- #1

michelcolman

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- TL;DR Summary
- I came up with a layman's explanation of what it means for "space itself" to be expanding faster than light. But is it correct?

Hi,

I always used to struggle with the concept of "space itself expanding" (didn't Einstein say that the aether did not exist?) until one day an idea struck me that seemed to explain it all, without any need for complicated math. After talking about it with others, I got some great feedback from people profusely thanking me for finally explaining it to them in a way that they could understand, but a couple of days ago I also got a totally opposite reaction from someone claiming to be a theoretical astrophysicist on Slashdot. He or she was posting as "Anonymous Coward" but basically said I did not understand what I was talking about, I was just throwing jargon around as if it meant something, and I was suffering from the Dunning-Kruger effect.

So I thought I'd try my~~theory~~ description of the way I understood established science here. What do you think, does it make any sense or is it completely off the mark? I do understand that it may be simplistic, and insufficient to explain some of the finer points and recent discoveries of cosmology (it neglects gravity, for example, which would kinda sort of seem like an important thing to miss), but I really do feel it does a great job explaining where this concept of "space itself" comes from. So, here it goes:The way I see it, "space itself" is an artefact of the co-moving coordinates that are usually used in cosmology. Those coordinates have the advantage of making the universe look homogenous at a large scale, and independent of the choice of any particular reference point. But the disadvantage is that they violate the axioms of Special Relativity, requiring General Relativity and this concept of "space itself".

It is perfectly possible to describe the universe with a different reference frame that does obey Special Relativity. You need to pick some point as the central, stationary reference point (for example some point in our immediate neighbourhood that appears stationary relative to the cosmic radiation background) and define coordinates so that the speed of light is constant everywhere (relative to us).

In this reference frame, distant galaxies are moving away from us at great speed (but always less than the speed of light) so that they are Lorentz contracted and time dilated. Time is moving more slowly at those distances, and has been moving more slowly ever since the big bang, so those objects are also younger than us (less evolved after the big bang). They don't just look younger because their light took a long time to get to us, they actually are younger right now even if we take the travel time of light into account. ("Right now" being defined as "the events having the same time coordinate as us with this particular choice of reference frame").

If we "look" at distant objects using an infinitely fast way of looking that can only exist in a theoretical model, without needing to wait for light to get to us, we see the universe getting younger and younger the further we "look", and also more Lorentz contracted. When we reach a distance equal to the age of the universe multiplied by the speed of light, things are moving away from us at light speed and the big bang is just beginning at this moment, stuck in time forever (as an asymptotic limit, or a singularity, or whatever you want to call it). This means the entire infinite universe (not just the observable part, but all of it, everything after the big bang) actually fits inside a finite sphere expanding around us. An infinite amount of stuff fits in a finite sphere thanks to Lorentz contraction which approaches infinity near the edge.

Of course this view of the universe can hardly be called objective. If, instead of our own location, you would have taken some other distant galaxy as the reference point, they would suddenly be the oldest while our part of the universe would be much less evolved, in fact our civilisation would not even exist yet in their reference frame. That's not a contradiction, it's perfectly OK for different observers to disagree on which events happen "now", in the past, or in the future.

To avoid this kind of subjectivity, though, co-moving coordinates were invented, precisely tailored to our expanding universe. They redefine time at any point of the universe to be the local time as experienced by a local observer traveling together with the expansion of the universe. Space coordinates are defined so that the universe looks about the same everywhere, which can be achieved by requiring that the speed of light is c relative to those same moving observers. This reference frame by definition gets rid of time dilation and Lorentz contraction from the expansion of the universe. Everything now looks the same age and the same size everywhere, and the universe is truly infinite. Of course time dilation and Lorentz contraction still exist for local movements relative to local space, but not for the general movement of the expanding universe.

The disadvantage is that the speed of light is no longer constant relative to us. Instead, it is c relative to "space itself", which is expanding and even makes things move away from us faster than the speed of light. That doesn't mean "space itself" is a real, physical thing. It's just a result of using coordinates that don't comply with Special Relativity. Fortunately General Relativity works on just about any coordinate system you can come up with, as long as you apply the appropriate corrections for the metric of the resulting "space".

Even though these descriptions seem very different, they do yield the same conclusions when you actually try to calculate an observable event or any other testable prediction.

For example, using co-moving coordinates you may say that we will never see certain events that ere happening "now" in some distant galaxy because that part of space is receding faster than light, and its light can never get to us. It's as if this light was trying to move towards us along a cosmic conveyor belt moving the other way at a higher speed. My special-relativistic reference frame explains this differently: with those coordinates, the event has a time coordinate infinitely far in the future, it has not happened yet and never will happen because time in that part of space is moving very slowly and is even slowing down to an asymptotic standstill long before the event ever gets a chance to happen, as the galaxy continues to accelerate away from us.

Two totally different explanations, but with the same result: we will never see it happen.

Another example: will we ever be able to reach that location if we fly towards it? With co-moving coordinates, we can't because space is expanding faster than we can catch up with it. With special-relativistic coordinates, the location seems to be within reach (a finite distance away) but as soon as we start to accelerate towards it, our plane of simultaneity tilts so that they are catapulted into the future and therefore further away and accelerating to even higher speeds. No matter how much we accelerate (shrinking our local surroundings along the axis of our motion), faraway objects will fast forward through time and space so that their distance to us actually increases faster than the Lorentz Contraction of our own speed can shrink it. Again, the same result, we will never reach them.So, what do you think, is this really a totally wrong explanation, or is it actually a pretty good way of explaining what "space itself" means?

I always used to struggle with the concept of "space itself expanding" (didn't Einstein say that the aether did not exist?) until one day an idea struck me that seemed to explain it all, without any need for complicated math. After talking about it with others, I got some great feedback from people profusely thanking me for finally explaining it to them in a way that they could understand, but a couple of days ago I also got a totally opposite reaction from someone claiming to be a theoretical astrophysicist on Slashdot. He or she was posting as "Anonymous Coward" but basically said I did not understand what I was talking about, I was just throwing jargon around as if it meant something, and I was suffering from the Dunning-Kruger effect.

So I thought I'd try my

It is perfectly possible to describe the universe with a different reference frame that does obey Special Relativity. You need to pick some point as the central, stationary reference point (for example some point in our immediate neighbourhood that appears stationary relative to the cosmic radiation background) and define coordinates so that the speed of light is constant everywhere (relative to us).

In this reference frame, distant galaxies are moving away from us at great speed (but always less than the speed of light) so that they are Lorentz contracted and time dilated. Time is moving more slowly at those distances, and has been moving more slowly ever since the big bang, so those objects are also younger than us (less evolved after the big bang). They don't just look younger because their light took a long time to get to us, they actually are younger right now even if we take the travel time of light into account. ("Right now" being defined as "the events having the same time coordinate as us with this particular choice of reference frame").

If we "look" at distant objects using an infinitely fast way of looking that can only exist in a theoretical model, without needing to wait for light to get to us, we see the universe getting younger and younger the further we "look", and also more Lorentz contracted. When we reach a distance equal to the age of the universe multiplied by the speed of light, things are moving away from us at light speed and the big bang is just beginning at this moment, stuck in time forever (as an asymptotic limit, or a singularity, or whatever you want to call it). This means the entire infinite universe (not just the observable part, but all of it, everything after the big bang) actually fits inside a finite sphere expanding around us. An infinite amount of stuff fits in a finite sphere thanks to Lorentz contraction which approaches infinity near the edge.

Of course this view of the universe can hardly be called objective. If, instead of our own location, you would have taken some other distant galaxy as the reference point, they would suddenly be the oldest while our part of the universe would be much less evolved, in fact our civilisation would not even exist yet in their reference frame. That's not a contradiction, it's perfectly OK for different observers to disagree on which events happen "now", in the past, or in the future.

To avoid this kind of subjectivity, though, co-moving coordinates were invented, precisely tailored to our expanding universe. They redefine time at any point of the universe to be the local time as experienced by a local observer traveling together with the expansion of the universe. Space coordinates are defined so that the universe looks about the same everywhere, which can be achieved by requiring that the speed of light is c relative to those same moving observers. This reference frame by definition gets rid of time dilation and Lorentz contraction from the expansion of the universe. Everything now looks the same age and the same size everywhere, and the universe is truly infinite. Of course time dilation and Lorentz contraction still exist for local movements relative to local space, but not for the general movement of the expanding universe.

The disadvantage is that the speed of light is no longer constant relative to us. Instead, it is c relative to "space itself", which is expanding and even makes things move away from us faster than the speed of light. That doesn't mean "space itself" is a real, physical thing. It's just a result of using coordinates that don't comply with Special Relativity. Fortunately General Relativity works on just about any coordinate system you can come up with, as long as you apply the appropriate corrections for the metric of the resulting "space".

Even though these descriptions seem very different, they do yield the same conclusions when you actually try to calculate an observable event or any other testable prediction.

For example, using co-moving coordinates you may say that we will never see certain events that ere happening "now" in some distant galaxy because that part of space is receding faster than light, and its light can never get to us. It's as if this light was trying to move towards us along a cosmic conveyor belt moving the other way at a higher speed. My special-relativistic reference frame explains this differently: with those coordinates, the event has a time coordinate infinitely far in the future, it has not happened yet and never will happen because time in that part of space is moving very slowly and is even slowing down to an asymptotic standstill long before the event ever gets a chance to happen, as the galaxy continues to accelerate away from us.

Two totally different explanations, but with the same result: we will never see it happen.

Another example: will we ever be able to reach that location if we fly towards it? With co-moving coordinates, we can't because space is expanding faster than we can catch up with it. With special-relativistic coordinates, the location seems to be within reach (a finite distance away) but as soon as we start to accelerate towards it, our plane of simultaneity tilts so that they are catapulted into the future and therefore further away and accelerating to even higher speeds. No matter how much we accelerate (shrinking our local surroundings along the axis of our motion), faraway objects will fast forward through time and space so that their distance to us actually increases faster than the Lorentz Contraction of our own speed can shrink it. Again, the same result, we will never reach them.So, what do you think, is this really a totally wrong explanation, or is it actually a pretty good way of explaining what "space itself" means?

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