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### Energy = Mass x Speed of Light Squared ??

12/18/2009 2:30 PM

Astrophysics tells us that not only is the universe expanding, but that it is accelerating, due to the effect of Dark Energy which is said to comprise 74% of the mass of the universe. With unbridled acceleration, we are told that our view of galaxies will start to "blink out" in time as they reach the speed of light, an obvious consequence of eternal acceleration. What will actually happen however, when a mass like a galaxy reaches a speed that Einstein tells us will result in infinite mass. I know this is a big universe, but won't something of "infinite" mass be a problem?

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The Engineer

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#1

### Re: Energy = Mass x Speed of Light Squared ??

12/18/2009 3:39 PM

You Wrote:"What will actually happen however, when a mass like a galaxy reaches a speed that Einstein tells us will result in infinite mass."

As I understand it, that won't happen. You are mistaking "adding space in between galaxies" with "objects moving away from each other".

The common example given is the two points on a balloon example. As you blow up a balloon, the space between the two points increases. Imagine now if you had an ant crawling from one point to the other as the balloon was being blown up. As the balloon expanded, the ant would find that the distance between the two points was longer than when it began its journey, but it would still make progress, just at a slower rate than it expects given it's speed. If the balloon is blown up so that it produces as much new distance per second between those two points as the ant can can travel, then the ant will get no closer to the second point. In fact, both points will move away from it, one faster than the other. The ant is trapped on its journey forever (or until the balloon pops).

Notice that the two points aren't moving on the balloon in the example above, there is just more balloon surface area between them. The points are on the same part of the balloon that they started on. So even though the distance between the points is growing and growing, it isn't because the points themselves are moving. The infinite mass you speak of would only occur if the reason the distance between galaxies was increasing was becasue they were moving away from each other through space. That however isn't the reason the space between galaxies is increasing.

Hopefully that helps.

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#10

### Re: Energy = Mass x Speed of Light Squared ??

12/21/2009 12:18 PM

Hi Roger, The speed of the walls of the universe cannot be measured, hence the balloon concept cannot be determined. The acceleration concept has been proven by measuring the speed (acceleration) of the galaxies. Based on measurements, the galaxies are accelerating away and will blink out from our perspective eventually, when the speed of light is attained. This speed is certain for all galaxies in the known universe. Hi All, While I understand that Einstein diddled in "relative" thought, the equation means if I (or a galaxy) can fly through space at the speed of light, I will be infinitely massive. Is there something wrong with my thought on this, or is the equation incomplete?

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#11

### Re: Energy = Mass x Speed of Light Squared ??

12/21/2009 1:20 PM

You Wrote:"The speed of the walls of the universe cannot be measured, hence the balloon concept cannot be determined."

What do you mean by "the walls of the universe"?

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Roger Pink
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#12

### Re: Energy = Mass x Speed of Light Squared ??

12/21/2009 2:19 PM

The "walls of the universe" are the point in space time where an interface occurs between nothingness and the photon, neutron, anti-neutron soup mixture generated during the big bang. Although there is no physical wall, the collissions between these three particles are dense to the extent that they form a wall, and the collissions are continuing the expansion.

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#13

### Re: Energy = Mass x Speed of Light Squared ??

12/21/2009 2:52 PM

Expansion doesn't work like that. The universe isn't pushing out from a center, there is no center. All space is expanding everywhere at a set rate. The space between the Earth and the Moon, the space between the Earth and the Sun, every meter of that distance is growing larger as though the universe is being supersized (but the planets and the suns stay the same size).

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#14

### Re: Energy = Mass x Speed of Light Squared ??

12/21/2009 3:58 PM

It does indeed work that way, and in fact that is exactly what happened and is happening. There was an initial point in space from which the big bang occurred, and everything is moving away from that point. The phenomenon is identical to setting off an explosion in a vacuum. The exploded material forever moves away from the initial point. In this case however, 4% of the exploded material (all the stuff we can see) is subject to the gravity of Dark Energy and Dark Matter (the 96% of the mass of the universe we can't see), which is causing the 4% to accelerate away from the initial point of explosion.

In the Beginning

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#15

### Re: Energy = Mass x Speed of Light Squared ??

12/21/2009 4:07 PM

You Wrote:"There was an initial point in space from which the big bang occurred, and everything is moving away from that point."

That's incorrect. Everywhere in the universe is that point. That's why cosmic background radiation is homogeneous. The universe is not expanding from any point. The universe is the point expanded.

You Wrote:"The phenomenon is identical to setting off an explosion in a vacuum. The exploded material forever moves away from the initial point."

No it isn't.

You're misunderstanding cosmic expansion and it is leading you down all kinds of incorrect tangents.

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#17

### Re: Energy = Mass x Speed of Light Squared ??

12/23/2009 5:47 AM

-"The space between the Earth and the Moon, the space between the Earth and the Sun, every meter of that distance is growing larger as though the universe is being supersized (but the planets and the suns stay the same size)." --- Does this mean the Sun and the Moon were closer to us million years ago than it is now?. How much distance we move away in a year from the Sun?. If addition of space is happening at every point in the Universe, then is it happening at constant rate ?.Or will it slow down and finally start reversing. By reversing I mean deletion of space.

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#18

### Re: Energy = Mass x Speed of Light Squared ??

12/23/2009 9:06 AM

You Wrote:"Does this mean the Sun and the Moon were closer to us million years ago than it is now?"

No. But not because the universe isn't trying. You see, the amount of cosmic expansion is very small and easily overcome by gravity at such small distances as between the Earth and Sun and Earth and Moon. Even the distance between some galaxies are too small and you get galaxy clusters. When you get far enough away though, the Hubble Flow takes over.

You Wrote:"If addition of space is happening at every point in the Universe, then is it happening at constant rate?"

When viewed over billions of years, the constant has changed. It is however constant throughout the universe at any given time (as far as I know).

These are all good questions and you seem genuinely interested in learning about this topic. For these reasons I strongly recommend that you visit this blog on Relativity by Jorrie. He is by far much better equipped to correctly and precisely answer your questions than I am (indeed, most of what I know I've learned through his blog and his book).

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#33

### Re: Energy = Mass x Speed of Light Squared ??

12/23/2009 10:36 PM

Thanks a lot for clearing my doubts.

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#19

### Re: Energy = Mass x Speed of Light Squared ??

12/23/2009 9:31 AM

You don't explicitly say this, but am I right that we do not expect galaxies to "blink out"? My reasoning is that if a galaxy is to retreat beyond our observational range then: either everything between you and that galaxy would also need to cease to be observable, or the galaxy would cease to be observable from anything within your range of vision. This is on the basis that if we can see an object between you and the "vanishing" galaxy we could also see some of the light that impinges on the intermediate object - including light from the galaxy itself.
(My understanding is that what we should observe is an ever-increasing rate of red shift).

In the confines of this discussion, the following is probably pure pedantry; however:
Isn't the (small) variation in the level of the background radiation supposed to be evidence that the expansion rate is not quite uniform?

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#20

### Re: Energy = Mass x Speed of Light Squared ??

12/23/2009 10:30 AM

Hi Fyz,

You Wrote:"You don't explicitly say this, but am I right that we do not expect galaxies to "blink out"?....(My understanding is that what we should observe is an ever-increasing rate of red shift)."

To be honest, I'm not sure. Certainly we should observe an ever-increasing rate of red-shift, but I would expect there is a distance at which the expansion between galaxies would exceed c and then we would stop receiving light from the source. I could be wrong though and if that's incorrect please let me know.

You Wrote:"In the confines of this discussion, the following is probably pure pedantry; however: Isn't the (small) variation in the level of the background radiation supposed to be evidence that the expansion rate is not quite uniform?"

As I understand it, and I'm no expert on this so it could be totally wrong, the small variations in the level of background radiation are explained as quantum fluctuations in the early universe. However, I don't know whether the cosmic expansion is inhomogeneous when mass is inhomogeneous distributed (as would be the result of the quantum fluctuations). I wouldn't be surprised if the result of inhomogeneous mass distribution is inhomogeneous expansion. If you know anything regarding this please let me know as I would be interested.

I wouldn't mind hearing Jorrie's explanation of these things.

Roger

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#21

### Re: Energy = Mass x Speed of Light Squared ??

12/23/2009 11:49 AM

"Blinking out": I believe not. To my mind it must be in the realms of half-thought out science fiction. It can't happen purely as a result of expansion; the requirements for "blinking out" would either be a locally infinite expansion rate (not part of present cosmology SFIK) or gravitational anomalies that redirect the light from a particular galaxy away from you (so not connected with accelerating expansion).

Explanation:
If you can see an object X you will see it at a previous time, and all light that was passing that object in your direction will also be visible. So either X lost visibility of distant objects before you did, or you lose sight of X (or the light is diverted from you - but that's a highly non-uniform hypothesis). Find the first location to lose sight of distant galaxies - the same applies to it, so there is no first site. So either:
The earliest point you can see can never reduce; or
You will lose sight of all objects however close.

Another way of looking at this is to consider the acceleration as a continuing reduction in the range at which you see a given red-shift, and red-shift actually multiplying the wavelength by a factor (of >1). The red shift becomes arbitrarily great, but never quite infinite. (It's equivalent to the reason that two objects moving in opposite directions at velocity c-δ are still not moving at c relative to each-other).

Yes, agreed quantum fluctuations initially. If solids are to retain their properties, the expansion rate can't be uniform within the solid. Otherwise put, the relationships between electric fields, gravitation and short-range forces will enforce non-uniformity at a macroscopic level. At larger scales I would expect non-uniform "surfaces" to also expand non-uniformly - but I'm no expert in this area.

I too would be happy to hear from someone who has looked into this in more depth.

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#22

### Re: Energy = Mass x Speed of Light Squared ??

12/23/2009 2:06 PM

The following is from the website space.com: "

Loeb, a theoretical astrophysicist at the Harvard-Smithsonian Center for Astrophysics, peers through Einstein-colored glasses. His view of the end of the visible universe is rooted in the General Theory of Relativity and based on the notion that everything is expanding at an ever-increasing pace.

All distant galaxies are moving away from us and moving faster all the time. Few researchers debate this point. Few have predicted its ultimate consequence quantitatively as Loeb did.

Eventually, Loeb says, galaxies will recede at the speed of light, making it impossible for their light -- or any other radiation or information -- to traverse the cosmos to our home in the Milky Way Galaxy.

"Any given source accelerates away from us and eventually reaches a speed larger than the speed of light so that photons emitted from it cannot catch up with the cosmic expansion, relative to us," he said.

Already, galaxies more than 6 or 7 billion light-years away are beyond contact, Loeb figures. Such galaxies, measured by astronomers to have a redshift of 2 or more, will not be able to transmit any signal to us in the future due to the accelerated expansion of the universe."

Whether this is science fiction or not is debatable, but the best astrophysics people in the world think it will happen. This is the crux of my initial question. Since these people say it will happen, I can only accept it as a possibility. My question is "when these galaxies reach the speed of light, will their mass go to infinity as Einstein declares in his equations?"

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#23

### Re: Energy = Mass x Speed of Light Squared ??

12/23/2009 2:27 PM

I say again, it is relative to us. If we were traveling with the galaxy, the mass would be the same as if it was stationary (from our perspective). What part of relative do you not understand?

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#24

### Re: Energy = Mass x Speed of Light Squared ??

12/23/2009 2:43 PM

When an object that emits radiation, moves away from us at a speed that no longer allows that radiation to be seen by us it IS moving away from us at the speed of light RELATIVE to us. What part of this are you struggling with?

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#28

### Re: Energy = Mass x Speed of Light Squared ??

12/23/2009 3:15 PM

Please read this carefully. What you are talking about refers to when things are moving THROUGH SPACE. The recession velocity of galaxies due to the hubble expansion is NOT due to these galaxies moving THROUGH SPACE. Therefore your question doesn't apply.

Here's another analogy (lets use them all). Imagine raisins in dough. As you heat the dough it expands and the raisins are farther away from each other.....HOWEVER the raisins aren't growing apart because they are moving THROUGH THE DOUGH, the dough in between the raisins is expanding.

Does that make sense to you?

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#29

### Re: Energy = Mass x Speed of Light Squared ??

12/23/2009 3:30 PM

Yes, actually it does. So basically you're saying we are stationary in our own part of the universe even though we may be moving at the speed of light relative to another galaxy. Furthermore you are saying that the nothingness outside the "walls of the universe" into which the expansion occurs is not considered when one computes relative velocity. That was the part that was throwing me (and still frankly has me ready for the eggnog). Thanks Roger, I was hoping you would stick with me until I could grab it. While I don't understand it completely, I can at least see it now.

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#31

### Re: Energy = Mass x Speed of Light Squared ??

12/23/2009 3:53 PM

You wrote:"While I don't understand it completely, I can at least see it now."

You and me both. Trust me, nothing is harder on your intuition than Relativity.

Take my advice and forget about "what is it expanding into" because that by definition would be outside the Universe and general relativity only covers the universe (at a very basic level with basic assumptions). You need only know that it's expanding (like dough).

The key to this discussion, and your question, is that it gets harder and harder to accelerate something through space as an object's velocity moving through space approaches the speed of light, but "recession velocity" is due to space expanding (like dough), not objects moving through space.

To beat the raisin and dough analogy to death. When the dough expands, the raisins mover further apart, yet they don't experience friction. Yet if you move the raisin through the dough it definitely experiences friction. Hopefully that makes sense.

When it comes to Relativity I've developed the following rules:

1. Don't trust your intuition when it comes to relativity. Don't underestimate how the addition of time as a coordinate wreaks havoc on our intuition. It takes years for your intuition to adjust (I'm not close to there yet).

2. Trust Jorrie. You know how I said above it takes years for that intuition to develop? Jorrie has that intuition. He has a blog here on CR4, reading it is good for developing an intuition over time.

3. Learn to read and understand space-time diagrams (seriously Roger, you need to learn how to read and understand these better (sorry, sometimes my inner-monologue leaks out)).

You may have saw Fyz and I discussing galaxies blinking out. On this subject more so than most I am completely prepared that I'm completely wrong. Relativity is tough, don't ever worry about having a misconception.

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#32

### Re: Energy = Mass x Speed of Light Squared ??

12/23/2009 4:09 PM

I am not struggling with any of this but your attitude. Your comment has nothing to do with your question! Perhaps this will clue you in.

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#25

### Re: Energy = Mass x Speed of Light Squared ??

12/23/2009 2:48 PM

This time I'll type louder. Einstein did not say that.

All velocities are relative. No object goes faster than the speed of light. No object goes slower than the speed of light. All objects travel at the speed of light. Some go through time, some through space, and some through space-time.

You must do the measuring from your reference frame. There is no absolute frame. You cannot measure an object going at the speed of light if you also measure that object as having a rest mass in your reference frame.

If you add energy to an object in your reference frame, it will go faster. In order to accelerate that object to the speed of light, you would have to add an infinite amount of energy (providing it had rest mass in your frame). Energy and mass are equivalent.

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#27

### Re: Energy = Mass x Speed of Light Squared ??

12/23/2009 3:00 PM

OK, that makes sense. But what does Loeb mean then when he says

"Eventually, Loeb says, galaxies will recede at the speed of light, making it impossible for their light -- or any other radiation or information -- to traverse the cosmos to our home in the Milky Way Galaxy."

I guess this is what I can't figure out. Loeb says they WILL reach the speed of light relative to us. Even if this speed is relative and we are moving in opposite directions, won't we/they eventually reach the speed of light due to this acceleration? And if so, do we assume infinite energy has been input into the system, and infinite mass will follow?

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#30

### Re: Energy = Mass x Speed of Light Squared ??

12/23/2009 3:45 PM

No. We didn't add the energy.

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#41

### Re: Energy = Mass x Speed of Light Squared ??

12/24/2009 12:44 PM

"All velocities are relative. No object goes faster than the speed of light. No object goes slower than the speed of light. All objects travel at the speed of light. Some go through time, some through space, and some through space-time."

Did Einstein say that? If so, please provide a reference. If all objects travel at the speed of light, then how can they be relative?

P.S. Dont type so loud.

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#42

### Re: Energy = Mass x Speed of Light Squared ??

12/24/2009 1:00 PM

It's possible to reconcile the 'all objects travel at c...' if you do the Laplace transform on the coordinates of 3-D space and the 4th of time and refer to all separations using Einstein's "interval".

Now I have a kwestion if you're ready to look at it that way... What is the speed of space? {ouch}

I believe that to evaluate it the notion of 'speed' has to be abandoned, primarily because it's a ratio. The invariant is mass, just like Einstein said. Only by working with the 4-vector does the ambiguity clearly fall away.

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#43

### Re: Energy = Mass x Speed of Light Squared ??

12/24/2009 1:07 PM

Nah, Einstein didn't say that. That's from Epstein. The common usage of speed is only in space; that's OK but it completely misses the geometry. The whole thing looks a lot more sensible in Minkowski space-time.

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#38

### Re: Energy = Mass x Speed of Light Squared ??

12/24/2009 9:38 AM

Loeb writes that the universe will split into separate gravitationally-coupled entities. This corresponds to the all-or-nothing scenario I described earlier.

But there is an apparent problem with the expansion rate - adjacent "points" (however close) in the inter-entity vacuum will need to separate at greater than the speed of light; this is the infinite separation velocity I wrote about earlier. SFIK there is no mathematical problem in this happening after the "empty" regions are decoupled from the gravitational regions. However (again SFIK) no-one has satisfactorily modelled the transition from coupled to decoupled - the best I've heard about is a bit of arm-waving and cries of "quantum effects". Not that I'm either close to the field or expert, of course.

(As ever, any popular-level article has to ignore these issues)

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#26

### Re: Energy = Mass x Speed of Light Squared ??

12/23/2009 2:59 PM

Hi Fyz,

Based on this Wiki article, it seems like it can occur (blinking out):

"If, as is inferred from current observations, the expansion of the universe is in fact accelerating then at a later time, some objects within the Hubble limit no longer will be observed (by us) as they are today."

I realize the above "observed (by us) as they are today" can be interpreted as red shift, but I think if you read the whole article (it isn't too long) the context means "no longer detectable"

I also found this paper that discusses this issue (actually not this exact issue):

I think I understand what they are saying. Since as the further we look outward in space we look further back in time, and since expansion was slower back then, the hubble sphere (sphere that we can't see beyond) was larger (expands) the further we look back in time (slower expansion rate, larger distance required for recession speed > c).

What do you think? It really seems to me as though blinking out is possible if the recession speed exceeds the speed of light (once you correct for the change in the acceleration of the expansion over the age of the universe).

Roger

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#35

### Re: Energy = Mass x Speed of Light Squared ??

12/24/2009 12:26 AM

Hi Roger.

Fyz is right in that it is redshift tending towards infinity that eventually makes galaxies (that were once observable) 'unobservable', at least in in the very distant future of a vacuum energy dominated universe. It is fairly obvious that the farthest light that we can see, the CMB photons, will never just "blink out"...

Also Look at the graph in my "Cosmic Ballistics" blog entry. It does not matter how close I push the start of the graph to 'age zero', a photon will at first recede, but it will eventually make it towards us. There are obviously galaxies that are unobservable today that will never become observable - their photon origins lie in the 'minus age' side of the graph.

You may be right for a phantom energy dominated 'Big Rip'[1], which seems an unlikely scenario, but not quite ruled out. This may perhaps cause a "blink-out" of presently observable distant galaxies.

You wrote: "However, I don't know whether the cosmic expansion is inhomogeneous when mass is inhomogeneous distributed (as would be the result of the quantum fluctuations)."

The standard cosmological models assume that the expansion rate of space is only a function of the overall energy density and some initial conditions, because it assumes large scale homogeneity. It is however possible to have localized differences in expansion rate - local like on the scale of voids and super-clusters. This is normally modeled as perturbations of the homogeneous model.

-J

[1] Phantom energy is a hypothetical form of dark energy with equation of state w < - 1. If it exists, it could cause the expansion of the universe to accelerate so quickly that a Big Rip would occur. I'm not too familiar with this model.

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#36

### Re: Energy = Mass x Speed of Light Squared ??

12/24/2009 8:20 AM

Hi again Roger.

I wrote: "Fyz is right in that it is redshift tending towards infinity that eventually makes galaxies (that were once observable) 'unobservable', at least in in the very distant future of a vacuum energy dominated universe."

Since this is a difficult concept to get one's head around, a few more lines of prose may be in order.

There is obviously also the trivial issue of increasing proper distance that will decrease the observed luminosity of observable galaxies towards non-observability.

What WJMFIRE probably read is that (with eternal accelerating vacuum energy expansion) we can never observe any light that a galaxy with present redshift of more than about 1.66 emits now. Such a galaxy is now some 15.3 Gly from us, while it was only 5.7 Gly away (and t ~ 4 Gy) when it emitted the light that we see now. As Fyz pointed out, we will always be able to observe some photons, however feeble, emitted earlier than t = 4 Gy.

Hope this helps.

-J

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#37

### Re: Energy = Mass x Speed of Light Squared ??

12/24/2009 9:22 AM

Thanks Jorrie and Fyz,

To help me understand where I'm going wrong, can you help me with this:

I guess the part I'm confused about is this. If the size (radius) of the hubble sphere is changing, can't a galaxy that was within it be found outside of it in the future? If so, wouldn't that mean the galaxy blinks out?

My misunderstanding is that as any galaxy approaches the surface of the hubble sphere from the inside, it's redshift grows larger and larger till it approaches infinity at the surface of the hubble sphere and blinks out when it moves beyond (the light just can't catch up to us).

That's where my thought process is, any links or explanations that can help me revise it (fix it) would be appreciated.

Roger

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#40

### Re: Energy = Mass x Speed of Light Squared ??

12/24/2009 12:39 PM

The difficulty comes from the notion that the 'sphere' cannot be observed instantaneously. We see light coming from the 'edge' of the universe and say it's 13.8 GLy away... but is that *now* or *then*. If you take its apparent velocity and multiply that by the time it's been receding, you come up with a new radius.

I believe someone else noted that the receding galaxy will *never* wink out the light will simply continue to redshift and the time will dilate towards the ultimate freeze-frame... All the while the galaxy will be 'receding' as the space between us and it continues to expand into that extra radius that the popular explanations don't adequately investigate.

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#45

### Re: Energy = Mass x Speed of Light Squared ??

12/26/2009 2:27 PM

Hi Roger.

After having recovered somewhat from the festive meals, here is a preliminary response to your problem.

The 'Hubble sphere' is a concept that exists only on paper, really. It is not even related to any real radius or distance in the cosmos, since it is expressed as the distance light can travel in the time since the BB in empty, static, Minkowskian space. This does not represent an expanding universe, let alone one with accelerating expansion.

I think part of the misunderstanding originates in the historical truth that for the Einstein-de Sitter universe (decelerating until expansion stops), more and more galaxies would come into view ("blink-on") when their light has had time to reach us, hence "crossing the Hubble sphere from the outside", so to speak. A common misconception is that for an eternally accelerating expansion, the opposite must happen: galaxies should "cross the Hubble sphere from the inside" and hence "blink-out". This is not so: once a galaxy is observed, the string of photons linking it to us will not be broken by vacuum energy driven expansion - it can only be redshifted and it will take infinite time to redshift it to infinite wavelength.

Fyz has explained the issue well in his post 21. I'm working on a balloon-analogy schematic 'proof' of the same and will post it when finished and tested...

-J

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#46

### Re: Energy = Mass x Speed of Light Squared ??

12/26/2009 5:39 PM

Jorrie,

Ok, you seem certain so I believe you. Plus the "it will take an infinite amount of time as redshift goes to infinity" sounds like relativity, if you know what I mean.

An equation would be usefull, but I don't know if that's possible for this problem in a way that's useful. I would appreciate any explanation you can offer (or Fyz can offer) to help me better understand this.

Roger

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#47

### Re: Energy = Mass x Speed of Light Squared ??

12/27/2009 9:06 AM

Hi Roger.

Before attempting equations, let's try the 'trusted' old cosmic balloon again. The diagram to the right was done for a perfectly spherical balloon, but then I stretched it horizontally in order to make the plot more readable (hence the different horizontal and vertical scales).

The 'teardrops' are CMB photon paths from t~400 thousand years after the BB, originating from two points on opposite sides of the origin. (We only need the path of one side, but the teardrops look so so much prettier ;) We are at the top of the teardrops, moving 'up' with the expansion. The teardrops are obviously light 'crawling' along the surface of the balloon, while we and all other galaxies just sit on the surface and only 'move' with the expansion, as the balloon gradually grows.

The blue teardrop is for CMB light reaching us now, t~13.6 Gy and the red teardrop for light that will reach us much later (at t~24 Gy), when the balloon has doubled in size. The green radial line represents the hyperspace path of one early galaxy, having formed very soon after the BB. The blue bullet, where the green radial intersects the blue teardrop is where the galaxy was when we observe it now, at redshift z=4. The red bullet is where this galaxy will be when observed at t~24 Gy (by someone in our galaxy, because Earth won't be around). The gray radial line and bullet represent a galaxy that is outside of our present observable universe and will remain so forever.

Now, what does or doesn't this 'prove'? Not much, but a few important facts are fairly obvious. Firstly, that 'green galaxy' at z=4 must always stay on the teardrop - once on our teardrop, always on our teardrop. Secondly, the 'gray galaxy' at z=4 will stay outside our teardrop forever (at least for eternally accelerating expansion).

Instead of me waffling further, maybe you should question what is not clear to you. Do not feel perturbed if it is as clear as mud - I find it generally difficult to explain it!

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#48

### Re: Energy = Mass x Speed of Light Squared ??

12/27/2009 11:07 AM

Hi Jorrie,

Thanks for the diagram, I'm starting to understand. What I think would be tremendously helpful, if it isn't too much trouble, would be two other diagrams just like the one you just provided, one in which expansion is decelerating (and thus we would expect "blinking on" and one where expansion isn't accelerating or decelerating but rather just steady. Does what I'm asking for make sense? I think it would help me start to develop a feel for what's going on.

Roger

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#49

### Re: Energy = Mass x Speed of Light Squared ??

12/27/2009 11:56 PM

Hi Roger.

Without the annotation frills, the bare graphs are easy to produce, so here are 3 cases. The brackets (e.g. 0,0,0) in the titles indicate present energy density parameters as decimal fractions of critical density Ω0, in the order: matter, radiation, vacuum energy density. Hence (0,0,0) means zero total energy density, with a constant expansion rate.

The green "galaxy lines" were chosen so that an early galaxy, formed at t~1 Gy, sits just outside the limits of present observability (the blue teardrop) for the specific case. It is reasonably clear that it is the matter-only case (1,0,0) where there is a possibility of 'blinking-on'. This is due to the very fast initial expansion rate required by the 'heavy' cosmos.

The vacuum-energy-only case has the almost 'heart-shape' because the expansion starts of slower than in the others and then builds up as the vacuum energy increases with volume. All the curves were drawn with the present expansion rate of H0 ~ 72 km/s/Mpc.

Hope this helps. I found these graphs to confirm intuition - there is no 'blinking-out'...

-J

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#50

### Re: Energy = Mass x Speed of Light Squared ??

12/28/2009 1:08 AM

Hi Jorrie,

Ok, I am now making my frustrated exhalation sound, not because I don't believe you, because I do, but because I can't understand the diagrams completely and it frustrates me. I think the best approach is for me to just ask questions until I get it,

Question #1 - What are the units of the x and y axis?

Question #2 - Does the top vertex of the teardrop represent when light arrives at Earth?

Question #3 - cZ=Vrecession, when you say Z=4, is that Vrec=4c or am I misunderstanding?

Roger

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#51

### Re: Energy = Mass x Speed of Light Squared ??

12/28/2009 1:35 AM

#1: You can view it as Gly, but it is actually dimensionless, just a scale factor (the expansion factor a scaled up by a factor 50). I should have rather used a, but I already had a spreadsheet for a 100 Gly radius cosmic balloon. The present expansion factor is a0 = 1, as always.

#2: Yea, I think I said that in a previous post...

#3: No, z is not a Doppler shift, it is cosmological redshift, z = 1/a - 1, so z = 4 means a = 0.2. Hence, z = 4 sits at 10 units radius, where the present radius is 50 units.

-J

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#52

### Re: Energy = Mass x Speed of Light Squared ??

12/28/2009 2:09 AM

Hi Jorrie,

Quick answers are best for now I think as it gives me more opportunities to ask follow-up questions.

Question 1: The blue vertex in the original diagram represents us now (z=0) and it is located at 50. I still don't understand what that 50 is. I'm sorry, I know I'm being thick here, but it's really messing me up. You said "a scaled up by a factor of 50". What is a agian? I'm just forgetting what these variables represent.

Question 2: What is the meaning of the negative axis. How can the scale factor be negative?

Roger

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#53

### Re: Energy = Mass x Speed of Light Squared ??

12/28/2009 2:27 AM

1. a is the expansion factor: a very simple, linear thing - 0 at the BB (origin), 1 at present and 2 when all distances have doubled due to expansion.

2. The balloon is an expanding sphere, a cut through an oblate view of it here plotted in polar coordinates...

-J

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#54

### Re: Energy = Mass x Speed of Light Squared ??

12/28/2009 3:11 AM

Right, so that's where I'm getting confused.

In the diagram above, the blue vertex is at 50a, which is labeled Z=0. Now Z=0 means a=1, so how can a=50 at the same spot? This is the source of my confusion, what am I missing here?

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#55

### Re: Energy = Mass x Speed of Light Squared ??

12/28/2009 3:34 AM

Hi Roger, yup, the hyper-radius can be very confusing! But, I did say that my graph scale is just the scale factor a multiplied by 50...

It is easiest to view it as just a completely arbitrary number. You remember that we have decided before (during the "design the perfect cosmic balloon" saga), that it has no physical meaning. For a flat universe, it is completely arbitrary what dimension we give to it, the maths stay exactly the same. This is exactly what cosmologist do for their hyper-spherical model. I use it for the balloon analogy just like they do.

So that R=50 at z=0 is just defined to be the scale for 'now'. I could have made it 1, or anything I fancied.

-J

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#56

### Re: Energy = Mass x Speed of Light Squared ??

12/28/2009 2:00 PM

Ok, that actually helps a lot. I couldn't get past it because I kept thinking it had some meaning I wasn't understanding. I will think on this (I need to think before I have any more questions). Thanks so far,

Roger

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#58

### Re: Energy = Mass x Speed of Light Squared ??

01/05/2010 6:53 AM

Roger,

This may (or may not) help. (Indeed, I suspect you have already understood the basics of this, and the issue is elsewhere)

Assuming we can receive light from region A, all light from (or passing through) A will have its wavelength red-shifted by a multiplying factor. That means that, if we can see point A (at a given time) we can also see light from anything that was visible from A at that time (for this purpose I'm including scattered light that might not allow of interpretation). Consequently, if A can see B, and we can see A, we can also see light from B.

Clearly, this sort of "blinking out" must divide the universe into regions - albeit these will change with time.
(A question for Jorrie: would the gravitational constants change once the bulk of the universe becomes invisible?)

Some further notes:

I think the above would imply that it is not the rate of expansion that causes "blinking out", but the rate of change of expansion - equivalent to the gravity of a black hole.

I'm not clear at what point (if at all) standard models allow of such a high rate of expansion in the presence of light (because of its finite mass). Could it even be that "blinking out" would only occur when there is nothing to be blinked?

At the other extreme, if we were to assume that this effect is possible, there is a question about Hawking-type radiation from the resultant "pseudo-black-hole". It might correspond to a much lower temperature than 2K, but might we still think we were seeing the residue of a "big bang"?

Mischievous regards

Fyz

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#59

### Re: Energy = Mass x Speed of Light Squared ??

01/05/2010 8:40 AM

Thanks Fyz.

I'm still a little confused, but I'm hoping time and thought will fix that. Thanks for your (and Jorrie's) explanations.

Roger

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#60

### Re: Energy = Mass x Speed of Light Squared ??

01/05/2010 10:32 AM

Hi Fyz,

Not sure what you meant by: "Clearly, this sort of "blinking out" must divide the universe into regions - albeit these will change with time. (A question for Jorrie: would the gravitational constants change once the bulk of the universe becomes invisible?)"

AFAIK, no 'blinking out' can happen in the ΛCDM model, but perhaps only in the 'phantom energy' models, with which I'm not too familiar.[1] In the current ΛCDM model, regions invisible today will remain invisible, so in this sense, there are different regions outside our 'horizon' (like the 'gray galaxy' in this post's figure. Gravitational events happening outside of our horizon will also never have any influence on us, i.e. remain undetectable.

As far as gravitational constants changing, no, I don't think so. If the ΛCDM model is right, even the Hubble 'constant' will eventually become a true constant. It is some 72 at present and will drop to around 64 or so and stay there. Again, I'm not sure what may happen in the phantom energy models.

About the "pseudo-black-hole", I'm not sure. There is an event horizon, but I do not quite see it operating like a black hole with Hawking-type radiation. If you have any more info on that, I would be very interested.

-J

[1] Phantom energy is a hypothetical form of dark energy with equation of state w < -1. If it exists, it could cause the expansion of the universe to accelerate so quickly that a Big Rip would occur.

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#61

### Re: Energy = Mass x Speed of Light Squared ??

01/05/2010 4:15 PM

Hi Jorrie

I'm not trying to suggest that I favour the model that predicts "blinking out" (to me it seems to speculative and requires too many unnecessary assumptions). 'All' that I'm doing is looking at what must happen in the event that blinking out does occur.

One crucial feature of an isolated region in such a universe is that, although it cannot receive radiation from elsewhere, radiation can still leave it (i.e. the radiation will pass into a region that is expanding away from the gravitationally coupled region). That would be the ultimate "big freeze". Gravitational waves would presumably do something similar - so the density of traversing g would fall; I'm not au-fait with current theories on this, but my half-understanding was that gravitational distortions depended on the apparent density of the universe - which presumably is determined by the local traversing g? (Please forgive incorrect terminology - but hopefully the gist is clear)

Regarding the radiation, I was basing that on only entropy considerations - and my instinct that rate-of-increase of entropy may be expected to escalate under these disrupted low-g conditions. Perhaps that might even provide some relief from the freeze.

Other than the splitting into gravitationally-coupled regions and the basic freeze (both consequences of a specific phantom energy model), all of this is pure ignorant speculation; but at least I'm not claiming my speculations are the expected outcome of presently accepted theories, as Loeb appears to be claiming for his.

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#62

### Re: Energy = Mass x Speed of Light Squared ??

01/05/2010 5:56 PM

The 'blinking out' part is inconsistent.

there could be galaxies that are so far away *now* that the light they emit will never reach us due to the expansion of *existent* space between us and it. But we've never observed that galaxy and never will.

But if that galaxy was visible to us at *any* time in the past is shall *always* be embedded in a patch of space that we will *always* be able to observe. It might become infinitely redshifted, but if a string of observation posts were to exist between us and it, the outposts could always make an observation, mechanically blueshift the observed spectra and send the message along the chain at the speed of light.

The blinking out as described in the 'big rip' case corresponds to the shredding of space-time itself. the light is on it's way, but the very 'medium' it travels in is being destroyed... compare it to two ants following a scent trail on the surface of a hydrogen bomb as it is being detonated. ^_^ Did the scent trail become stretched as the bomb skin was ripped apart or did the energy flux blow the electrons in the chemical bonds straight out into space? The point is moot to the ants, although we can solve it in higher dimensions. The similarity to the big rip is only a matter of degree. Our space-time may shred, but in higher dimensions it can still be analyzed even if the components are too dispersed to observe.

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#63

### Re: Energy = Mass x Speed of Light Squared ??

01/06/2010 3:21 AM

Yea, I wonder what would happen to the photons 'crawling' on my 'cosmic balloon' if it is blown up to much/fast and it pops...

-J

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#65

### Re: Energy = Mass x Speed of Light Squared ??

01/06/2010 8:00 AM

I cannot understand how you can say that the "blinking out" part (of my posting) is "inconsistent", as your descriptions appear consistent* with what I have already written.
. Maybe you are reading this single post without considering the context of my other postings?
. Or maybe you are reading into my posting things that aren't intended. Could it be that you read "light leaving the** gravitationally coupled region" as meaning that light arrives at some other gravitationally coupled region? Clearly (perhaps that's not the best word for non-transparency) light leaving the gravitationally coupled region simply "vanishes" into the super-expansion at the boundary. And therein lies the problem. Does this boundary resemble the event horizon of a "black hole": - external gravitational influences apparently remaining constistent, outgoing light being (effectively) absorbed, etc. - and if so is Hawking-like radiation generated. These effects would of course be observable, as would hyper-red-shifted light from everything that had previously been observable.

*The only significant difference I can see is that "ripping" describes the case where inter-g-coupled regions consist of continuities of mathematical singularities, and I'm not clear that all isolation models lead to such a conclusion (although, as you said, this particular difference is of no consequence to the observer).
**"the ... region" - because other regions may as well not exist.

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#66

### Re: Energy = Mass x Speed of Light Squared ??

01/06/2010 12:05 PM

I interpreted your blinking out statement in the realm of the Hubble expansion. Regardless of the ever increasing redshift that a galaxy will acquire in the future, the question of whether we can observe it was determined long ago. In chaos theory it's referred to as "sensitive dependence on initial conditions".

The *only* criterion is the original distance from us when the expansion began. If the product of H and D was <= c then we saw the galaxy and always will. Only if the product was >c then does the notion of the Hubble Horizon isolate the galaxy from us from the beginning and forever more. The confusion seemed to be that the Hubble Horizon was at a fixed distance. It was bit only at a specific time in the past. The HH too is expanding with the space-time fabric. That is probably the hard part to grasp and perhaps where we're misunderstanding each other.

Space-time is free to expand at any rate imaginable, but the big rip still represents a discontinuity from Z approaching infinity (continuous spacetime) and Z = infinity (big rip).

About the only thing I can conclude (heh-heh-heh) is that there is come conservation law in higher dimensions that allows observers to distinguish the condition of our universe as it "evolves" from big bang to it's ultimate demise; whatever that might be...

Another mention was made regarding the gravitational influence of a galaxy beyond the HH. In order to examine that question, I believe it's necessary to examine what I call "the speed of space". In human terms, picture a snow mobile climbing a wall of snow as it begins to avalanche. Even if the snowmobile is capable of an acceleration >1g and can hold it's position on the avalanche & mountain... The mountain is still the dominant factor that determines the local topography i.e. the curvature of space-time by gravity by an unobservable mass is still curvature, and objects/light in our space tile will still curve and bend their trajectories to the curvature established in the space-time by a distant mass.

I came to these realizations a long time ago when I was first exposed to the Laplace transform; It rocked my world. I still try to relate the quantities & dimensions to 'units', because we are physical beings. Sometimes it helps sometime it doesn't. How about this:

Is volume measured in m3 * seconds --or-- in m(x) * m(y) * m(z) * m(t)

Sorry for digressing, but it seems that when the pros talk about higher dimensional space, they don't ever try to bridge the gap or explain what all those other dimensions are. I'm not either, I'm just pointing to the path to find them ^_^

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#68

### Re: Energy = Mass x Speed of Light Squared ??

01/06/2010 1:23 PM

"I interpreted your blinking out statement in the realm of the Hubble expansion. Regardless of the ever increasing redshift that a galaxy will acquire in the future, the question of whether we can observe it was determined long ago. In chaos theory it's referred to as "sensitive dependence on initial conditions"."

In that case you dramatically misread what I wrote - which included an attempted explanation of why blinking-out can never occur under conditions of regular (Hubble) expansion.

Anywhere I have worked that time and space can be handled in a single mathematical entity, time appears as an imaginary number - so the "s" in m3.s has very different characteristics from the m's. Of course this unit does have a substantial (albeit Newton-compatible) meaning - for example if you are renting out warehouse space

SFIK, the minimum dimensions for analysis is currently six - but the relationship between these dimensions does not readily allow of a multi-dimensional volume..

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#69

### Re: Energy = Mass x Speed of Light Squared ??

01/06/2010 1:38 PM

Ah-ha. I think I see the confusion. I was responding to statements made by the OP who was confused about objects crossing the HH due to the expansion. We're apparently reading from the same sheet music. <- (that's a toothy, cheezy grin I think???) ;^)

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#72

### Re: Energy = Mass x Speed of Light Squared ??

01/06/2010 2:56 PM

Apology accepted. I suppose you clicked on the wrong reply-to box.

(I thought that one was tape sealing the mouth - now this is a cheesy grin

{:-D

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#71

### Re: Energy = Mass x Speed of Light Squared ??

01/06/2010 2:53 PM

tick-tock, you wrote: "The *only* criterion is the original distance from us when the expansion began. If the product of H and D was <= c then we saw the galaxy and always will. Only if the product was >c then does the notion of the Hubble Horizon isolate the galaxy from us from the beginning and forever more."

If I correctly interpret what you are saying here, I don't quite agree. It is not clear what D you are using, but if it is proper cosmological distance*, the product of H and D was (and still is) > c for many galaxies that we observe today. AFAIK, when the light of a galaxy presently at z=8 (co-moving distance some 9000 Mpc) left it, its recession velocity was ~ 3.3c and today it is still ~ 2.2c. Its original proper distance was ~ 1000 Mpc, with H ~ 990 km/s/Mpc

-J

* Presently, proper distance is the same as the co-moving distance of a galaxy. In the past it was less than the co-moving distance, but then H was much higher.

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#75

### Re: Energy = Mass x Speed of Light Squared ??

01/06/2010 3:20 PM

I can't fault your reading or analysis. In any case, we cannot see further back in time than the "last scattering"; and, IMHO, such gravitational waves as originated earlier will be so planar as to be undetectable.

Am I right that the existence of a distance horizon beyond which we will never see would depend on the expansion law being than exponentially rapid?

BTW, I personally find the whole thing much more tractable if we work our way forwards rather than backwards.

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#77

### Re: Energy = Mass x Speed of Light Squared ??

01/06/2010 4:26 PM

Hi Fyz, you asked: "Am I right that the existence of a distance horizon beyond which we will never see would depend on the expansion law being than exponentially rapid?"

I do not think true exponential expansion is required, just accelerated expansion, like we have today. This causes some galaxies, that did not make it to within our event horizon during the decelerating epoch, to forever stay behind the event horizon. (Maybe even a constant acceleration can be viewed as exponential expansion?)

"BTW, I personally find the whole thing much more tractable if we work our way forwards rather than backwards."

Problem with working forwards is that we can only see back into the past. Also, most of the expansion parameters are given for today, not for the 'beginning'...

-J

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#78

### Re: Energy = Mass x Speed of Light Squared ??

01/06/2010 5:00 PM

Working forward: I was referring to calculating the total angle that the light can propagate around the hyperspherical surface. By "exponential expansion" I mean that the rate of expansion is proportional to the size. Taking a naive view, light travels a fixed distance around the universe for each doubling of size - so the total angular increase (from now) converges to twice the increase for a single doubling.

All though not strictly exponential, I would regard laws such as dR/dT=R/(1+logR) as being indistinguishable for this purpose.

So my question is as follows: what is the minimum acceleration law that is needed for a finite angular trajectory? Alternately, is there an expansion law that is substantially less than exponential for which the angular range is still finite?

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#80

### Re: Energy = Mass x Speed of Light Squared ??

01/06/2010 10:48 PM

Hi Fyz, your view is close enough for all practical purposes - the present ΛCDM model indeed approach an exponential expansion law in the far distant future: da/dt = a Hmin, where a = 1 today and approaches infinity over time; Hmin is the future constant Hubble parameter (about 64 km/s/Mpc, if the ΛCDM model holds).

The angle that light propagates against time is obtained from the integrating dχ = dt/a, so if a -> infinity, will approach zero and eventually remains constant and finite. What you ask is something like the 'minimum' law that just keeps χ finite? I think you need a dark energy density that diminishes over time, but never becomes quite zero. I know of no present model that sports this characteristic, but there may be one...

-J

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#82

### Re: Energy = Mass x Speed of Light Squared ??

01/07/2010 6:07 AM

I was being much more naive than this - the family of expansion "characteristic equations" rather than the causes (unfortunately, once we have defined a characteristic equation there could still be multiple mechanisms that allow it). But it's a relief that our hymn-sheets continue to bear some resemblance.

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#87

### Re: Energy = Mass x Speed of Light Squared ??

01/08/2010 5:05 PM

Has anyone ever tried to measure the Hubble Constant at conventional distances?

If my math is correct it's on the order of 2.074 x10-18 m sec-1 m-1

Certainly not an easy measurement to take... did someone say gamma ray interferometry???

My point was that 13.6 billion years ago a meter should have been 0.85 mm shorter, about the thickness of a matchbook cover. It's not much ^_^, but it seems to be in the numbers... or am I all wet?

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#89

### Re: Energy = Mass x Speed of Light Squared ??

01/08/2010 10:48 PM

Hi tick-tock, your conversion of H0 is in the right ballpark. I've got it as 2.33 x10-18 sec-1.

The problem with measuring it at "conventional distances" is that local gravitational inhomogeneities mask the Hubble flow completely. It is only from distances like the Coma cluster (over 300 Mly or 1024 m) that the Hubble flow is large enough to be fairly 'clean'.

Why do you say the meter was shorter soon after the BB?

-J

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#90

### Re: Energy = Mass x Speed of Light Squared ??

01/09/2010 11:26 AM

The reason I believe the meter was shorter is an emotional appeal to an "invariant higher dimension" ;^) If we assume c was constant over the age of the universe that then wouldn't a second have been quicker then too? I guess I'm opening a messy issue by asking this. Is there a renormalization that I've overlooked by asking the question? Am I unjustified seeking an invariant to compare the meter to in a higher dimension?

If we assume space-time is expanding uniformly -- then I believe we have to include the expansion at all scales. It may be stretching the dots on a balloon analogy too far...{sorry about the pun} but the dots would expand. The galaxies may be gravitationally bound, and as you said that makes the signal too difficult to isolate from the noise in a physical sense, however the theory should be able to take this tiny amount of creep into consideration.

But seriously, why is there a thermodynamic arrow of time? Perhaps the it's the side effect of the expansion of space. We know that matter decays (albeit very slowly) and we observe that space is getting bigger. Is it possible that the decay of matter produces 'space' and other particles that diffuses into the the existing spacetime? Is it possible that the expansion of spacetime pulls on the 'pure essence' of mass causing it to shred/decay into other particles?

I know the logic is a bit circular, and that separating cause/effect might be difficult/impossible. But what if the number 2.33 or 2.07 x10-18 sec-1 (or some future refinement) has some deeper significance? As if the expansion of the universe isn't significant enough ;^)

For my next trick I'll ask if h is flexible too ^_^

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#91

### Re: Energy = Mass x Speed of Light Squared ??

01/09/2010 12:10 PM

What do you use as your references for a second or for the length of a metre?

I ask because, relative to the wavelength of atomic lines, both the second and the metre are invariant over time - by virtue of the definition of the measure for time and the constancy of the speed of light (see post #86)

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#93

### Re: Energy = Mass x Speed of Light Squared ??

01/09/2010 12:56 PM

Reference... that's the \$64 question. If the frame was moving we'd normalize using the 1/(1- v2/c2)1/2 in the direction of proper motion. Since the frame is expanding in 3 spatial, or 4 space-time, directions, it makes me wonder if the quantities 'length' (space as the cube) and 'duration' or time are or can be considered invariant. Einstein showed us they are not. Is this (my question) just the same thing as treating spacetime as curved when our minds scream for it to be flat? Am I ironing on a saddle?

When we observe a galaxy at great distance, we know we're looking back into deep time. If the meter was shorter then and the second was too do we have to account for that?

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#94

### Re: Energy = Mass x Speed of Light Squared ??

01/10/2010 5:42 AM

Given the nature of the multidimensional surfaces, I think we should all be ironing on a powdering of swarf. But that doesn't change the fact that time and the metre are both invariant with respect to the only observable related physical measure that we have from any period. This is by virtue of their definitions.

The consequence is that any change in physical relationships between then and now can only be accounted for by changes in the relationship between the other "physical ?constants" (again by virtue of the definitions). I use ?constants to describe the parameters usually taken to be constant - clearly a change in their relationships means that they become variables - presumably based on a physical law that includes some parameters whose relationships truly are constant. Unfortunately, no measures are available to support such a theory - though improved simplicity while still matching observations would lend credence to such a (not ?yet available) theory. Alternatively, measurements of gravitational waves from that period (bad joke?) might give clues to such a theory.

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#95

### Re: Energy = Mass x Speed of Light Squared ??

01/10/2010 11:31 AM

Perhaps I didn't state my question well enough... I tried to keep it short. Feynman said: "In the realm of conservation rules, a total conspiracy is a law of nature." But the fact that space is expanding requires that something else is not being conserved. Is Ho a quantum number?

The expansion causes a change in gravitational attraction, a change in electromagnetic attraction, changes in the included angles, potential energy, spin, momentum, etc. I see no way to null or normalize everything away.

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#96

### Re: Energy = Mass x Speed of Light Squared ??

01/10/2010 2:01 PM

You asked a very specific question "does the measure of distance contract in the early universe". For that question to be meaningful, it must relate to a specific model; and the answer is a resounding NO according to all the models so far addressed in this thread.

If (as you later did) you extend the question to time, we can say that this is related to the only properly measurable parameter we have: radiation lines from atomic transitions - so the answer is even stronger: at the present stage of knowledge it would be perverse to make this variable in any model.

It also happens that all "working"models that I know define the speed of light to be constant. Which means that distance measures do not expand or contract relative to the only currently physically relevant measure that we have: the wavelength of the emission lines in the frame of reference of the emission. This may or may not be a good idea - but (SFIK) no useful model has been proposed to date where the speed of light varies.

I'm evidently not making myself clear in other respects: in any usable physical model (be it of the universe or anything else) there will be some "fundamental" physical constants, and other things that depend on these constants and on the state of the universe at that instant and location. In so far as the model is accurate, the "constants" will actually be constant; in applying the model, the changes in behaviour are simply a result of the interaction between the constants and the situation being modelled.

If we are asking the question "would it be better to model using a variable speed of light", the answer is merely that no-one has yet found a model where this provides any advantage. Maybe one will be found, and the metre will have to vary relative to the wavelengths of atomic transitions; if so, either it will be constant relative to some other physical reality or it will cease to be a fundamental measure of anything (i.e its validity will be purely local).

Regarding conservation: most aspects of conservation have been abandoned in one or other of the models of the universe. My expectation is that conservation of some sort will be found to be maintained - but the old definitions that we are so used to working with clearly will need substantial revision. (But even this is probably an emotional response).

Is H0 a quantum number? If your H0 is a Hamiltonian, I believe that the quantum numbers are its eigenvectors - not the Hamiltonian itself (see here). If you mean Higgs (h0x), then I believe that the answer is still "not strictly" - though the states should be.

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#97

### Re: Energy = Mass x Speed of Light Squared ??

01/10/2010 3:16 PM

Well... Lemme say thanks, and that your answers are clearer than my questions. It's difficult to condense so many ideas into a clear, concise question...

I've gotta find some new books that bring me up to date. Any recommendations?

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#98

### Re: Energy = Mass x Speed of Light Squared ??

01/10/2010 4:10 PM

I'm probably the last person to ask about references - other than in my own areas of specialism (where it is essential to give references as a matter of courtesy) I am only capable of operating on an "assimilate and forget where I learned it" basis.

Have you read Jorrie's book yet? Given his CR4 writings on the topic I have confidence that it will be much more precise than "popular science" books, and vastly more transparent than the specialist stuff.

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#99

### Re: Energy = Mass x Speed of Light Squared ??

01/10/2010 9:04 PM

Hi Phz, You bring up a good point. The second and the metre are invariant because of their definitions. Wishing for something to be so does not make it so, and defining something to be so (that isn't) will certainly lead us down blind alleys. Einstein showed us that time and distance are not fixed like we wanted them to be. Maybe he only took the first step. If we knew the truth, maybe it would show us that the universe isn't expanding at all. I like where Tick-Tock is going here. Since the universe is composed of space-time according to Einstein, it seem logical that if space is expanding, that time is too. -S

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#100

### Re: Energy = Mass x Speed of Light Squared ??

01/11/2010 6:23 AM

This is not a matter of "wishful thinking". It's a matter of measurement.

Surely you can only define space and time relative to some physical entity - be it the size/spacing of an atom or the wavelength of an emission line. We can't see the size of atoms in the distant universe, but we can observe emission lines. If we use these as the local measures of time and space it is inevitable that space and time will remain constant locally.
If is of course possible that other sizes and timings may vary relative to this measure.
In terms of space, for example, we don't actually have any way of measuring whether nuclear or electronic orbit sizes, inter-atomic distances or gravitational orbits* maintain their current relationships versus the periods of atomic emissions.
In terms of time, we don't have direct evidence that the relationship between nuclear half-lives and the period of the atomic radiation lines has remained constant.

However, I think what you may be missing is that the universe appears-to-be** expanding with respect to these specific measures. Clearly, both the distance between uncoupled galaxies and the time that light takes to travel between them increases - so long as we measure these with respect to the "constant" second and metre.

*On the other hand, the orbital decay time of star-pairs is strong indirect evidence that at least this part of the model holds up.
**I say "appears to be" because the evidence is the red shift, and the expansion is then a result of (model-based) interpretation. On the other hand, all attempts at different interpretation have so-far failed to match other aspects of the data. This does not of course mean that a different model is impossible. (But - unless we change our definitions, at least the second will remain invariant with respect to molecular transitions)

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#101

### Re: Energy = Mass x Speed of Light Squared ??

01/11/2010 12:06 PM

Phyz said: "Surely you can only define space and time relative to some physical entity - be it the size/spacing of an atom or the wavelength of an emission line."

Wait... that's circular too. Michaelson-Morley couldn't find the aether, that was my inspiration for the bad joke on gamma ray interferometry. Clearly the experiment to measure the stretching cannot be embedded in (or permeated by) the medium it's trying to measure. Null results cannot prove it.

I think the mind demands that if space-time were perfectly scaled by any arbitrary amount that we'd be incapable of noticing the effect. If we reject that premise and look for an effect that doesn't scale with the rest we might find something interesting.

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#102

### Re: Energy = Mass x Speed of Light Squared ??

01/11/2010 4:30 PM

It is indeed a circular argument - if you define time with respect to a specific physical phenomenon then either it is invariant with respect to that phenomenon, or it is multivalued. Again, we have no proof that time was single-valued in the early universe - but for it to take multiple-values (in the relativistic sense) would require a mathematical description that is completely different in type from the description that works in today's universe. Life is difficult enough without invoking complexities for (or against) which there can be no evidence.

What Michelson and Morley did was look for a change in the relationship between the wavelength of light and the velocity of movement. What they found was that (contrary to what might be expected if light consisted of waves in an aether) the wavelength of light was independent of the motion of the system. Physically, this and its successors demonstrated that if the velocity of light were changing the sizes of everything else changed in a manner that precisely compensated for the effect. What the null result proved was that all the definitions of the speed of light led to a single result.
Einstein developed (found?) an elegant theory that showed how this might work - but it appears he started from a relatively simple viewpoint: if it looks like the same velocity, it quacks like the same velocity - then we should say that it is the same velocity (that man Occam again). But the success of the theory was not of course only in its elegance - it was in the fact that it made predictions that could be falsified - but were found to be accurate, and within successively tight experimental limits.

This all started because you modified a preliminary statement about the metre to one about time - that "you would expect it to run slower" in the early universe. I'm trying to explain that such a statement is at least one of the following:
. inherently false (if you take the measure relative to a currently observable physical phenomenon - because we only have one such that we can observe)
. currently undiscoverable - if you take the statement as relating to nuclear decay or to orbital frequencies of objects of given masses and spacings; or
. meaningless - because no reference was given against which time was to be measured.

Maybe it would be simpler to address the meaning that current physics applies to time dilation - misapplication of which is, I suspect, behind this whole sorry saga

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#79

### Re: Energy = Mass x Speed of Light Squared ??

01/06/2010 5:28 PM

Well, I was oversimplifying (mea culpa) and assuming the Hubble variable er,um, constant -- H is a purely scalar term. I also see why the proper distance D between the source and observer can be difficult to describe.

In your diagrams you showed a distant galaxy (grey I believe) that was outside the possible light cones making if forever unobservable. For the other galaxy on or inside the line which we will always be able to observe, the redshifts we observe today are the redshifts the object had the time it emitted plus the the dilation it incurred during the voyage. The redshift we observe tomorrow will be just a little bit greater than it was today.

Then it gets really weird... If we hitch a ride with the photons until we get to the other side of the observable universe and stop, we'll conclude the z we observed at Earth was low, or worse inconsistent with the z of the galaxy on the other side.

What I'm saying is that it doesn't matter what H x D is today only what it was "then". As for the 1000Mpc distance (D), I have to ask "when" was it that far away, and what was the "speed of time" and the "length of a meter" at that earlier era?

It's all so confusing! ^_^

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#81

### Re: Energy = Mass x Speed of Light Squared ??

01/06/2010 11:18 PM

Hi tick-tock, you wrote: "For the other galaxy on or inside the line which we will always be able to observe, the redshifts we observe today are the redshifts the object had the time it emitted plus the the dilation it incurred during the voyage."

In a strict sense, you are right, but large scale cosmic models usually leave out any inherent gravitational redshift that the light had when emitted (the homogeneous and isotropic case). In any case, it is small compared to cosmological redshift for very distant objects.

"If we hitch a ride with the photons until we get to the other side of the observable universe and stop, we'll conclude the z we observed at Earth was low, or worse inconsistent with the z of the galaxy on the other side."

As you hypothetically 'travel with the photon' (on a null-geodesic), you will be instantly transported there, by your own clock. In the meantime, cosmological time went on and the cosmos has expanded quite a lot. When you stop, you should observe the Milky Way red-shifted much more than what the destination galaxy was before you left. I see no problem with that, or perhaps am I missing something(?)

"As for the 1000Mpc distance (D), I have to ask "when" was it that far away, and what was the "speed of time" and the "length of a meter" at that earlier era?"

According to my Cosmo Calculator, the z=8 galaxy was ~1000 Mpc distant when t ~ 660 My, or ~13 Gy ago. I reckon the "speed of time" and the "length of a meter" was then the same as it is today. IMO, the redshift based time dilation that Fyz was talking about is not applicable, since it is an 'apparent' or 'choice of coordinate' effect (i.e., it is reciprocal in the two directions).

-J

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#83

### Re: Energy = Mass x Speed of Light Squared ??

01/08/2010 2:18 PM

You Wrote:"IMO, the redshift based time dilation that Fyz was talking about is not applicable, since it is an 'apparent' or 'choice of coordinate' effect (i.e., it is reciprocal in the two directions)."

What did you mean by "not applicable"?

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#84

### Re: Energy = Mass x Speed of Light Squared ??

01/08/2010 3:06 PM

Hi Roger,

By "not applicable" in the context I used it was that the apparent time dilation does not change "the (real, physical) speed of time" or "the (real, physical) length of the meter" in the early universe. In standard cosmology, cosmological time is taken to be same everywhere and to have the same rate, despite the expansion.

We do observe things to happen more slowly at a large distance and someone "out there" similarly observe things in our galaxy to happen more slowly, both due to the cosmic redshift. This is a reciprocal time dilation effect and it has no bearing on the actual rate of natural clocks.

-J

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#85

### Re: Energy = Mass x Speed of Light Squared ??

01/08/2010 3:24 PM

That's good. I was just getting comfortable with my new found understanding and I got nervous. I can't believe that to this point I missed that there was time dilation proportional to the redshift. Makes perfect sense, I just never thought about it for some reason.

Thanks for the clarification.

Roger

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#86

### Re: Energy = Mass x Speed of Light Squared ??

01/08/2010 4:44 PM

Great - we all appear to share the same view.

Actually, this equivalence is a matter of definition: we define time in terms of the period of a radiative atomic transition - precisely the means by which we observe the red shift. Similarly, the in-vacuo speed of light is defined to be uniform - so distance is automatically defined as uniform in the same sense.

On the other hand, we forget at our intellectual peril that most of the remainder of our physical modelling of the early universe is based on reasonable assumptions. For example, that the relationship between atomic forces and electronic forces has remained constant in the sense that atomic and molecular sizes have remained constant as measured in terms of distances as defined above. Similarly, and more commonly acknowledged, that we have a reasonable model for gravity.
Could modifying these (or other) assumptions result in simpler models that still fit observations. Or even result in simpler predictions? I suspect not, but it's still worth reminding ourselves how much is assumption, and to wonder whether we are (sic) balking up the wrong cul-de-sac whenever uncheckable interactions are needed to improve the fit

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#88

### Re: Energy = Mass x Speed of Light Squared ??

01/08/2010 10:27 PM

On the one hand, I hope a simpler cosmic 'toy-model' will be found, doing away with the need for dark matter and/or dark energy, while still compatible with all observations. Currently this has not been achieved.

On the other hand, I fear that quantum gravity, if found workable in the future, may be even more complex than the present 'toy-model' for the cosmos. Some "uncheckable interactions" are however bound to remain...

-J

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#92

### Re: Energy = Mass x Speed of Light Squared ??

01/09/2010 12:14 PM

Agreed that we are unlikely ever to be able to measure enough entirely to remove imponderables. If in doubt, I personally favour Occam's (E)razor...

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#64

### Re: Energy = Mass x Speed of Light Squared ??

01/06/2010 3:32 AM

Hi Fyz

I'm also no clued up on such cosmic topology issues. As I was busy replying to tick-tock, I tried to imagine what may happen to the photons and gravitons that encounter a ripped spacetime. I couldn't...

-J

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#70

### Re: Energy = Mass x Speed of Light Squared ??

01/06/2010 2:51 PM

Hi Fyz (and Jorrie (and Tick-Tock)),

Having had more time to think on this, and having read the comedy of errors between you and tick-tock (who's explanation I found also helpful), and having read some external source, I am more convinced of what you all agree to.

However, my question now is, is there any time dilation when we view the distant universe? I read the following from a website which seems to indicate as much:

"The image of the most distant galaxy will freeze and fade away about 50 billion years from now," Loeb said Tuesday. "Its image will be frozen at an age of 5 billion years (roughly the age of the sun today). This means that we will never be able to see how stars age in this galaxy to having an age larger than the current age of the sun." We'll see no more births or deaths of stars in that realm, though those processes will continue.

http://www.newsfinder.org/site/more/where_did_that_galaxy_go/

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#73

### Re: Energy = Mass x Speed of Light Squared ??

01/06/2010 3:06 PM

There will certainly be massive time dilation, as the region that does-not-quite-rip (to use the fashionable jargon) is still expanding at just below the rip limit. So, similar to the event horizon of a black hole, if we can once see a certain region we should in principle continue see it for ever; it's just that (at any given distance) the time we are looking back to will freeze (no future beyond a certain limit), and the image will get redder and redder and the number of photons will tend to zero.

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#74

### Re: Energy = Mass x Speed of Light Squared ??

01/06/2010 3:15 PM

Ok, so then I can reconcile the idea of "galaxies never blinking out" with my statement of "if we are receding faster than the speed of light, how can light ever make up that ground".

So galaxies don't blink out, but they do freeze.

So doesn't that mean that any distance we look in space we see some time dilation due to Hubble expansion?

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#76

### Re: Energy = Mass x Speed of Light Squared ??

01/06/2010 3:22 PM

Yes, Hubble expansion implies dilation of observed time - in exactly the same ratio as the red shift.

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#57

### Re: Energy = Mass x Speed of Light Squared ??

01/05/2010 3:49 AM

Gentlemen,

Just come across this post, what an awesome string of questions and answers. Maybe one day if I keep at it on Jorrie's site I will get my head part way around it.

Roger - thanks for asking all the questions as well as answering a good few yourself. It all helped my vague understanding.

Just had to give a couple of GA's to Jorrie, but should really give to all of them but got tired. It is absolutely amazing to me that no one else gave GA's, but then I think also that this would not phase Jorrie one jot.

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#67

### Re: Energy = Mass x Speed of Light Squared ??

01/06/2010 1:07 PM

To all,

Thanks so much for the wealth of information and speculation on this topic. I feel like I now understand a very little of this, which is MUCH more than I did previously. This has also been an extremely interesting and fun thread.

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#44

### Re: Energy = Mass x Speed of Light Squared ??

12/24/2009 9:56 PM

If space alone can increase between two galaxies then the gravitational pull will also alter and this has to affect the energy system as something is working against it. Anything accelerated to the speed of light has to become light entirely or partially and gradually in the process of acceleration near speed of light. It will no longer be a mass of matter and will eventually turn into pure energy and then light can not be accelerated any further as velocity of light does not change in vacuum.

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#2

### Re: Energy = Mass x Speed of Light Squared ??

12/18/2009 6:23 PM

No, no, no! Einstein didn't say that would result in infinite mass. He said that, if from your inertial frame, you wish to accelerate a body to the speed of light, you must add an infinite amount of energy. You might want to wander over to Jorrie's blog and talk to him. He's pretty smart about all this, considering he lives at a place where his head is lower than his feet.

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#5

### Re: Energy = Mass x Speed of Light Squared ??

12/19/2009 9:40 AM

It's been ages since I looked at the equations, but I think that mass went to infinity as the velocity increased to the speed of light. It then follows that it would take an infinite amount of energy to increase the speed.

Someone familiar with particle accelerators needs to get in on this discussion. Some of the particle speeds approach the speed of light, and I'm sure they have to use relativistic equations for their calculations about the magnetic fields needed to produce the acceleration to restrain the particles to a circular orbit.

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#6

### Re: Energy = Mass x Speed of Light Squared ??

12/19/2009 11:09 AM

Relative to the rest frame.

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#3

### Re: Energy = Mass x Speed of Light Squared ??

12/18/2009 8:24 PM

I just love this subject. Einstein was a smart dude, but I think he was a little of an entertainer, too. In the old days, folks would sit around the parlor and talk, and I'm sure he had fun spinning his mind puzzles.

If we ever figure out stuff like light and gravity, we are going to really move ahead. As it is, we don't really know what either really are. Light acts like wave and a particle.....great....maybe it is a waving, or spinning particle. Or a waving or spinning flow of energy that exhibits the properties of a particle when it interacts with a particle..... If it can move a solar sail in space, it must have properties besides a wave. If it does have such properties, we are accelerating something up to light speed every time we turn a flashlight on. A photon drive is supposed to have push, more particle properties, more light speed.....?

I still like my question about two spaceships going in opposite directions at more than half lightspeed. Relative to each other, the other is exceeding lightspeed. Like Albert always said, "It's all relative".

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#7

### Re: Energy = Mass x Speed of Light Squared ??

12/19/2009 1:54 PM

I reflect that mass sensed by a reasoning concious is still in arrogance just as in

past millenia Western humanity thought that they were the center of the Universe. In order to fully

perceive universal laws that are not inherently provided by our encoded DNA, objective level concious is required for a true enlightenment of one's partipation in

this order to chaos /mass to energy conversion ride. I sense an illusionary reallity.

If I see my twin brother falling into a Black hole he may be seeing me falling into a black hole during his last moments of foresight.

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#4

### Re: Energy = Mass x Speed of Light Squared ??

12/18/2009 11:59 PM

Also remember to decode spooky language correctly: Dark Matter = we don't know what's going on so we make up a cool name for it for a placeholder until we do know and so it doesn't seem like we are totally clueless in the meantime...

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#8

### Re: Energy = Mass x Speed of Light Squared ??

12/19/2009 3:40 PM

Hi WJMFIRE, The mass from the speed is only from your perspective (because the speed is only from your perspective). The rest mass remains the same. The universe won't have a problem with it. Think of it as kinetic energy. See: http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence -S

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#9

### Re: Energy = Mass x Speed of Light Squared ??

12/21/2009 11:27 AM

Does this mean that if I am on a planet in a solar system in a galaxy that is the first to hit the speed of light, my girlfriend will need new clothes?

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#16

### Re: Energy = Mass x Speed of Light Squared ??

12/22/2009 6:02 PM

Because Time Matter resulted

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