measured by the clocks and rulers at that location, even when one object falls into a black hole.

If you fall into a black hole and a beam of light falls into the black hole with you, for instance, you will measure the speed of the light beam falling into the black hole to be exactly "c" (using your clocks and rulers).

 

[disregardthat]

i don't know what the "event horizon" is. what is it? and what has black holes to do with this. i was talking about galaxies, and teir speed througout the universe. And another question popped inside my head... What is the speed of light compared to. (like a car travels 60 km\h at the observer on earth. who is the observer when light travels in empty space?

 

[LURCH]

A black hole is an event; the occurrance of a gravitational field so strong that light cannot escape. The strength of a gravitational field gets stronger as you get closer to it. The event horizon is the distance (from the center of the gravitational field) at which escape becomes impossible. Litteraly, the horizon of the "event" called a black hole.

 

[JesseM]

A black hole is an event; the occurrance of a gravitational field so strong that light cannot escape. The strength of a gravitational field gets stronger as you get closer to it. The event horizon is the distance (from the center of the gravitational field) at which escape becomes impossible. Litteraly, the horizon of the "event" called a black hole.

I agree with that description of what an event horizon actually is (the point beyond which nothing can escape the black hole), but I don't think the origin of the term comes from considering the black hole itself as an "event"; rather, I think the term comes from the fact that there will be some events whose light will eventually reach you, and others whose light can never reach you, and the event horizon marks the boundary between the two.

 

[disregardthat]

can nothing escape? what if something with almost as high density as a black hole passes in a speed close to lightspeed, just in the outermost spot of the event horizon will it just plop into the black hole? but do anyone knows the answer to my other question? who is the observer on the speed of light. As far as i understand, nothing has a speed, unless it is "observed".

 

[Farsight]

Thankyou pervect. I was rather thinking of a very very large mass where we are already within the event horizon. Like the Universe, but with a hard centre rather than an average distribution. Are you basically saying that the effective distance to the centre is reduced?

 

[pervect]

i don't know what the "event horizon" is. what is it? and what has black holes to do with this. i was talking about galaxies, and teir speed througout the universe. And another question popped inside my head... What is the speed of light compared to. (like a car travels 60 km\h at the observer on earth. who is the observer when light travels in empty space?

[edits]

If we assume that an object has a constant density any object will eventually become a black hole if it is large enough.

THe defintion of a black hole is an object where the escape velocity is greater than the speed of light. Thus a non-black hole will be an object where the escape velocity is less than the speed of light.

Note that Escape velocity, the velocity needed to escape from an object, is the same velocity that an object will have when it falls from infinity to the object's surface.

Thus if you are considering galaxies, etc, and other things that are not black holes, you can see that by defintion the velocity you have when you reach the object falling from infinity is less than 'c' - that's the defintion of "non-black hole", anything with an escape velocity lower than 'c'

Black holes are a special case which is relavant to your question - "can gravity accelrate an object to the speed of light".

The answer here is a little tricker than the case where the object is not a black hole, which is why the answer is longer.

 

[pervect]

Thankyou pervect. I was rather thinking of a very very large mass where we are already within the event horizon. Like the Universe, but with a hard centre rather than an average distribution. Are you basically saying that the effective distance to the centre is reduced?

If we are already inside an event horizon of a black hole, we are doomed to be torn apart in a fairly short amount of time when we reach the central singularity.

For a large enough black hole, the tidal forces from the central singularity won't be obvious at the horizon. As we get closer and closer to the central singularity, the tidal forces from the central singularity will become more and more obvious, eventually they will become so strong that they turn us into spaghetti.

If we are in a black hole, and shine a light outwards, it will appear us, using our local clocks and rulers, to travel at 'c', the speed of light. In Schwarzschild coordinates, the rate of change of the r coordinate with respect to the t coordinate (actually, this should be reversed, because inside the event horizon r is timelike and t is spacelike) will not in general be equal to 'c'.

However, according to our clocks and rulers, or any other observer's clocks and rulers when the light is at the same loation as that observer, the velocity of that light beam will be 'c'.

However, that light beam will not escape the black hole, it will be sucked in, eventually.

 

[Parlyne]

I have heard that nothing can overcome the light in speed, (that will say in vacuum) but when i read abot the big bang, the mass extended itself in a speed that was much faster than light. can someone explain this for me?

The expansion described in the big bang theory is that of space itself, not of matter through space. Imagine the universe as the surface of a balloon and bits of matter as dots drawn on with a marker. As you inflate the balloon, the dots are progressively farther apart, even though each individual dot has remained in the same place on the balloon that it started.

Similarly, in the expansion of the universe objects which stand perfectly still will, nonetheless, end up farther apart as the universe evolves. Of course, these objects could also move through space, in which case the light speed limit applies. However, since the expansion is not a motion through space, but actually a change in space itself, there is no "speed limit."

And another question, can gravity make an object go faster than the speed of light?

Locally, no. Globally, yes.

This is to say that if a photon and a massive particle are racing along the same path, the photon will always win. However, since GR is all about the curvature of spacetime, there are situations where a free photon can take any of several paths between two points. In such a case, it is possible that the photon could take a path so long that a massive particle could win by taking a shorter path.

 

[LURCH]

can nothing escape? what if something with almost as high density as a black hole passes in a speed close to lightspeed, just in the outermost spot of the event horizon will it just plop into the black hole?

Correct; nothing can escape. The very massive object you propose would still be pulled in despite its great momentum. In fact, its momentum would contribute to its inward progress because inside the event horizon (as weird as this may sound) cetrifugal force works in the opposite direction from what we're accustomed to. Centrifugal force is a force pulling things in, not flinging them outward.

 

[Farsight]

pervect: Thanks for your answers so far. But I'm not getting a handle on something:

The definition of a black hole is an object where the escape velocity is greater than the speed of light.

...the same velocity that an object will have when it falls from infinity to the object's surface.

So if an object falls from infinity, as it passes the event horizon it is "travelling faster" than light. Assuming it's a very very large black hole where we don't have to worry about tidal forces for a while, can you tell me what then happens to time and distance?

 

[JesseM]

So if an object falls from infinity, as it passes the event horizon it is "travelling faster" than light.

Not locally though, only in Schwarzschild coordinates. And in Schwarzschild coordinates, I believe light itself is traveling faster than c after it crosses the event horizon (correct me if I'm wrong, pervect).

Assuming it's a very very large black hole where we don't have to worry about tidal forces for a while, can you tell me what then happens to time and distance?

Among other things, the black hole's radial dimension as seen in the coordinate system of an outside observer (like in Schwarzschild coordinates) becomes the time dimension for the infalling traveler...

 

[Farsight]

Thanks JesseM. Can you tell me about the space dimension(s) in simple terms?

 

[JesseM]

Thanks JesseM. Can you tell me about the space dimension(s) in simple terms?

Do you mean the radial dimension of the black hole? As seen by an outside observer, that's just any direction radiating outward from the center of the black hole, like the radial dimension in polar coordinates. If you're asking why this becomes the time dimension for observers who cross the event horizon, it has to do with the observers' light cones tilting as they approach the black hole, so that once they have crossed the horizon the radial dimension (as seen by outside observers) lies within their future light cone...you can see some explanation and diagrams of this http://www.phy.syr.edu/courses/modules/LIGHTCONE/schwarzschild.html , for example, and there's another diagram in fig. 12 of http://www.theorie.physik.uni-muenchen.de/~marco/poster/5.html more technical page.

 

[pervect]

Correct; nothing can escape. The very massive object you propose would still be pulled in despite its great momentum. In fact, its momentum would contribute to its inward progress because inside the event horizon (as weird as this may sound) cetrifugal force works in the opposite direction from what we're accustomed to. Centrifugal force is a force pulling things in, not flinging them outward.

Interestingly enough, centrifugal force changes sign even earlier - at 3/2 the Schwarzschild radius, the so-called "photon sphere" where light orbits a black hole.

An object free-falling past a black hole can get no closer than 3/2 the Schwarzschild radius. To hold station at a constant Schwarzschild R coordinate any closer to the event horizon requires a powered orbit (one must accelerate away from the black hole with rockets).

Inside the photon sphere of a non-rotating (Schwarzschild) black hole, attempting to orbit the black hole is counter-productive, the minimum value of thrust required to hover is when one is standing still.

 

[pervect]

pervect: Thanks for your answers so far. But I'm not getting a handle on something:

The definition of a black hole is an object where the escape velocity is greater than the speed of light.

...the same velocity that an object will have when it falls from infinity to the object's surface.

So if an object falls from infinity, as it passes the event horizon it is "travelling faster" than light. Assuming it's a very very large black hole where we don't have to worry about tidal forces for a while, can you tell me what then happens to time and distance?

Velocity has to be measured relative to something. Relative to a hypothetical stationary observer (one stationary in Schwarzschild coordinates), an object falling into a black hole would exceed the speed of light at some point in its journey - but only at some point past the event horizon.

However, such "statinoary" observers do not actually exist inside the event horizon - they only exist outside it. The velocity relative to such stationary obsrevers outside the event horizion is always less than 'c'.

The hypothetical FTL velocity can not ever actually occur, for no object or observer can remain stationary (at a constant Schwarzschild R coordinate) at or inside the event horizon of a black hole.

Note that an object falling into a black hole will appear to approach 'c' according to a hovering observer near the event horizon. At the event horizoin itself (in the limit) the velocity would be c, but that limit is never actually reached.

Interestingly enough, an object falling into a black hole will appear to have a velocity of zero according to an observer watching from infinity, due to the time dilation effects. (The velocity approaching 'c' is measured by local, "hovering" obsevers near the event horizon).

Also note that there are some coordinate singularities near the event horizon when Schwarzschild coordinates are used. They can be avoided by using non-singular coordinate systems, like Eddington-Finklestein or Kruskal-Szerkes coordinates.

 

[Farsight]

Thankyou Jessem and pervect.

 

[Farsight]

I found these black hole gifs on google. They look pretty good.

http://casa.colorado.edu/~ajsh/schw.shtml