Physics Help Forum Dark Energy, is it legitimate?

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 Sep 4th 2017, 08:18 PM #1 Senior Member   Join Date: Nov 2013 Location: New Zealand Posts: 534 Dark Energy, is it legitimate? This video: Here are my concerns. On the Youtube clock from: 9:25 Can he really simply draw a sphere around certain galaxies and say only those galaxies matter in the calculations? Why does he assume the other galaxies outside the sphere cancel out? 19:35- Can the K term of $\displaystyle \frac{\dot{a}^2(t)}{a^2(t)} = \frac{8 \pi G}{3} \rho(t) - \frac{K}{a^2(t)}$really cause $\displaystyle \frac{\dot{a}^2(t)}{a^2(t)}$ to become negative for certain values of K given that its a squared quantity and the density term must also be positive? 29:00 Can a photon really be modelled in an expanding cube arguing that the wavelength increases as it expands? Doesn't that assume the existence also of an expanding ether? Otherwise why would an expanding universe cause the wavelength of a small wave packet of light to expand if we can't even detect this expansion from within our own solar system? 38:00 Now it claims that a matter dominated universe based on the equation $\displaystyle a = c t^\frac{2}{3}$ is asymptotic. Really? I thought it was a value that was the square of a cube root which I never knew was asymptotic!! Is Dark Energy really the house of cards that a careful study of this video would cause us to believe? Is dark energy really just a flawed idea based upon faulty maths? __________________ Burn those raisin muffins. Burn 'em all I say. Last edited by kiwiheretic; Sep 5th 2017 at 01:21 AM.
Sep 5th 2017, 01:20 PM   #2
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 Originally Posted by kiwiheretic This video: Here are my concerns. On the Youtube clock from: 9:25 Can he really simply draw a sphere around certain galaxies and say only those galaxies matter in the calculations? Why does he assume the other galaxies outside the sphere cancel out?
It's a consequence of how the inverse square law of gravitational attraction works,. If the universe is homogeneous and isotropic, then the attraction from any one galaxy outside the sphere is precisely cancelled by attraction(s) to other galaxies on the opposite side of the sphere, as he describes at 10:10 in the video. As an example: if you dig a hole in the Earth and lower yourself down into it say, 100 miles, then the gravitational force you would feel from the Earth would equal G time the mass of the Earth for the portion closer to the center than you are, divided by your distance from the center squared. In other words the mass of the Earth that is above your head has no effect (again, assuming the Earth is a perfect sphere with homogeneous and isotropic distribution of mass). The same phenomenon applies to electric fields as well as gravitational fields - if you are inside a metal spherical shell that has a charged surface the electric field at every point inside the sphere is precisely zero (this is how a Faraday Cage works).

 Originally Posted by kiwiheretic 19:35- Can the K term of $\displaystyle \frac{\dot{a}^2(t)}{a^2(t)} = \frac{8 \pi G}{3} \rho(t) - \frac{K}{a^2(t)}$really cause $\displaystyle \frac{\dot{a}^2(t)}{a^2(t)}$ to become negative for certain values of K given that its a squared quantity and the density term must also be positive?
Good question. I think he misspoke - what he should have said (I think) is that if K >0 you get an ever-expanding universe, if K < 0 you get a shrinking universe, and if K=0 you get a flat universe. I see he uses this definition of open vs closed vs flat at 24:00 in the video. If you go back to the original equation at the beginning of his derivation and make the sign change for K like he does than you are essentially starting with:

$\displaystyle \frac 1 2 m v^2 = \frac {GMm}D - K$

In other words KE = PE plus a value K, and K cannot exceed the value of KE alone, because if it does then you have PE being a positive value, which makes no sense.

 Originally Posted by kiwiheretic 29:00 Can a photon really be modelled in an expanding cube arguing that the wavelength increases as it expands? Doesn't that assume the existence also of an expanding ether?
His argument for this as presented is not complete. He's using basic math to try to present concepts that really require much more complicated analysis in 4 dimensions (i.e. using General Relativity). So no - his argument as presented uses a lot of "hand waving" as opposed to mathematical rigor. That doesn't mean he's wrong - it's just that he's made a video using only high school math that really requires a much more rigorous and difficult treatment to be truly complete.

 Originally Posted by kiwiheretic Otherwise why would an expanding universe cause the wavelength of a small wave packet of light to expand if we can't even detect this expansion from within our own solar system?
Not sure what you mean here. We can't detect expanding wavelength is real time, now that the universe is 14 billion years old or so. But we can detect the effect of expanding wavelengths on photons that have been traveling for billions of years - we see it in the red shift of light from distant galaxies, ad well as in the 3-degree background radiation.

 Originally Posted by kiwiheretic 38:00 Now it claims that a matter dominated universe based on the equation $\displaystyle a = c t^\frac{2}{3}$ is asymptotic. Really? I thought it was a value that was the square of a cube root which I never knew was asymptotic!!
Again his argument is not rigorous. What he should have said is that the velocity of expansion in a flat system approaches zero over an infinite amount of time. Now that seems to imply that there is some max size that the universe would reach as expansion velocity approaches zero. But it's not clear from his explanation that this value isn't infinity. Since all his math is based on classical mechanics (not GR), the analogy is what happens if you throw a stone upward from the Earth: throw it fast enough and it escapes Earth's gravity and recedes forever- that's analogous to an open universe. Throw it slower and the Earth's gravity eventually causes the stone to stop rising and then fall back to Earth - that's analogous to the closed universe. There's a middle value in which the stone slows but never quite reaches zero velocity - that's the flat universe analog. How high does such a stone rise? The answer using Newtonian mechanics is infinitely high, even though it's velocity approaches zero after an infinite amount of time.

 Originally Posted by kiwiheretic Is Dark Energy really the house of cards that a careful study of this video would cause us to believe? Is dark energy really just a flawed idea based upon faulty maths?
I stopped the video at 38:0 because that's as far as your questions went. The dark energy conjecture is based on observations of an expanding universe, to which math is applied to try and develop a model that "explains" why this is so. The conclusion I reach is that classical mechanics doesn't do good job at explaining much of this, so if you're going to make a video explaining the expansion of the universe based on high school level math you're going to have to use some short cuts. But that does not mean that this is all a "house of cards" or that the math behind it is faulty.

Sep 5th 2017, 01:46 PM   #3
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 Originally Posted by ChipB Good question. I think he misspoke - what he should have said (I think) is that if K >0 you get an ever-expanding universe, if K < 0 you get a shrinking universe, and if K=0 you get a flat universe. I see he uses this definition of open vs closed vs flat at 24:00 in the video. If you go back to the original equation at the beginning of his derivation and make the sign change for K like he does than you are essentially starting with: $\displaystyle \frac 1 2 m v^2 = \frac {GMm}D - K$ In other words KE = PE plus a value K, and K cannot exceed the value of KE alone, because if it does then you have PE being a positive value, which makes no sense.
I have a bigger issue with $\displaystyle \frac 1 2 m v^2$ being able to be less than zero which is what I think your statement implies.

Yeah, the lack of rigor, as you put it, has left me dissatisfied. It's frustrating how people put these videos out and then make it so people like me are "not qualified to have an opinion about it". It would be better if there were videos to walk you gently through the real stuff than tell you over simplified "lies" because they think we're not "grown up" enough to know "there is no Santa Claus".

Thanks for taking time to watch the video.
__________________
Burn those raisin muffins. Burn 'em all I say.

Last edited by kiwiheretic; Sep 5th 2017 at 01:48 PM.

Sep 6th 2017, 07:45 AM   #4
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 Originally Posted by kiwiheretic I have a bigger issue with $\displaystyle \frac 1 2 m v^2$ being able to be less than zero which is what I think your statement implies.
Yes, basically the same thing. Having a negative value of KE is the stuff of science fiction.

 Originally Posted by kiwiheretic Yeah, the lack of rigor, as you put it, has left me dissatisfied. It's frustrating how people put these videos out and then make it so people like me are "not qualified to have an opinion about it". It would be better if there were videos to walk you gently through the real stuff than tell you over simplified "lies" because they think we're not "grown up" enough to know "there is no Santa Claus".
I think you're being too harsh. Understanding the tensor calculus behind GR requires a lot more than a "gentle walk." I have a masters in engineering and have taken many graduate level mathematics courses in preparation for a PhD, and I find the math behind GR too difficult to really comprehend. The real problem is even if you understand the steps behind the math at the end you still don't have an intuitive understanding of how a 4-dimensional model behaves. I take solace in the fact that it was difficult for Einstein himself - it took him ten years to advance from Special Relativity to GR, and during that time he had to rely on the mathematical help of some of the world's preeminent mathematicians to hold his hand, so to speak. Having said that, if you'd like a basic introduction to the math behind relativity theory I suggest reading "A Most Incomprehensible Thing, Notes Towards a (very) Gentle Introduction to the Mathematics of Relativity" by Peter Collier. It builds the mathematical basis first for SR (which really only requires high school level math ability) then GR, which even for a "gentle introduction" is a pretty rough ride.

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