Does an expanding Universe mean a violation of the law of Conservation of Energy?

----------------- #1227 - Does Expanding Universe Violate the Conservation of Energy?
As the Universe expands the light waves get stretched to lower energies. Where does this loss of energy go? This review discusses the law of Conservation of Energy and how spacetime causes us to see this is a loss of energy.

- Attachments - Expanding Universe.

- The law of Conservation of Energy is fundamental to all of physics. It says that energy can never be created or destroyed. It can be transformed from one form to another but the total energy always remains unchanged. The energy released in the Big Bang is the same energy we have in the Universe today. If we could add up all the different forms of energy, including mass, the Universe total would remain unchanged. If true, how do we explain the expanding Universe that is continually diluting itself and loosing energy?

- The Universe is expanding. As space expands the electromagnetic wavelengths get stretched. Light wavelengths get “red-shifted”. The longer wavelengths and lower frequencies have lower energy. That is why the Cosmic Microwave Background radiation we see today is 1,000 times longer wavelength than when it left the source 300,000 years after the Big Bang. When light started on its journey to us it was Gamma Ray radiation at a temperature of 3,000 Kelvin. What we see today is Microwave radiation at about 3 Kelvin. The Universe has expanded by a factor of 1,000 and the radiation has cooled by a factor of 1,000.
　
- Light is loosing energy in the expansion of the Universe. But, where does this energy go? It must transform into something else? If thermal energy goes down something else must go up if the law of Conservation of Energy is to hold up. Energy can not be destroyed? Here are the direct proportional relationships. (See footnotes (1) to (4)):

----------------------- Energy = a constant * Temperature

---------------------- Temperature = a constant * Frequency

--------------------- Energy = a constant * Frequency

- The point of this review is that energy appears to be lost, but, on the scale of the individual photons the energy is conserved. How does this figure?

- Emmy Noether is a mathematician who proved that the Laws of Conservation depend upon the Symmetry in the Universe. Wherever the Universe displays Continuous Symmetry there is a conservation law associated with it. The physical laws stay the same with the passage of time. Because the physical laws stay the same with the passage of time then, Time is in Continuous Symmetry. The same is true with space. The physical laws remain the same regardless of location in space. There is Spatial Symmetry too.

- Temporal Symmetry dictates the Law of Conservation of Energy. Spatial Symmetry dictates the Law of Conservation of Momentum. Rotational Symmetry requires that the laws of physics do not change with at change in direction. Rotational Symmetry dictates the Law of Conservation of Angular Momentum. If a law does not change regardless of the situation it obeys the law is in Continuous Symmetry. Noether’s law of mathematics states that whenever you have a Continuous Symmetry you must have a Law of Conservation.

- The way astronomer’s know that the light from distant galaxies is redshifted is because the wavelengths of photons emitted or absorbed by the hydrogen atom are the same everywhere ( Spatial Symmetry). When the photons arrived at the astronomer they were stretched in proportion to the distance from the source. You are familiar with the Doppler Shift of sound waves caused by relative motion. Cosmological redshifts are different, but analogous. Although the distant galaxies appear to be flying away from us actually the space between us is expanding. The photons are not loosing energy they simply look different from our frame of reference. To us they appear stretched by expanding space. The Geometry of Spacetime is changing the Law of the Conservation of Energy is not. What appears as a loss of energy ( increasing wavelength) is actually photons slowing down as geometry changes. This is the basis of spacetime in the Theory of Relativity. Time slows down as a function of motion speeding up.

- Particles have wavelike properties and the larger the particle’s momentum the smaller its wavelength and the greater its energy. Particles can have higher momentum by having higher mass or higher velocity, or both.

- For example: A baseball traveling 90 miles per hour has a wavelength of 1.1*10^-34 meters. Not so the batter would notice. However, an electron traveling at 90 miles an hour has a wavelength of 1.8*10^-5 meters. That is very small also , but, relative to the electron it is 29 magnitudes larger than the size of the electron. ( See footnote (5))

- A particle’s wavelength increases by exactly the same proportions as a photon’s wavelength. Light and matter behave the same when it comes to energy loss in an expanding Universe. Again the energy loss paradox is resolved when you take into account that you are measuring velocity in different frames of reference.

- How it appears to us: It appears that Dark Energy is expanding the Universe but it does not dilute as the Universe expands. It represents 73% of the total mass-energy in the Universe and it remains the same percentage as the Universe expands. Noether’s law of symmetry falls apart in this changing spatial geometry. Changing geometry breaks the Temporal Symmetry and the Conservation of Energy no longer holds. In reality the total energy in the Universe becomes “ indefinable. It appears that empty space does not have a physical reality.

- The hard part to grasp is that with relative motion we see photons from different perspectives. The drop in energy is just a matter of perspective and relative motion. To gain this perspective think of two galaxies receding from each other in an expanding Universe. The galaxy’s redshift is identical to the Doppler shift to an observer receding at the same velocity as the galaxy. To measure the velocities you must trace the trajectories of the galaxy and the observer not in space, but in spacetime. Compare the velocity of the galaxy at the time the photon was emitted with the velocity of the observer at the time the photon was received. Now calculate the relative velocity. The redshift observed can be accounted for with relative motion and not to the energy loss. The race car sounds faster coming towards you and slower after it passes you. Even though the race car is traveling at the same speed.

- In the same way, the Universe is expanding it is not leaking energy.
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(1) How do we calculate the apparent loss in energy from the CMB release till today?
Energy is directly proportional to Temperature.
If two things are proportional they can be turned into an equality with the proper constant of proportionality.

------------ Energy = Constant * Temperature
------------- E = k * T

The temperature of the CMB when light was released corresponded to the ions of atomic nuclei capturing electrons and become neutral atoms. This occurs at 3,000 Kelvin. If the energy is measured in electron volts the constant is 0.000428

------------- E = 0.000428 * 3,000
------------ Energy = 1.28 electron volts.

- This is the energy level of a Gamma Ray photon.
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(2) After the Universe expanded and cooled by a factor or 1,000 the temperature measured today is about 3 Kelvin.

---------------- E = 0.000428 * 3

The energy in the Microwave Background is 0.00128 electron volts.
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(3) How the constant k above was calculated: The constant = k = Planck’s constant * Constant speed of light / Wien’s displacement Constant.

---------------k = h * c / 0.0029
------------- h = 4.136*10^-15 electron volt * seconds.
------------- c = 3*10^8 meters per second
--------------Wien’s Displacement = 0.0029 meter * Kelvin
--------------k = 0.000428 electron volts / Kelvin.

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(4) The same calculations can be made with the change in wavelength or the change in frequency of the CMB radiation.

- Temperature is directly proportional to frequency

--------- T = K * f
-------- T = 10^-11 * f
--------- Temperature = 10^-11 * frequency
----------- K = 0.0029 / c

- Temperature is indirectly proportional to wavelength
-------- T = 0.0029 / w
--------- 0.0029 is Wien’s Displacement Constant.

- When T = 3,000 Kelvin the frequency is 3 * 10^14 cycles per second = 300 terahertz.
Wavelength = 10^-6 meters. Gamma Rays.

- When T = 3 Kelvin the frequency is 3 * 10^11 cycles per second = 300 gigahertz.
Wavelength = 10^-3 meters = 0.1 centimeters. Microwaves.
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(5) The baseball traveling 90 miles per hour is traveling 40 meters per second. The mass of the baseball is 0.15 kilograms. The electron’s mass is 9.108*10^-31 kilograms.

-------------------- Wavelength = Planck’s Constant / Momentum.
-------------------- Momentum = mass * velocity
-------------------- Wavelength of the baseball = 1.1*10^-34 meters
-------------------- Wavelength of the electron = 1.8 * 10^-5 meters.
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(6) The Cosmic Microwave Background, CMB, wavelengths are not a single frequency but cover the range from 0.5 to 0.05 centimeters with a peak at 0.11 centimeters. The peak energy level is 0.00124 electron volts.
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707-536-3272, [email protected] Tuesday, November 30, 2010