Understanding Hubble's Graph: Velocity and Time Relationship Explained

[fencewalker]

EEE degree w/ phys minor.
hubble's graph shows velocity increasing over distance, not time.
an image 10 mil ly away is 10 mil y old (t = -d/c)
the origin of hubble's graph is d=0 and t=now, not 0
older images are faster and older image means younger galaxy
distance is proportional to age, which is negative time
if V increased further back in the past, it is decreasing in the future
V accelerates into the past (hubble's graph), means V decelerates into the future
is there error in my logic?
also, if the claim is that everything started at the same point at the same time, how do we not know what that time is?

 

[mfb]

Older, but mainly further away. You cannot just attribute an observed relation to one of the things without comparing both.

Hubble studied galaxies closer than 100 million light years simply because he didn't have the tools to get distance estimates further out. Within 100 million years, the expansion speed does not change much. Within the measurement uncertainty of his measurements, it does not matter at all. The different distance matters a lot - 100 million light years away is 10 times as far away as 10 million light years away. For all practical purposes he make a picture of the expansion speeds now: More distant galaxies recede faster.

Today, we can measure galaxies much further away, and this simple interpretation does not work any more. For every measurement, you have to consider the expansion history of the universe from the time of emission to today.

 

[fencewalker]

ok, but haven't more modern examinations shown hubble's graph to continue onward to the farthest galaxies?
my issue is with the interpretation that the universe is accelerating, when i see the units on the graph and come to the opposite conclusion.

 

[PeterDonis]

if V increased further back in the past, it is decreasing in the future

Not necessarily. The fact that the universe started out decelerating does not mean it must decelerate forever.

In fact, the transition from deceleration to acceleration happened a few billion years ago. So strictly speaking, it's only further back in the past than that that we see V increasing as we go further back. If we start from "now", we see V decreasing as we go back further until we hit the transition point, then increasing as we go back further than that.

The diagram in the Wikipedia article on Hubble's Law, linked below, shows various possible histories of the Hubble constant vs. time that would all result in the same Hubble constant "now". The $\Omega_M = 0.3$, $\Omega_\Lambda = 0.7$ curve is the one that describes our actual observations.

https://en.wikipedia.org/wiki/Hubble's_law#Ultimate_fate_and_age_of_the_universe

 

[fencewalker]

Not necessarily. The fact that the universe started out decelerating does not mean it must decelerate forever.

In fact, the transition from deceleration to acceleration happened a few billion years ago. So strictly speaking, it's only further back in the past than that that we see V increasing as we go further back. If we start from "now", we see V decreasing as we go back further until we hit the transition point, then increasing as we go back further than that.

The diagram in the Wikipedia article on Hubble's Law, linked below, shows various possible histories of the Hubble constant vs. time that would all result in the same Hubble constant "now". The $\Omega_M = 0.3$, $\Omega_\Lambda = 0.7$ curve is the one that describes our actual observations.

https://en.wikipedia.org/wiki/Hubble's_law#Ultimate_fate_and_age_of_the_universe

please show where i am wrong on my original post

 

[PeterDonis]

please show where i am wrong on my original post

I already did: it's the statement I quoted in post #4.

Or, if you want to pin it down to an earlier assumption in your OP, it's this one:

older images are faster

The graph I linked to shows that "older images are faster" is not correct from now back to a few billion years ago; during that period, older images are slower, not faster.

 

[fencewalker]

I already did: it's the statement I quoted in post #4.

Or, if you want to pin it down to an earlier assumption in your OP, it's this one:
The graph I linked to shows that "older images are faster" is not correct from now back to a few billion years ago; during that period, older images are slower, not faster.

is the oldest image of a galaxy 13-14 billion lightyears away? therefore 13-14 billion years old? it is the youngest galaxy in in the universe and it is going the fastest. older image = younger galaxy = faster
velocity at time = -13.5 billion years is the highest.
velocities at later times are slower.

 

[mfb]

ok, but haven't more modern examinations shown hubble's graph to continue onward to the farthest galaxies?

Not exactly, and the deviations are significant.

velocity at time = -13.5 billion years is the highest.

The result is right, but your argument is not.
At those distances (and universe ages), the concept of velocity gets problematic. Velocity relative to what, measured in which frame? It is better to talk about the scale factor: The relative distance between things.

 

[jbriggs444]

As mfb hints, the idea of galaxies accelerating away from one another is not a good description of what goes on in an expanding universe. The distance between the galaxies increases. But they do not have to "move" or accelerate for this to happen. Google "metric expansion".

 

[fencewalker]

Not exactly, and the deviations are significant.
The result is right, but your argument is not.
At those distances (and universe ages), the concept of velocity gets problematic. Velocity relative to what, measured in which frame? It is better to talk about the scale factor: The relative distance between things.

i mentioned in the first post that the origin of the graph is d=0 on the x-axis, which means that the time is now. from d=rt, r=c, then the time at each distance is -d/c

 

[fencewalker]

ok we're talking about different graphs then...
http://www.sciencephoto.com/media/140551/view
is what I'm talking about. it implies a constant acceleration equal to hubble's constant, but the units are not (m/s^2) but hz (1/s)
convert that to the time domain and t = -d/c
the universe may still be expanding, but is decelerating going along time in the positive direction.

 

[mfb]

Imagine two cars moving away from you, starting at the same time. One drives at 50 km/h, the other one at 100 km/h. After an hour, you see the first car at a distance of 50 km moving at 50 km/h, the other one at a distance of 100 km moving at 100 km/h. If you plot that, you get exactly a Hubble-like plot. Add more cars as suitable - they will all end up on the same straight line in the plot.
What is your conclusion from that? Would you expect any acceleration? Would you calculate how many microseconds the light needed for your observation? Probably not, those microseconds don't matter.

 

[fencewalker]

Imagine two cars moving away from you, starting at the same time. One drives at 50 km/h, the other one at 100 km/h. After an hour, you see the first car at a distance of 50 km moving at 50 km/h, the other one at a distance of 100 km moving at 100 km/h. If you plot that, you get exactly a Hubble-like plot. Add more cars as suitable - they will all end up on the same straight line in the plot.
What is your conclusion from that? Would you expect any acceleration? Would you calculate how many microseconds the light needed for your observation? Probably not, those microseconds don't matter.

ur example does not fit the graph. if speed depends on distance then the cars would never leave the origin, and they would certainly not remain at constant speed if the farther away they were the faster they become.
i'm considering the equation of position (distance) according to time.
d(t) = at^2 + v(0)t +d(0)
hubble's plotting dV/dD. V is a function of time and so is distance, d=rt. his x-axis is not an independent variable. convert to time domain and we see where things are heading in the future, which my physics friend says is the goal of physics. btw, i haven't been able to convince him either, which is partly why I'm here.

 

[Chalnoth]

EEE degree w/ phys minor.
hubble's graph shows velocity increasing over distance, not time.
an image 10 mil ly away is 10 mil y old (t = -d/c)
the origin of hubble's graph is d=0 and t=now, not 0
older images are faster and older image means younger galaxy
distance is proportional to age, which is negative time
if V increased further back in the past, it is decreasing in the future
V accelerates into the past (hubble's graph), means V decelerates into the future
is there error in my logic?
also, if the claim is that everything started at the same point at the same time, how do we not know what that time is?

The short answer is: this is all taken into account in standard methods for examining distance and recession velocity.

Yes, the fact that the universe has expanded over time, and that that expansion has changed in rate over time, means that distance and velocity in cosmology are pretty complex topics. But they are tractable. If you want to see some of the mathematical details, I recommend taking a look at some of the distance measures used in Cosmology:
https://arxiv.org/abs/astro-ph/9905116

The recession velocity at a particular time is the Hubble expansion rate at that time multiplied by the proper distance at that time.

 

[fencewalker]

The short answer is: this is all taken into account in standard methods for examining distance and recession velocity.

Yes, the fact that the universe has expanded over time, and that that expansion has changed in rate over time, means that distance and velocity in cosmology are pretty complex topics. But they are tractable. If you want to see some of the mathematical details, I recommend taking a look at some of the distance measures used in Cosmology:
https://arxiv.org/abs/astro-ph/9905116

The recession velocity at a particular time is the Hubble expansion rate at that time multiplied by the proper distance at that time.

i saw no mathematical details at that link. i covered position formulae in the post just prior to urs. please check those and show where i might not b getting it.

 

[PeterDonis]

i saw no mathematical details at that link. i covered position formulae in the post just prior to urs. please check those and show where i might not b getting it.

Please be aware that "text-speak" of this sort is not acceptable per the PF rules. Please express yourself using normal English.

 

[Bandersnatch]

ur example does not fit the graph. if speed depends on distance then the cars would never leave the origin, and they would certainly not remain at constant speed if the farther away they were the faster they become.

The cars were never concentrated at the origin, though. There was always non-zero separation between cars. Zero separation is in the limit as you extrapolate the model back in time, but it's not included in the model, and besides the model loses applicability long before that, as cars start to overlap (which is unphysical).

When you look at the Hubble law: $V=Hd$ as shown on the original graph*, it is not the $H$ that is constant in time. It's the $V$. Each galaxy, at separations $d_A=1$, $d_B=2$, $d_C=3$ and $d_D=4$ today ($t_0$) recede at velocities $V_A=H_0*1$, $V_B=H_0*2$, $V_C=H_0*3$, $V_D=H_0*4$. At $t_1$, when all the distances have doubled, the recessional velocity of each galaxy must remain the same, so $H_1=H_0/2$. At $t_3$ when the scale factor is 3, the Hubble parameter is 1/3rd, and so on.

*the caveat is needed in order to disregard effects of matter content retarding the rate of expansion (trying to make $V_n<V_0$) and dark energy acting in the opposite way. At the distances measured by Hubble these effects are swamped by measurement errors, as are the effects of light travel time.

i saw no mathematical details at that link.

Click on the 'PDF' under downloads to read the actual paper rather than just its abstract.

 

[PeterDonis]

i'm considering the equation of position (distance) according to time.
d(t) = at^2 + v(0)t +d(0)

This is not a relativistically correct formula. Also, even if you correct that issue, this formula assumes that spacetime is flat, and the spacetime of the universe is not.

 

[mfb]

ur example does not fit the graph.

It fits the graph exactly.

if speed depends on distance then the cars would never leave the origin

That statement is wrong.

and they would certainly not remain at constant speed if the farther away they were the faster they become.

I never said "for a given distance the speed is constant". It is not. For a given car, the speed is constant (in this simplified car universe). For a given point in time, cars faster away move faster.
Plot the cars and you'll see how they perfectly fit to a straight line on the Hubble plot.

btw, i haven't been able to convince him either

You are wrong. It is pointless to try to convince others. Try learn the right thing.

 

[Chalnoth]

i saw no mathematical details at that link. i covered position formulae in the post just prior to urs. please check those and show where i might not b getting it.

You have to click through to the PDF. Here's the direct link to the paper:
https://arxiv.org/pdf/astro-ph/9905116.pdf

 

[fencewalker]

This is not a relativistically correct formula. Also, even if you correct that issue, this formula assumes that spacetime is flat, and the spacetime of the universe is not.

these velocities are not at relativistic speeds, so i don't understand your response. thank you for your input, however.

 

[mfb]

these velocities are not at relativistic speeds, so i don't understand your response. thank you for your input, however.

The apparent galaxy speeds are relativistic for distances of several billion light years. But see above: Interpreting them as speed is not really useful.

In the region where they are nonrelativistic, the car example works nicely.

 

[fencewalker]

It fits the graph exactly.That statement is wrong.I never said "for a given distance the speed is constant". It is not. For a given car, the speed is constant (in this simplified car universe). For a given point in time, cars faster away move faster.
Plot the cars and you'll see how they perfectly fit to a straight line on the Hubble plot.You are wrong. It is pointless to try to convince others. Try learn the right thing.

It fits the graph exactly.That statement is wrong.I never said "for a given distance the speed is constant". It is not. For a given car, the speed is constant (in this simplified car universe). For a given point in time, cars faster away move faster.
Plot the cars and you'll see how they perfectly fit to a straight line on the Hubble plot.You are wrong. It is pointless to try to convince others. Try learn the right thing.

from your example:
Imagine two cars moving away from you, starting at the same time. One drives at 50 km/h, the other one at 100 km/h. After an hour, you see the first car at a distance of 50 km moving at 50 km/h, the other one at a distance of 100 km moving at 100 km/h. If you plot that, you get exactly a Hubble-like plot. Add more cars as suitable - they will all end up on the same straight line in the plot.
What is your conclusion from that? Would you expect any acceleration? Would you calculate how many microseconds the light needed for your observation? Probably not, those microseconds don't matter.

i was assuming spherical co-ordinates, so i see them starting on top of each other, moving away from me at the origin. car A starts at r=0 km (my assumption), v=50 km/hr. after one hour car A is 50 km away and still moving at 50km/h, which sounds constant for all intents and purposes. i would not calculate the time it took for the images to get to me because the distances are too small.
let's say galaxy A is 50 million light years away, then any data i record from it is 50 million years old. at the same time we see galaxy A, we also see galaxy B at 100 million light years and that data is 100 million years old. that is my view of now at the origin. i could continue but first i would like your confirmation so far. it is the basis of my understanding, or perhaps misunderstanding.

 

[Chalnoth]

from your example:
Imagine two cars moving away from you, starting at the same time. One drives at 50 km/h, the other one at 100 km/h. After an hour, you see the first car at a distance of 50 km moving at 50 km/h, the other one at a distance of 100 km moving at 100 km/h. If you plot that, you get exactly a Hubble-like plot. Add more cars as suitable - they will all end up on the same straight line in the plot.
What is your conclusion from that? Would you expect any acceleration? Would you calculate how many microseconds the light needed for your observation? Probably not, those microseconds don't matter.

i was assuming spherical co-ordinates, so i see them starting on top of each other, moving away from me at the origin. car A starts at r=0 km (my assumption), v=50 km/hr. after one hour car A is 50 km away and still moving at 50km/h, which sounds constant for all intents and purposes. i would not calculate the time it took for the images to get to me because the distances are too small.
let's say galaxy A is 50 million light years away, then any data i record from it is 50 million years old. at the same time we see galaxy A, we also see galaxy B at 100 million light years and that data is 100 million years old. that is my view of now at the origin. i could continue but first i would like your confirmation so far. it is the basis of my understanding, or perhaps misunderstanding.

Sure. But at some point that calculation will break down, so nobody within cosmology bothers with this sort of classical approximation. They make use of the full General-Relativistic calculation, which I linked to you earlier.

This calculation does assume that the universe is perfectly uniform. That assumption isn't strictly true, but the universe is uniform enough that it works well enough for most calculations.

 

[fencewalker]

Sure. But at some point that calculation will break down, so nobody within cosmology bothers with this sort of classical approximation. They make use of the full General-Relativistic calculation, which I linked to you earlier.

This calculation does assume that the universe is perfectly uniform. That assumption isn't strictly true, but the universe is uniform enough that it works well enough for most calculations.

Sure. But at some point that calculation will break down, so nobody within cosmology bothers with this sort of classical approximation. They make use of the full General-Relativistic calculation, which I linked to you earlier.

This calculation does assume that the universe is perfectly uniform. That assumption isn't strictly true, but the universe is uniform enough that it works well enough for most calculations.

i will try to re-examine your previous link, otherwise could you be more specific regarding 'But at some point that calculation will break down', and by 'this calculation' do you mean my calculations or the ones in your link?

 

[Chalnoth]

i will try to re-examine your previous link, otherwise could you be more specific regarding 'But at some point that calculation will break down', and by 'this calculation' do you mean my calculations or the ones in your link?

The non-relativistic calculations will break down at sufficiently-large distances. I couldn't tell you exactly where, because I don't know.

 

[fencewalker]

The non-relativistic calculations will break down at sufficiently-large distances. I couldn't tell you exactly where, because I don't know.

trying to comprehend 'sufficiently large distances.' since the assumption is the farther away it is the faster it will go, and given enough distance the velocities will approach c?
but the farthest we see is 13-14 billion light years away, which i recall the velocity was not relativistic. beyond that we see no galaxies, just W-map. my interpretation of that is there were no galaxies before that time. the oldest images are of the youngest galaxies which are moving the fastest. the younger the images get as we view closer galaxies, we see lower velocities. closer galaxies are older than the galaxy we see at the edge, in universal time. as time goes forward to the present, galaxies get older and slower, up to the closest (oldest in universal time) galaxy which has decelerated so much it is moving toward us, not away.

 

[Chalnoth]

trying to comprehend 'sufficiently large distances.' since the assumption is the farther away it is the faster it will go, and given enough distance the velocities will approach c?

It has nothing to do with that, actually. It has to do with how much space-time curvature there is between us and the location. The speed is unrelated because the speed of far-away objects is not a concept that is found in General Relativity at all (relative speed in GR is only well-defined for objects at the same physical location). We tack on "recession velocity" afterwards only as a heuristic, not as anything describing reality.

The amount of space-time curvature, in turn, is a function of how much expansion there has been since the photon was emitted. My naive guess would be that this will start to become a significant factor long before hitting $z=1$, which is a pretty tiny fraction of the observable universe.

 

[mfb]

let's say galaxy A is 50 million light years away, then any data i record from it is 50 million years old.

That is still negligible compared to the age of the universe.

As mentioned before, what we measure is not an actual velocity. What we see is the expansion of the universe that happened in the last 50 million years. Our datapoint is not 50 million years old, it is the accumulated expansion that happened in the last 50 million years. For just 50 million years, the difference between those two is negligible.

but the farthest we see is 13-14 billion light years away, which i recall the velocity was not relativistic.

If you just multiply the Hubble constant by 13 billion light years, you get about the speed of light. That is certainly relativistic. And it also means you should not do such a simple multiplication.

We don't see 13 billion light years far, however, as the universe expanded while the light was away. The most distant things we see today (the cosmic microwave background) was 42 million light years away from us at the time the light was emitted, and it is 46 billion light years away today. As mentioned earlier: As soon as you look for objects a few billion light years out, things get more complicated.

as time goes forward to the present, galaxies get older and slower

They don't get slower (at least not in a way that would be relevant here). Those galaxies were slow all the time. The other galaxies were fast all the time. To a good approximation, the speeds of galaxies (with the usual caveat) don't change.