Why don't you start a new thread on the BABBling forum on division by 0 and infinity. I would be happy to continue this conversation in a more apropriate forum!

Here it is:

infinity and division by zero

Hi Pi Man

1. Link to Energy Lost with General Relativity.
I checked the link and it works but I can’t link from the BA page. Cut and past the link into your browser directly. Hopefully this will help convince you that at least others argue that GR “violates” the conservation of energy principle. The expansion of space causes photons to loose energy. (Actually it is an effect that my balloon example I mentioned earlier explains the situation better, ie the energy is not lost, it is the result of the “work extracted” as the universe expands. )

2. Fallacy of the wave properties of light.
You also responded to another mistake that I believe is made by physicists regarding the wave properties exhibited by light
“A wave description of light is not a falicy. Light exibits every property that any other wave does. (ie. diffusion, interference, etc...) One can't even view it as a particle (photons) unless one is trying to measure the particle properties of it.”
I will illustrate in the next posting how the effects of diffusion, interference, etc, can occur even if light is ONLY a particle.

3. Questions of my 10 Photon example.
You questioned my 10 photon example “There's no way to say that the 10 photons have been 10 photons since they left the source. QM 101 says that the light has no state at all, let alone a specific number of photons in the beam, until you measure it. “
This is true, but it is possible to statistically determine how many photons are being detected per unit of time. This is how we measure intensity. All calculations associated with distance to stellar objects and the observed brightness are essentially include determinations of the number of photons received per unit of time.
We can predict that with a certain type of star, at a given distance, with the given telescope, with the given atmospheric conditions, with the given amount of space dust. etc, a specific number of photons should be detected per unit of time. For those situations where it is possible to actually measure distance, the number of photons are not increased with the increase in red shift. This effect (more photons with increased red shift) would be required in your explanation of the “standard” Doppler shift in order to keep the energy received constant.

4 Reiterate concept. Energy is lost with the expansion of space.
Not only do photons loose energy as they travel through an expanding space-time field (a point accepted by most of those followers of general relativity) but I assert that even mass looses energy with the expansion of space time. Again, this is because of the equivalence indicated by E= mcc. What ever happens on one side of the equation (when E = electromagnet energy) must be valid for the other side of the equation (when Mass carries properties of energy)

Note this is not a new idea, some have predicted Proton decay, which is in accord with this relationship. (Once the energy is liberated from the proton decay as electromagnetic energy, energy will be lost due to the expansion of space. This can be argued to maintain the necessary balance implied by the E = mcc). Despite millions of dollars spent looking for proton decay, no decays of protons were found. The problem here is that matter was not lost, it is just that the energy of the proton is diminished, not destroyed. This is a much harder effect to detect and present research techniques will not find it the way they are looking.

5. Deceleration of Universe
Regarding the assertion that the universe is decelerating, I still assert that it is. Objects moving faster in the past than the present are decelerating. Nothing changes that logic. Granted one can select a reference frame that makes these measures relative, but I argued that it is best to use coordinate systems that all would agree on for the same description of the same physical phenomenon. The fact that I used the word “acceleration” for a car, I did not mean to imply the universe was accelerating, it was given to illustrate the energy associated with the expansion of space since it takes energy to accelerate.)
There is one very major point I should clarify, In my model the distance between points decreases with the passage of Cosmic Time. This is therefore deceleration. But on the other hand, the rate of deceleration between points is exactly at the rate that predicts that the VOLUME of space ACCELERATES with the expansion of space. This is a very specific relationship that allows the distance between two points to decelerate, but the volume of space that includes the two points to accelerate with time.

6. Problem. Decelerating distance, accelerating volume
Assume a balloon is expanding. The distance from the center of the balloon to the edge of the balloon is always increasing, and the rate of linear expansion is less and less but never equals 0. What expression describes this rate of expansion if the volume of the balloon is accelerating ie the volume is increasing at a faster and faster rate? (Initially this would appear to be impossible, but I bet Informant can figure out the rate, if he has time.)

snowflake

sfu, I have no idea what you mean when you say that "mass loses energy over time". A particular mass M embodies a particular amount of energy, specifically, M times the speed of light squared (when all quantities are given in the appropriate units).

There are only two ways this equivalent energy can decrease over time. Either that mass M must decrease, or the speed of light c must decrease. Which of these things do you think is happening? If M is decreasing, what's happening to it? Is it getting converted to something else? Is it just shrinking like a deflating balloon? Is every individual particle becoming less massive? What evidence is there for any such effect?

If c is decreasing, why can't we see the effects of that change when we observe distant galaxies (whose light was emitted when c was larger)?

Unless you have a reasonable answer for one of the above questions, the phrase "mass loses energy" is utterly meaningless. It's like saying "force loses acceleration".

You're correct that the issue of conservation of energy becomes a much more complex one under general relativity. For those of you who are interested, here is a pretty good discussion of the issues involved. I general, the derivative forms of conservation of energy still hold (energy is always conserved in any infinitesimal region of space), but we run into some problems with the integral forms (so energy conservation over a large region may be harder to pin down).

Your logic is correct, but distant galaxies are not examples of such objects. You still fail to see that in none of your examples were you comparing the velocity of one object to the velocity of that same object at a later time and in the same reference frame. You compared the velocities of different objects at different times, or compared the velocities of a single object in several different reference frames. If you do look at the recession velocity of a galaxy, wait a billion years, and then measure it again, you'll find that it's receding faster the second time. Moreover, you'll find that the recession velocity has increased more than linearly with the distance. The expansion of the universe is accelerating.

However, let's not spend too much time dwelling on that. Instead, you've said that you have a model, based on formulae. So, let's see the model and the equations that describe it! From there we can continue to talk about it meaningfully.

I agree with informant. You misinterpreted Pi Man, and you misrepresented the mathematics.

Ah, found it... and then found that you had already posted all of the relavent info...

Okey smokey... I'll be looking forward to that.

Yes, we can measure how many photons have struck our detector, but that doesn't say anything about how many photons they were when they left the source. And, by Hisenburg, there is no way to say, "the number of photons are not increased with the increase in red shift" and verify it with measurements.

Okey smokey... if the expansion of space did cause light to lose energy, then yes, it would cause mass to loose energy.

Ummm... Protons decay into neutron/electron pairs (and eject an electron neutrino)

The missing matter is released in a small burst of energy, released mostly as momentum.

You keep refering to the "missing" energy from the expansion as "dark energy". The dark energy is what is causing the universe to accelerate. If the universe is not accelerating in it's expansion, then there is no need for dark energy.

For the purpose of discussion, I will reduce the universe by one dimension and speak of it that way. If you wish, I will redo the calculations for a higher dimensional universe in a later post.

Our universe is a 3 dimensional space wrapped into the 4th dimension, so the analogy would be a 2 dimensional plane wrapped into a 3 dimensional sphere.

Since we live on the "surface" of the sphere, what we need to look at is the surface area of the sphere.

The surface area of a sphere of radius r is:

S(r)=4*pi*r^2

The distance between two points on the sphere is:

D(r)=2*pi*r*k (where k is a constant between 0 and 1, signifying the distance around the circle)

the first derivitive will give us the rate of change "velocity" functions.

S'(r)=8*pi*r
D'(r)=2*pi*k

The second derivitive will give us the acceleration

S''(r)=8*pi
D''(r)=0 (since k is a constant)

If you notice, the acceleration of the surface area (the volume of the universe) cannot ever be greater than the acceleration of the radius.

Are you still there, Snowflake? 8-[

(I'd call you "Flakey" but you might take it the wrong way...)

So do you agree that energy is not conserved on the largest of cosmic scales?

__________________
Everyone is entitled to his own opinion, but not his own facts.

I follow your logic, but I don't know if this is valid. The photon loses energy because it is traveling through expanding space at c. Mass, however, is not traveling at c, so I see no mechanism for it to lose any energy. Still, I don't think E=mcc requires modification because it doesn't really speak to the scenario where the "E" is covering billions of lightyears.

__________________
Everyone is entitled to his own opinion, but not his own facts.

No! I do not!

Cosmic expansion just "spreads" the same amount of energy over a longer distance/time.

Pi
Congratulations, You have a good mind. You are close, I think I should have more carefully defined what acceleration of a volume is. I think you will find the following relationships interesting. They are also important to my theory. I am finally beginning to write down formulas that pertain to my theoretical model that describes how the universe expands. The following example leads to important relationships of my theory.

If the radius of a balloon is described by the following expression
R = k T^(2/3) ( R = radius, k constant, T = measure of time)
The rate at which the distance changes with respect to T is
d/dT R = d/dT (k T^(2/3)) = (2/3 k) T^(-1/3)
If you use your plotting calculator with y = x^(-1/3) you will find that the slope is negative and is continuously approaching 0. The radius of our balloon is always increasing but at a slower and slower rate.

Now lets look at how the volume of this balloon increases when the radius expands at the above rate.
V = kk R^3 (kk = constant) and R = k T^(2/3)
V = kk (k T^(2/3))^3 = (kk x k ) T^2
The volume is increasing at the squared elapsed measure of time. Every time the elapsed time doubles, the volume of space is increased 4 times, yet the increase in distance is T^(2/3) or 2^(2/3) = 1.587… times bigger.
But this is not acceleration,. The rate that the volume is increasing is
dV/dT = d/dT ((kk x k )T^2) = K T (K is a constant) . The volume of space is increasing linearly with the passage of time.
The rate that the rate of the volume is increasing is acceleration, so taking the next derivative we get.
d/dT KT = K
The acceleration rate describing the growth of a volume of space is constant and positive, (like the acceleration of a ball in a uniform gravitational field is constant).

The balloon's radius is increasing at a slower and slower rate, yet the volume within the ballon is constantly accelerating, or increasing at a faster and faster rate.

dV/dT is increasing at a rate described by a linear measure of time. This is a very important relationship in my Theory since the relationships above forms the basis by which I propose the expansion of space is described.

If a volume of space is represented by S, then the above expansion is described by dS/dt = KT. If we state this expression as a “word sentence” it could be stated that a change in space per time equals time, or because space changes, time exists. (I know you are probably responding with “what a bunch of ****”). Irregardless of how you may respond to a formula that has some kind of metaphysical association, please do not give up on me yet. The above rate of expansion will be shown to allow a uniform expansion of space, yet maintain celestial and atomic stability. In fact, the above theoretical rate of expansion will be shown to predict Newton’s gravitational Laws a lot more simply than Einstein’s theory of General Relativity.

snowflake

Gray

Thank you for the post that the current accepted description of the expansion of space states that local events are described differently from global events. One of my points is that in my proposed model there is no separation. The expansion of space is uniform so its effect is everywhere the same. Just as the expansion of space decreases the energy of a photon as it travels through a “global” field, so to do local events lose energy in an expanding spacetime field. This includes matter itself. (Matter in my theory is actually a relationship defined by three dimensions of space and two of time. Since Mass is part of an expanding space time field, it, just like the photon, matter looses energy with the expansion of space.)

Also, I prefer to use systems, instead of global or local events, with systems being defined as anything that can be contained in a volume of space.

I also appreciate your explicit example which differentiates our two interpretations of how the universe is expanding, Ie is it accelerating or decelerating?

IS SPACE ACCELERATING OR DECELERATING?

You stated that “Your logic is correct, but distant galaxies are not examples of such objects. You still fail to see that in none of your examples were you comparing the velocity of one object to the velocity of that same object at a later time and in the same reference frame. You compared the velocities of different objects at different times, or compared the velocities of a single object in several different reference frames. If you do look at the recession velocity of a galaxy, wait a billion years, and then measure it again, you'll find that it's receding faster the second time. Moreover, you'll find that the recession velocity has increased more than linearly with the distance. The expansion of the universe is accelerating.”

Thank you for the perspective, We have two fundamentally different ways of looking at the same events. We both would agree that type 1a supernovas appear to be further away than a linear rate of expansion, which is the reason astronomers are asserting that the expansion of space is accelerating. But this can still be decelerating, I will use your “waiting for a billion years” observation of galaxies to illustrate my point.
(QUICK CALCULATION IGNORE)
(9.5 x 10^15 meters/ light year T = D/v 1,000,000 ly x 9.5 x 10^15 metes/ly / 75,000 meter/sec = 1.26 10^17 seconds
= /365 24 3600 = 4 x 10^9 years )

Lets say that from our location we see three galaxies lined up in a row called A,B and C. The A galaxy is the closest and the C the furthest. Each galaxy is a million light years apart, so galaxy A is one million light years away from us. After waiting about 4 billion years, (based on current values of h, based on napkin calculation) the closest galaxy A appears to be located where the middle galaxy B was , and the middle galaxy is eventually located about where the furthest galaxy C was (after correcting for the extra time lag due to the expansion of space and the time required for the light to reach us, and leaving the issue of acceleration/deceleration of question) . It is my contention that when the closest galaxy A is located where the middle galaxy B is now, it’s red shift will not be as great as we presently observe of the middle galaxy. The middle galaxy B, when it is located where the furthest galaxy C was, will not have as great a red shift as the most distant galaxy presently has, this is due to deceleration of space-time.

I do agree with you that our observation of the red shift of the closest galaxy when it reaches the location of the middle galaxy will appear to be greater than it presently has, giving the appearance of each galaxy accelerating away. When the closest galaxy A reaches the apparent distance of the furthest galaxy C, it will have an even greater red shift. Eventually when the galaxies reach high red shifts, they will appear to be even further away than a linear rate of expansion would describe; therefore the universe appears to be accelerating.

Again the difference is the frame of reference. Mine is a kind of universal or Absolute Frame of Reference. If an outside frame of reference is used to describe the “absolute” motion of each galaxy over time, every galaxy would be measured as moving faster in the past than the present; therefore the universe is decelerating. Notice that in your frame of reference our galaxy is NEVER moving, yet from any other galaxy, it is determined that our galaxy has motion. Is it valid to assume that our galaxy is not moving when everyone else in the entire universe says we are? Is it better to use a frame of reference that provides a consistent description of events for everyone, or to use a frame of reference that is valid only locally, even if that local frame of reference is consistent for every global observer? Choices.

One last point, by assigning a real motion to galaxies over time from an independent frame of reference, it becomes more intuitive to apply special relativity to the duration of type 1a supernovas. Since the high red shift novas are observed at speeds which require adjustments due to special relativity, there is a “slowing” down of the duration of the nova. This adjustment of the light curve for special relativity is critical in establishing the distance of the supernova. This to me proves that there is a real motion to galaxies that is induced by the expansion of space. In the past, our galaxy was moving at relativistic speeds and now we are moving more slowly, we are decelerating. The question is, if we are moving, where are we moving? This requires another dimension since we are unable to locally observe it and it is only over the course of time that any evidence of this motion is realized. More on this later.

snowflake
P.S. your explanation of your perspective has been a tremendous help to me. Thank you.

“What we have here is a failure to communicate” from the movie “Cool Hand Luke”.

Hi Donnie B.

What I mean that mass loosed energy over time is that as time progresses the amount of energy associated with a mass in our universe slowly diminishes. Just as the energy of a photon diminishes while it passes through an expanding space time field, so to does matter.

You are right that currently it is believed that there is only two ways that matter can lose energy, but if mass can be converted to energy (E= mcc) and as light travels through and expanding space time field it loses energy, why shouldn’t mass also lose energy. Some small speck of dust in some vast empty region of space that is expanding should also lose energy. If that same speck of dust could lose energy, why not include the dust particle floating in the air on earth? What prevents the loss of energy from the expansion of space being truly uniform? Why is the speed of light constant? What is the structural relationship between space and photons?

Everything has a beginning and everything has an end.

The wavelength of light will expand until its wave length is so long there is no way to measure it. The fabric of matter will also expand till there is nothing holding it together.

Soon I will be posting some of the relationships, Trying to get most of the pictures and stuff on a web site. One of the relationships will argue that space-time, and mass are defined by the same dimensional relationships.

snowflake.

Why would the dust particle lose energy? Light loses energy as it travels, the dust particle just sits there. Space might be expanding, but the dust isn't.

The dust will lose energy until it reaches an equilbirium with the surrounding space and then remain at a pretty constant energy level, depending on the local conditions (falling into the shadow of a larger planet will cause a energy loss).

__________________
People who think they know everything are a great annoyance to those of us who do.

You are thinking as if we are confined within a large sphere. One made of a 2D membrane wrapped into the 3rd dimension. This is not what is commonly accepted. (If space is finite in extent without edge or boundary) We are living in a 3D space wrapped into a hypersphere. So, you shouldn't be looking for the volume of a sphere, you should be looking for the "surface volume" (just as you would be looking for the surface area of a sphere with one less dimension) of a hypersphere (a sphere, but whith one more dimension). I don't know how to get that figure, though.

For the "hypervolume" of the hypersphere, you use this:

for a straight line:
2*r (because it's just a diameter)
for a 1 dimensional line wrapped into a circle:
pi*r^2
for a 2 dimensional membrane wrapped into a sphere:
(4/3)*pi*r^3

So, the hypervolume must contain an r^4 term
It also must contain a pi term.
Aside from that, I don't know, maybe you can figure it out.

Sorry, I'm really perplexed by this. Your first statement says that the redshift will be smaller, but you second statement say that you agree with me that the redshift will be larger. Which is it that you believe?

I don't actually think there's a universal reference frame. But any reference frame you choose is "universal" in the sense that you'd get the same results. You'll get a "consistent description of events", since even though the speeds you'll measure for any individual galaxy will be different, the overall pattern will be the same.

What would you be using as your choice of reference frame, and how are you deciding that it's the best one? Are you imagining a hypersphere, and centering your frame of reference on the center? If so, remember that it's not the volume or the surface area that we're talking about when discussing how distance changes with time. The distance between two fixed points on a sphere of how ever many dimensions scales directly with the radius. So when astronomers talk about the acceleration of the expansion, they mean the rate at which distance changes, not the rate at which volume changes. Yes, that means that even if the Hubble constant really is constant, the rate at which the volume of the universe is changing is increasing steadily. Measuring the position of galaxies from a center point of a hypersphere won't change whether the rate of expansion is accelerating or decelerating. You'd get the same results if you picked any specific point on the hypersphere; our galaxy for example.

THis is pedantic, and shouldn't be taken as a real criticism. You shouldn't use the terms "nova" and "supernova" interchangeably. These are actually two completely distinct types of events involving very different objects, so it can be confusing if you use the one term to refer to the other.

No trouble at all. I'm enjoying the conversation. I'd be very happy if you'd provide further details of exactly how your theory works.

I can answer this one. The "hypervolume" of a hypersphere is 1/2 pi^2 r^4. The "surface volume" (the analog to the surface area of a sphere) is 2 pi^2 r^3. But note that as I pointed out above, these formulae have no effect on the rate at which objects on the surface of a hypersphere move apart. That goes like the radius, regardless of the number of dimensions.

Cool! Thanks, grey! How did you find out? Did you just figure it out, or did you find it on a website? If it's a website, I'd love to have the address!

As for the rate at which objects on the surface of a hypersphere move apard, the rate would just be this:

The distance would be:
D=2*pi*r*k (where k is a constant between 0 and 1)

The rate of change of the distance would be:
dD/dr=2*pi*k

No trouble. I'd actually worked this out once, so I knew the answer. But a quick check shows that entering "volume of a hypersphere" into Google gives all kinds of results. Here's one that gives a derivation of the volume analog for an n-dimensional sphere. And of course the surface area analog is always just the derivative of the volume with respect to the radius.

Well you should probably restrict k to less than 1/2, or take out that factor of 2 in the front. Otherwise, you're taking the long way around! If k were 1 it would mean that your target is right behind you, so it would be easier to just turn around rather than circumnavigate the hypersphere. Note that you'd use this exact same formula for a circle or a sphere. Oh, and even if the universe turns out not to have positive curvature (so there is no "radius"), which is looking pretty likely these days, you can still define a value of r as a scale factor, which works more or less the same for these kinds of calculations.

Well, technically it could be more than one, in which case it would just be the analog of going around the whole universe to get to it. If it was more than 2, then you'd have to go around twice to get to it... and so on... However, that's only a mathematical relationship. It has no real relavence.

What do you think, Snowflake?

Math has no relavence? How can you say that?

All I'm saying is that that particular relationship is much easier if you start out by taking the modulus of k with 1, and you know it!

?????????????????

Hi Wedgebert
Sorry for the long delay in returning a reply, You had an issue with my statement that matter also is “lost” due to the expansion of space. “Why would the dust particle lose energy? Light loses energy as it travels, the dust particle just sits there. Space might be expanding, but the dust isn't.”
Lets say we have a matter energy conversion machine.
I have two grams of matter. One gram of matter I convert into energy and I beam it across space to be reflected back by a mirror. As the light travels, it looses energy. The light hits a mirror and is reflected back to the source machine, which converts it back to mass. Now compare the “traveled” mass to the “stationary” mass, do they weight the same, or are they different?
The present accepted models (Minkowski) of the expanding universe would have the traveled mass weigh less than the stationary mass. The

Hi Wedgebert
Sorry for the long delay in returning a reply, You had an issue with my statement that matter also is “lost” due to the expansion of space. “Why would the dust particle lose energy? Light loses energy as it travels, the dust particle just sits there. Space might be expanding, but the dust isn't.”

Lets say we have a matter energy conversion machine.
I have two grams of matter. One gram of matter I convert into energy and I beam it across space to be reflected back by a mirror. As the light travels, it looses energy. The light hits a mirror and is reflected back to the source machine, which converts it back to mass. Now compare the “traveled” mass to the “stationary” mass, do they weight the same, or are they different?

The present accepted models (Minkowski) of the expanding universe would have the traveled mass weigh less than the stationary mass. The proposed theory will have the masses retain their proportional relationships. They will weigh the same, but both will weight less.
Which model provides a simpler more consistent description of reality?” Which one conforms to observation? ‘Which one really maintains “conservation” of mass principles? The E=mcc relationship becomes a much more powerful and unifying concept if the loss of energy in an expanding space time field results in no difference if the mass is a “solid” or as Photons.

snowflake

Welcome back, SnowFlake!

You've stated that it would be more scientifically sound if any mass also lost energy, but what's the specific mechanism that makes solid (or fluid... whatever) matter lose energy?

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Hi Pi man and Grey and everybody.

I finally got my web site up www.uniformexpansion.com

You guys are amazing. You brought out the concept of hyper space apparently out of intuition. The proposed model does consist of extra dimensional measures.

If you have time I would appreciate a response.

Thanks
snowflake

Hi Pi

You wrote “You've stated that it would be more scientifically sound if any mass also lost energy, but what's the specific mechanism that makes solid (or fluid... whatever) matter lose energy?”
This is a good question, But lets extend it a little, what is it that gives matter “intrinsic” energy in the first place? (“Intrinsic” is the word Einstein uses in his development of the E=mcc relationship). There is no theory I know of today that explains why matter has intrinsic energy, it is just there.

When you get a chance to read the theory, you will find that the intrinsic energy is the result of real kinematic motion via another dimension. As an object slows down in this extra dimension, it loses intrinsic energy.
This theory also adds another factor to the Cosmological red shift. While there is a recessional red shift due to the expansion of spacetime, there is now a real Doppler shift introduced. Since matter is moving in this unobserved dimension, the light emitted will be effected by the motion; As matter slows down in this “unobserved” extra dimension, the amount of Doppler effect will not be as much. This proposed red shift will be called the Cosmological Doppler effect. The recessional red shift will be a result of models proposed by Minkowski or General Relativistic models (which are necessary and valid in my model). The Cosmological Red shift will include both relationships.

Since the photon and the mass are both associated with motion in this unobserved dimension, they are both effected similarly, since they both slow down in this unobserved dimension, they both lose energy accordingly.

Thanks
snowflake