Stretched space far from our own

[marcus]

here is a link to Friedmann equations post at PF
https://www.physicsforums.com/showthread.php?p=210120#post210120
this link should be better---dont happen to have a better at the moment tho.
I actually am not sure I understand some of your questions about the
Hubble law proportionality.
Earlier I may have spoken too quickly or sloppily and given the impression that it is not a simple proportionality.
It is really really straightforward

Lets say we solve c = H d for a distance d at which things are receding at speed of light. and say it comes out d = 14 billion LY

then at 7 billion, things are receding at 1/2 c
and at 14 billion, at c
and at 21 billion, receding at 3/2 c
and at 28 billion, receding at 2 c
and so on

this is at this moment.

the presentday Hubble parameter does not tell about the past.

to find out about the past you have to solve the Friedmann equations going back into past----this is what Ned Wright and Siobahn cosmology calculators do for you and why it is important to play with the calculators a bit---there are also animations on the web that track a(t) graphically with various assumptions about how it starts off---but I like the calculators.

the thing is, in the past a(t) was different and a'(t) was different, and
H(t) was different! So how can you expect me to talk about past just using the information that right at this moment the expansion parameter H
is 71 km/sec per Mpc? Cant do it.

Yes one can do approximations, because H(t) changes only very slowly. So if you only go back 10 million or 100 million years it might look roughly the same.
But if you want to go back 10 billion years then H(t) will be very different.
However the Ned and Siobahn calculators will tell you what it is!
Like, I often see figures like H = 200 back early because expansion was faster then. then it slowed down, now it is very gradually speeding up.
this is what differential equations do. they generate beautiful curves.
but the curves have to be calculated! so you need a calculator to track the past history of a(t)-----the past history of the expansion of the U.

maybe I can find a graphic plot of the a(t) curve and give you a link.

anyway, at anyone instant of time there is a Hubble parameter H(t) and the recession speeds are proportional to distance by this straightforward
linear proportion v = Hd.

solving for the Hubble distance is easy, put c = 3E5 kilometers/sec
and put c = H D and solve for D
so 3E5 km/s = (71 km/s per Mpc) D

So you divide 300,000 by 71 and find that D has to be like 4225 Mpc :zzz:
or 4.2 Gpc and since a Gigaparsec is 3.26 billion LY you multiply by
3.26 and get that D is around 14 billion LY.

The problem here is that
specialists habitually use awkward units and for historical reasons astronomers got the nasty habit of saying parsec----a somewhat off-putting synonym for 3.26 light years.

 

[woodysooner]

thanx a lot that was very vey helpful but just one thing i asked that i wondered about. Is not the universe 15 billion years how do we see past that if it is nothing. I know it has to do with recesion speeds so can we not say how far it is to the end?? if so what is it, i though hawking mentioned it in his book like 45 billions yr but not sure.

 

[Nereid]

What are you saying? The speed of light is constant in space-time. Isn't that what your are trying to say? However, the speed of light is not constant in space or time, but only in space-time. There have been numerous demonstrations that the rate of motion of light through space is not constant. Neither is the rate of motion of light through time. It is only within the context of space-time that the speed of light is constant.

I too would also like to ask you Prometheus to please clarify this.

The only thing I can think of - re 'numerous demonstrations that the rate of motion of light through space is not constant' - is some difficult observations which seemed to show that alpha (the fine structure constant) is not constant, over cosmological time (a.k.a. billions of years). There have indeed been a number of projects to determine whether alpha does vary, and some teams have reported a positive result. However, later more detailed/more accurate work hasn't confirmed these results. So, the best observations we've got to date show alpha to be constant, to a few parts per million (IIRC), over the last 10 billions years (and ppb over the past ~2 billions years).

Of course, it's not possible (today) to determine whether alpha was constant or not over the first ~300,000 years since the BB.

 

[Prometheus]

That's irrelevant, we're talking about the speed of light in a vacuum.

I disagree. The statement that people seem to be making here is that the speed of light is constant, period, with no conditions. I claim that this is not true, that there must be a condition, and that the condition should be, in my opinion, that the speed of light is constant in space-time. Chronos maintained that no condition is needed, that the speed of light is invairant in space. I provided a simple demonstration that this is not true. You now cry foul, and tell me that we have an assumed condition, a vacuum. I disagree. How can you claim what "we" have an "assumed" condition as your justification for refuting my claim that we need to state our condition because we cannot have no condition?

VSL proposes that the speed of liught in a vacuum c is variable.

I am not attempting to support the theory known as VSL, because I do not know all of its tenets. However, I do consider that it is quite probable that the speed of light, even in a vacuum, is not constant in its rate of motion through space. Is it not well understood that as the rate of motion through space increases, the rate of motion through time decreases (recall the twin paradox). As the universe expands outward through space, why would this motion through space not have an impact on motion through time? If so, then the speed of light, although constant in space-time, would not be constant in space.

 

[Prometheus]

I too would also like to ask you Prometheus to please clarify this.

The only thing I can think of - re 'numerous demonstrations that the rate of motion of light through space is not constant' - is some difficult observations

Space and time are bound up as space-time. Examples such as the twin paradox show that as the rate of motion through space increases, the rate of motion through time decreaes. Motion through space time is constant, howver.

Rather than show a complex, controversial example that the rate of motion through space of light is not constant, I used a simple example of light through a medium such as water. This demonstrates that the rate of motion is not constant through space. Even a simple example such as this invalidates the gross generalization that the speed of light is constant in space.

What is the point of such a contension anyway? Space and time are bound up as space-time. To separate these into space and time is to introduce error. To integrate them into space-time forces us to consider, I believe, that as the universe continues in motion through space, there is an impact on motion through time.

 

[jcsd]

I disagree. The statement that people seem to be making here is that the speed of light is constant, period, with no conditions. I claim that this is not true, that there must be a condition, and that the condition should be, in my opinion, that the speed of light is constant in space-time. Chronos maintained that no condition is needed, that the speed of light is invairant in space. I provided a simple demonstration that this is not true. You now cry foul, and tell me that we have an assumed condition, a vacuum. I disagree. How can you claim what "we" have an "assumed" condition as your justification for refuting my claim that we need to state our condition because we cannot have no condition?

It's irrelevant to the topic at hand, infact it's to do with the absorbiton/re-emmison of light, so the speed of an actual photon in relativity is still c through a medium.

I am not attempting to support the theory known as VSL, because I do not know all of its tenets. However, I do consider that it is quite probable that the speed of light, even in a vacuum, is not constant in its rate of motion through space. Is it not well understood that as the rate of motion through space increases, the rate of motion through time decreases (recall the twin paradox). As the universe expands outward through space, why would this motion through space not have an impact on motion through time? If so, then the speed of light, although constant in space-time, would not be constant in space.

That the speed of light is constant for all inertial observers is an axiom of special relativity and that it's local coordinate velcotiy is a constant is axiomatic in general relativity, yet you're trying to argue from the concept of spacetime that it isn't constant! If you cannot see the paradoxial nature of this investigate relativity further.

Also it's meanigless to talk about the speed of light through spacetime, so I really do not know why you persist with this idea.

 

[Prometheus]

That the speed of light is constant for all inertial observers is an axiom of special relativity and that it's local coordinate velcotiy is a constant is axiomatic in general relativity,

I have no problem with these statements.

yet you're trying to argue from the concept of spacetime that it isn't constant! If you cannot see the paradoxial nature of this investigate relativity further.

That you consider it a paradox shows to me that you are locked into a view that is narrower than need be. I claim that it is constant in space-time. It seems to me that it is you who deny the relevance of space-time, and consider space as independent of time.

Also it's meanigless to talk about the speed of light through spacetime,

Do you find no meaning in the concept of space-time? It seems to me that you do not consider the unity of space-time, but instead think in terms of space and time distinct from each other. Given this perspective on your part, I understand your reticence. Do you place any significance on the concept of space-time?

The rate of motion through time is dependent on the rate of motion through space. As the rate of motion through space increases, the rate of motion through time decreases. Light is the arbiter of the interaction of space with time. As well, light is in motion through space over time. Therefore, I consider it reasonable to consider that the speed of light, while constant in space-time, is a function of the interaction of space with time, as space-time.

so I really do not know why you persist with this idea.

Surely you can guess. I do not completely agree with you.

 

[Nereid]

The rate of motion through time is dependent on the rate of motion through space. As the rate of motion through space increases, the rate of motion through time decreases. Light is the arbiter of the interaction of space with time. As well, light is in motion through space over time. Therefore, I consider it reasonable to consider that the speed of light, while constant in space-time, is a function of the interaction of space with time, as space-time.

Would you mind giving a specific, concrete example of these ideas please? If you can, with terms, definitions, and equations.

How do these ideas relate to Relativity (Special or General)?

Thanks in advance.

 

[woodysooner]

thanx a lot marcus

I just wanted to say thanks alot, I have learned a lot from you, and I'm going to try to follow all you said and go further with it, mathematically, I have already had all of calc just not DiffE yet but i want to understand this so you've got me started.

It's is people like YOU that give clarity to the questions some of us ask that make this forum work.

Thanx

 

[Prometheus]

Would you mind giving a specific, concrete example of these ideas please? If you can, with terms, definitions, and equations.

How do these ideas relate to Relativity (Special or General)?

Thanks in advance.

Surely you have a more complete set of criteria that you would like in order to satisfty your request. Why stop with this minimal set. Why not present me with a complete list of all of your conditions for my writing before you would feel comfortable providing your input.

Perhaps I can build a scale model as well.

 

[jcsd]

I have no problem with these statements.


That you consider it a paradox shows to me that you are locked into a view that is narrower than need be. I claim that it is constant in space-time. It seems to me that it is you who deny the relevance of space-time, and consider space as independent of time.

It's not a narrow view it's just one that comes from knowing a little about spacetime. What you are arguing is that because of the concept of spacetime - a concept that has the idea that the speed of light is constant in space as one of it's fundmanetal building blocks, the speed of light in space needn't be constant. So do you undrestand now?

Do you find no meaning in the concept of space-time? It seems to me that you do not consider the unity of space-time, but instead think in terms of space and time distinct from each other. Given this perspective on your part, I understand your reticence. Do you place any significance on the concept of space-time?

Space is space, time is time and spacetime is spacetime i.e. despite being described in a continuum ,space and time are not entirely equivalent in relativity.

Spacetime is a mathematical model that describes observation very well, I avoid drawing conclusions ontology.

The rate of motion through time is dependent on the rate of motion through space. As the rate of motion through space increases, the rate of motion through time decreases. Light is the arbiter of the interaction of space with time. As well, light is in motion through space over time. Therefore, I consider it reasonable to consider that the speed of light, while constant in space-time, is a function of the interaction of space with time, as space-time.

Please define what you mean by the speed of light is constant in spacetime.

I can only implore you to learn a little more about relativity and the concept of spacetime and then pereheaps you will see my points.

 

[marcus]

reply to woody, three posts back

thanx a lot woody!
writing for PF is lots of fun
(wouldnt do it otherwise since they don't pay)
and the live interest of people like you
is the key vitamin that makes it work, at least for me

 

[Prometheus]

I can only implore you to learn a little more about relativity and the concept of spacetime and then pereheaps you will see my points.

I do not fault you for your opinion. However, I have a different opinion. I am not demanding that you accept it.

Please define what you mean by the speed of light is constant in spacetime.

According to Lewis Carroll Epstein, in his book Relativity Visualized, everything in the universe always moves at the same speed, the speed of light. It is not possible to move faster or slower than the speed of light.

This constancy of the speed of light is not constancy through space or time, but through space-time. Changes in the rate of motion through space or time are accompanied by a symmetrical and opposing change in time or space. For example, as an object increases in motion through space, it decreases in motion through time, such that the rate of motion through space-time is constant.

As space-time travels outward from the Big Bang through space, it also travels through time. Time is not absolute in the universe, but is dependent upon the motion of the related space. Space-time on the fringes of the universe, which has moved the greatest motion through space since the Big Bang, is therefore younger than the space-time that has remained in the vicinity of the Big Bang.

Light is in motion through space-time. Once emitted, light does not change in its rate of motion through space or time. However, when light encounters and interacts with space-time, that space-time absorbs the light and reacts by emitting light.

When light is emitted by space-time, the rate of motion of that light through space is symmetrical to its rate of motion through time.

From our position in this corner of the universe, we can observe a small fraction of the universe, through its light.

Light in this corner of the universe is at a similar position in space, relative to the Big Bang, and so is at a similar position in time. However, in other parts of the universe, which we cannot see yet, the relationship of space and time is different.

At the edge of the universe, which has undergone the greatest motion through space since the Big Bang, the light is moving at its greatest motion through space, and at the least rate of motion through time.

Dark matter is the name given now to explain the fact that the edges of the universe are receding at a rate of motion through space that is greater than the speed of light. Perhaps the light in that part of the universe, where space has moved farther through space, is moving faster through space than the light here. That is why it seems to be receding at a rate faster than the speed of light, because it is faster than the speed of our light here, due to its lesser age.

I believe that the speed of light is constant in space-time, but that it is not constant in space. Just as everything else in motion through space-time is in motion through both space and time, and the relationship in the motion through space and motion through time is constant, so too is this true for the motion through space-time of light.

 

[jcsd]

I do not fault you for your opinion. However, I have a different opinion. I am not demanding that you accept it.

But you have to relaize tho', that your opinion is based partly on one or two misconceptions we I will try to illuminate for you:

According to Lewis Carroll Epstein, in his book Relativity Visualized, everything in the universe always moves at the same speed, the speed of light. It is not possible to move faster or slower than the speed of light.

Epstein seems to be the source of your misconception. What Epstein actually means is that the length of the velocity four vector is always c (the reason he uses the word 'speed' is that speed is the length of the velcotiy three vector). Note though this is not quite analgous to say that everything moves thrpugh spacetime at c (because things don't move through spacetime in the conventional sense, because time is already part of the continuum.


That said this is not the case for a photon! Conventionally, the 4 velcoity of a photon is either left undefined or it it is the null vector having a length of zero.

This constancy of the speed of light is not constancy through space or time, but through space-time. Changes in the rate of motion through space or time are accompanied by a symmetrical and opposing change in time or space. For example, as an object increases in motion through space, it decreases in motion through time, such that the rate of motion through space-time is constant.

You have to realize that speed is speed, the speed through time is even harder to define as conventionally speed is |dx/dt|. That siad what you call the speed through space (i.e. the speed) of light is infact consant in all inertial frames. This is one of the two postulates of special relativity and is also a fundamental feature of the geometry of spacetime. So you can argue if you wish that the speed of light isn't constant, but you must relaize you can't use spacetime to do this because if the speed of light is not constant then spacetime no longer applies.

Now you do have some of the basics down there, in particular you've got the idea that it's good to think of the Lorentz transformation as a rotation. Keep hold of this idea as it is useful.

As space-time travels outward from the Big Bang through space, it also travels through time. Time is not absolute in the universe, but is dependent upon the motion of the related space. Space-time on the fringes of the universe, which has moved the greatest motion through space since the Big Bang, is therefore younger than the space-time that has remained in the vicinity of the Big Bang.

This is very confused- spacetime traveling through space! As I said before famlairize yourself further with the concept of spacetime and you will see why it doesn't make sense to say this.

Light is in motion through space-time. Once emitted, light does not change in its rate of motion through space or time. However, when light encounters and interacts with space-time, that space-time absorbs the light and reacts by emitting light.

When light is emitted by space-time, the rate of motion of that light through space is symmetrical to its rate of motion through time.

From our position in this corner of the universe, we can observe a small fraction of the universe, through its light.

Light in this corner of the universe is at a similar position in space, relative to the Big Bang, and so is at a similar position in time. However, in other parts of the universe, which we cannot see yet, the relationship of space and time is different.

At the edge of the universe, which has undergone the greatest motion through space since the Big Bang, the light is moving at its greatest motion through space, and at the least rate of motion through time.

Dark matter is the name given now to explain the fact that the edges of the universe are receding at a rate of motion through space that is greater than the speed of light. Perhaps the light in that part of the universe, where space has moved farther through space, is moving faster through space than the light here. That is why it seems to be receding at a rate faster than the speed of light, because it is faster than the speed of our light here, due to its lesser age.

I believe that the speed of light is constant in space-time, but that it is not constant in space. Just as everything else in motion through space-time is in motion through both space and time, and the relationship in the motion through space and motion through time is constant, so too is this true for the motion through space-time of light.

Again I won't go into detail, but you will see your mistakes upon further famlairization of the subject matter. A good way would be to investiogate it mathematically, as the basic mathematics aren't particularly hard.

 

[Prometheus]

But you have to relaize tho', that your opinion is based partly on one or two misconceptions we I will try to illuminate for you:

You have to relaize tho', that your opinion is based partly on one or two misconceptions. I will not try to illuminate for you.

I am happy that your understanding of Special Relativity is perfect, and as well that you recognize that Special Relativity itself is perfect. The only attention that you should pay is to get me to recognize the truth of your understanding.

Epstein seems to be the source of your misconception. What Epstein actually means is

Thank you for telling me that he did not mean what he said, but that he means what you said.

You have to realize that speed is speed, the speed through time is even harder to define as conventionally speed is |dx/dt|.

Speed is speed. Excellent description. What does this mean, however?

That siad what you call the speed through space (i.e. the speed) of light is infact consant in all inertial frames. This is one of the two postulates of special relativity and is also a fundamental feature of the geometry of spacetime.

I am sorry to provide a reference again. You do not need any, I understand. I found the following on the Internet, at http://origins.colorado.edu/~ajsh/sr/postulate.html

The Postulates of Special Relativity

3. The Speed of Light is Constant
Statement: "The speed of light c is a universal constant, the same in any inertial frame".

Measuring speed requires being able to measure intervals of both space and time: speed is distance traveled divided by time elapsed. Inertial frames constitute a special class of spacetime coordinate systems; it is with respect to distance and time intervals in these special frames that the speed of light is asserted to be constant.

So you can argue if you wish that the speed of light isn't constant, but you must relaize you can't use spacetime to do this because if the speed of light is not constant then spacetime no longer applies.

The citation above states, as I do, that time is an element of speed. You seem to disagree with this. You claim that I argue that the speed of light is not constant. You seem to have completely misunderstood my statement to make this claim.

Thank you for telling me what I must realize. Surely you must realize that this is not an accurate assumption on your part. In fact, this whole quote of yours seems to tell me that I must realize that my statements do not mean what I said, just as Epstein's statement does not mean what it says. Do your statements mean what they say?

This is very confused- spacetime traveling through space! As I said before famlairize yourself further with the concept of spacetime and you will see why it doesn't make sense to say this.

I do believe that you are saying that if only I would understand and believe that what you believe that you are saying is true, then I would recognize that what you think that I am saying is false. This works both ways, you know.

Again I won't go into detail, but you will see your mistakes upon further famlairization of the subject matter.

I won't go into detail, but you will see your mistakes upon further famlairization of the subject matter.

I am sure that you believe that you understand Special Relativity well, and that Special Relativity is unalterable in all respects. Good for you.

Thank you for telling me how wrong I am, although, based on your statements it seems that you do not seem to really understand well what I am saying.

I appreciate your attempt to make your point in this forum. However, I have a slightly different take on these concepts. I believe that your understanding is incomplete. Physics is not a closed science, and your understanding of the current stand of relativity is not the end. You might consider what I have to say, or not.

 

[jcsd]

You have to relaize tho', that your opinion is based partly on one or two misconceptions. I will not try to illuminate for you.

please don't just repeat what I said as it's childish, if you really do think I have some misconceptions then illustrate them.

I am happy that your understanding of Special Relativity is perfect, and as well that you recognize that Special Relativity itself is perfect. The only attention that you should pay is to get me to recognize the truth of your understanding.

Saying that your understanding of special relativity is deeply flawed is not the same as saying that my understanding is perefect. Speical relativiyt isn't a huge subject and I know that I have a good grasp on it, but I don't claim to know everything there is to know about special relativity.

Thank you for telling me that he did not mean what he said, but that he means what you said.

If you read what he said literally, then he is simply and obviuosly incorrect as the speed of objects is obviously not invariant. In fact it's obvious this not what he means and he means what I said. If this is not the case what else could he mean?

Speed is speed. Excellent description. What does this mean, however?

I gave you a defintion of speed after that. What I mean is speed has a well-defined meaning, if you want to use the word in another context you must be 100% clear about what you mean.

I am sorry to provide a reference again. You do not need any, I understand. I found the following on the Internet, at http://origins.colorado.edu/~ajsh/sr/postulate.html

The Postulates of Special Relativity

3. The Speed of Light is Constant
Statement: "The speed of light c is a universal constant, the same in any inertial frame".

Measuring speed requires being able to measure intervals of both space and time: speed is distance traveled divided by time elapsed. Inertial frames constitute a special class of spacetime coordinate systems; it is with respect to distance and time intervals in these special frames that the speed of light is asserted to be constant.

Rather than go for the traditional 2 postulates of relativity they've gone for three postulates; they've taken an unconvetional approach by starting with the idea of spacetime, nevertheless I can see no reason why you can't get special relativity from those three postulates.

Notice what they have called the 3rd postulate is infact exactly what I said earlier: i.e. the speed of light is constant in all inertial frames.

The citation above states, as I do, that time is an element of speed. You seem to disagree with this. You claim that I argue that the speed of light is not constant. You seem to have completely misunderstood my statement to make this claim.

Time is related to speed, after all speed is: |dx/dt|.

What you said ealrier was:

the speed of light is not constant in space or time

which is completely in oppositon to the paragraph you quoted above.

Thank you for telling me what I must realize. Surely you must realize that this is not an accurate assumption on your part. In fact, this whole quote of yours seems to tell me that I must realize that my statements do not mean what I said, just as Epstein's statement does not mean what it says. Do your statements mean what they say?

I am trying to get you to realize your errors.

I do believe that you are saying that if only I would understand and believe that what you believe that you are saying is true, then I would recognize that what you think that I am saying is false. This works both ways, you know.

All I am asking is that you study relativity beyond some coffee table book.

I won't go into detail, but you will see your mistakes upon further famlairization of the subject matter.

I am sure that you believe that you understand Special Relativity well, and that Special Relativity is unalterable in all respects. Good for you.

Thank you for telling me how wrong I am, although, based on your statements it seems that you do not seem to really understand well what I am saying.

I appreciate your attempt to make your point in this forum. However, I have a slightly different take on these concepts. I believe that your understanding is incomplete. Physics is not a closed science, and your understanding of the current stand of relativity is not the end. You might consider what I have to say, or not.

I'm not saying special relativity is a complete description of the unievrse, only that you don't understand it. The speed of light may be variable, there's no way I can postively say it is not, but your 'argument from spacetime' is deeply flawed.

 

[Nereid]

I am finding it hard to follow what you're trying to say Prometheus, and your reply to my direct attempt to understand better got a reply from you that I was quite unprepared for.

Let me try again, also using your own ideas.

I am happy that your understanding of Special Relativity is perfect, and as well that you recognize that Special Relativity itself is perfect. The only attention that you should pay is to get me to recognize the truth of your understanding.

...

I am sure that you believe that you understand Special Relativity well, and that Special Relativity is unalterable in all respects. Good for you.

...

I appreciate your attempt to make your point in this forum. However, I have a slightly different take on these concepts. I believe that your understanding is incomplete. Physics is not a closed science, and your understanding of the current stand of relativity is not the end. You might consider what I have to say, or not.

This seems to imply that you have a different view of the success of SR as a theory than many of us here at PF. If this is so (please state clearly, one way or the other), is it SR's inconsistency with any experimental or observational results that concerns you? If so, which? Is it perhaps some internal inconsistency in SR (you recognise that SR has a perfect record re experiments and observations)? Maybe it's that SR claims a domain of applicability which you feel is unwarranted?

What else ... maybe it's that folk here at PF generally portray SR incorrectly?

Note to Mentors: the last few posts seem to belong more naturally in the Relativity section, could these be moved there please?

 

[Prometheus]

That the speed of light is constant for all inertial observers is an axiom of special relativity

You and I both claim that the speed of light is constant. We are in agreement on this point. However, we seem to have somewhat different understandings as to what this statement actually means. You claim that the speed of light is constant in space. I claim that this is not correct, and that the speed of light is not constant in space, but rather that the speed of light is constant in space-time. You do not share my concept of space-time, and you do not appreciate my contention of the significance of space-time. You point to the wonderful accuracy of observations in light of your interpretation. I claim that there is an error in your interpreation, and that by attempting to consider space outside of the context of time, in the form of space-time, mysterious fudge factors become increasingly necessary to enable the observations that you speak of to continue to seem accurate. These fudge factors necessitate such mysteries as dark energy and dark matter.

Can we find any common ground for our discussion? You have presented as your justification a postulate of special relativity. You worded the postulate as follows:

The speed of light is constant for all inertial observers

This is a good point for us to discuss, as I fully support this postulate and your wording. I believe that neither of us has any desire or interest at this time to attempt to refute this postulate. And yet, we are in disagreement as to what this postulate is really saying.

You claim that this postulate maintains that the speed of light is constant in space. I contend that you are reading more into the words than is there, and that this is the source of your error. I claim that this postulate does not concern the speed of light at all in the sense that I have been discussing heretofore, from the perspective of the universe as a whole.

Look at the last 4 words. These imply not that the speed of light is constant in space, but that the speed of light is perceived as constant from the perspective of observers such as us in our inertial frame. In other words, I contend that this postulate claims that the speed of light is perceived to be constant in space by observers, but not that the speed of light is constant in space in an absolute sense. The words "for all inertial observers" clearly suggest that the context of this postulate is the perception of observers in their inertial frame and not the context of the universe as a whole.

I have come up with an example, which I do not claim to be elegant, but which I do believe conveys my point.

The light from the sun all moves at (approximately) exactly the same rate of motion through space. We call this rate c. We have a definition of c, such that we can claim that the light from the sun moves through space at a rate of x meters per second. Every time that we can perceive that one second of time has elapsed, we can measure that the light has traveled x meters through space.

x m/s X 1s = x meters

For a number of reasons, I claim that the light that we see from sources at the most distant edges of the universe is moving faster through space than the light from our sun. Rather than go into the reasons now, let me assume that this is true, and then see if this leads to an inconsistency in the cited postulate. Rather than attempt to select a speed for this fast light in the interests of presumed accuracy, let me select a speed for purposes of simplicity of mathematical calculation. Let me assume that the light from a distant source is moving through space at twice the speed of our light. In other words, this light is moving through space at the rate of 2x m/s.

Is this inconsistent with the cited postulate? I think that it is not. We know from examples such as the twin paradox, and on the basis of my contention that space and time interact as space-time, that because this light moves faster through space, we perceive it to move slower through time. How much slower?

Since light is our absolute measure of motion, the answer is simple: Twice the rate of motion of light through space coincides with one half the rate of perceived motion of light through time.

Therefore:

When we, as observers on Earth in our inertial frame, perceive that one second of time has passed, we perceive that the fast light has passed through one half second of time. The rate of motion through space multiplied by the factor of time yields:

2x m/s X 1/2 s = x meters

This example demonstrates that whatever the rate of motion through space of light from different sources, observers in an inertical frame will perceive the rate of motion to be constant, as is claimed in the SR postulate. The postulate does not require that light actually be moving at the same rate through space, only that its perceived rate be constant for all inertial observers.

I consider that it is a fallacy to consider motion through space outside of the context of time. It is meaningful only to think in terms of space-time. All measurements of motion through space contain units of time. When we ignore time by considering it absolute, thereby failing to recognize that time interacts with space, error is introduced.

 

[jcsd]

You and I both claim that the speed of light is constant. We are in agreement on this point. However, we seem to have somewhat different understandings as to what this statement actually means. You claim that the speed of light is constant in space. I claim that this is not correct, and that the speed of light is not constant in space, but rather that the speed of light is constant in space-time. You do not share my concept of space-time, and you do not appreciate my contention of the significance of space-time. You point to the wonderful accuracy of observations in light of your interpretation. I claim that there is an error in your interpreation, and that by attempting to consider space outside of the context of time, in the form of space-time, mysterious fudge factors become increasingly necessary to enable the observations that you speak of to continue to seem accurate. These fudge factors necessitate such mysteries as dark energy and dark matter.

The problem is you still haven't taken the time to mathematically define what you mean by 'speed thorugh spacetime' and until you do I can only guess at what you mean.

Spacetime is signicant, but you should look closer into what it is and how it is defined.

Can we find any common ground for our discussion? You have presented as your justification a postulate of special relativity. You worded the postulate as follows:



This is a good point for us to discuss, as I fully support this postulate and your wording. I believe that neither of us has any desire or interest at this time to attempt to refute this postulate. And yet, we are in disagreement as to what this postulate is really saying.

You claim that this postulate maintains that the speed of light is constant in space. I contend that you are reading more into the words than is there, and that this is the source of your error. I claim that this postulate does not concern the speed of light at all in the sense that I have been discussing heretofore, from the perspective of the universe as a whole.



Look at the last 4 words. These imply not that the speed of light is constant in space, but that the speed of light is perceived as constant from the perspective of observers such as us in our inertial frame. In other words, I contend that this postulate claims that the speed of light is perceived to be constant in space by observers, but not that the speed of light is constant in space in an absolute sense. The words "for all inertial observers" clearly suggest that the context of this postulate is the perception of observers in their inertial frame and not the context of the universe as a whole.

No you cannot separate the 'perception' of observers from 'reality' in relativity the 2 go hand-in-hand. The speed of light will be constant for an inertial observer, in special relativity i's more normal to talk about inertial frmaes than non-inertial frmaes. (that isn't to say that it can't handle non-inertial frames). If we talk about the speed of ligh, we mena in an inertial frame.

I have come up with an example, which I do not claim to be elegant, but which I do believe conveys my point.

The light from the sun all moves at (approximately) exactly the same rate of motion through space. We call this rate c. We have a definition of c, such that we can claim that the light from the sun moves through space at a rate of x meters per second. Every time that we can perceive that one second of time has elapsed, we can measure that the light has traveled x meters through space.

x m/s X 1s = x meters

For a number of reasons, I claim that the light that we see from sources at the most distant edges of the universe is moving faster through space than the light from our sun. Rather than go into the reasons now, let me assume that this is true, and then see if this leads to an inconsistency in the cited postulate. Rather than attempt to select a speed for this fast light in the interests of presumed accuracy, let me select a speed for purposes of simplicity of mathematical calculation. Let me assume that the light from a distant source is moving through space at twice the speed of our light. In other words, this light is moving through space at the rate of 2x m/s.

In whose frame? if we are not talking about inertial frames, you must specify the frame and I warn ypou the maths is a lot harder in non-inertial frmaes.

Is this inconsistent with the cited postulate? I think that it is not. We know from examples such as the twin paradox, and on the basis of my contention that space and time interact as space-time, that because this light moves faster through space, we perceive it to move slower through time. How much slower?

The problem is your example is meaningless as you haven't specified a frame.

Since light is our absolute measure of motion, the answer is simple: Twice the rate of motion of light through space coincides with one half the rate of perceived motion of light through time.

Therefore:

When we, as observers on Earth in our inertial frame, perceive that one second of time has passed, we perceive that the fast light has passed through one half second of time. The rate of motion through space multiplied by the factor of time yields:

2x m/s X 1/2 s = x meters

This example demonstrates that whatever the rate of motion through space of light from different sources, observers in an inertical frame will perceive the rate of motion to be constant, as is claimed in the SR postulate. The postulate does not require that light actually be moving at the same rate through space, only that its perceived rate be constant for all inertial observers.

I consider that it is a fallacy to consider motion through space outside of the context of time. It is meaningful only to think in terms of space-time. All measurements of motion through space contain units of time. When we ignore time by considering it absolute, thereby failing to recognize that time interacts with space, error is introduced.

This is a hoplessly naive view of relativty, there are plenty of sites on the inertnet that explain the basic concepts of relativity; this is not been nasty or some undrehand debating tactic but you must brush up on the basics first.

 

[Chronos]

... I contend that this postulate claims that the speed of light is perceived to be constant in space by observers, but not that the speed of light is constant in space in an absolute sense. The words "for all inertial observers" clearly suggest that the context of this postulate is the perception of observers in their inertial frame and not the context of the universe as a whole.

There is no 'space in an absolute sense'. That implies a preferred reference frame. The speed of light within 'the context of the universe as a whole' is therefore meaningless.

For a number of reasons, I claim that the light that we see from sources at the most distant edges of the universe is moving faster through space than the light from our sun.

Light from distant quasars travels at precisely the same speed as light from your desk lamp. This has been demonstrated.

Rather than go into the reasons now, let me assume that this is true, and then see if this leads to an inconsistency in the cited postulate.

It leads to inconsistency with observation.

...The postulate does not require that light actually be moving at the same rate through space, only that its perceived rate be constant for all inertial observers.

Huh? The perceived speed of light is not the same as the 'actual' speed? What testable predictions does that make?