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Offline wanchung

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Temperature-Time equation!
« on: 13/11/2009 12:28:56 »
Title: Temperature-Time equation!

Wanchung Hu
PostDoc Fellow
Correspondence to: lukluk73_2006@yahoo.com.tw

Abstract
Dark energy is a mystery in current cosmological research. Professor Albert Einstein originally thought the universe is static. Thus, he added a cosmological constant in his universe equation to prevent the collapse due to gravity produced by mass in universe. However, due to Professor Hubbles observation, our universe is actually expending. Based on his observation, he obtained a physic law called Hubbles law: V=H*R (H=Hubble constant, V=recession velocity, R=comoving proper distance). Currently, we still dont know what the reason to cause universe expansion is. A term: dark energy is given to explain the universe expansion. Dark energy is still a puzzle in Astronomy. No one knows what dark energy is. In this article, we propose that radiation pressure is actually dark energy. It has several important characteristics to be the best candidate of dark energy. In addition, we will use radiation pressure to derive Hubbles law. However, further experiments and observations are helpful for confirming that radiation pressure is dark energy.


Introduction
Dark energy is a mystery in current cosmological research. Professor Albert Einstein originally thought the universe is static. Thus, he added a cosmological constant in his universe equation to prevent the collapse due to gravity produced by mass in universe. However, due to Professor Hubbles observation, our universe is actually expending. Based on his observation, he obtained a physic law called Hubbles law:

v=H*R (H=Hubble constant, v=recession velocity, R=comoving proper distance).

Currently, we still dont know what the reason to cause universe expansion is. A term: dark energy is given to explain the universe expansion. Dark energy is still a puzzle in Astronomy.

Radiation pressure is originally derived from Professor James Clerk Maxwell. It was derived from the momentum change of light. The formula of radiation pressure is:

P=(uT^4)/c (u=Stefan-Boltzmann constant=5.67*10^-8 JS^-1m^-2K^-4; T=absolute temperature; c=lightspeed)

The basic concept for deriving the formula is from the momentum of light: p=E/c. When light is arriving on the surface of substance, it will cause momentum change. Thus, radiation pressure is resulted. The radiation pressure from Sun to Earth is 4.6uPa. It is a very tiny amount compared to the gravity from Sun to Earth. It can almost be neglected compared to gravity. However, we propose here that radiation also causes pressure on space-time dimension. And, due to the high temperature of all stars of universe and the fourth magnitude of radiation pressure(~T^4), radiation pressure exceeds gravity and plays a dominant role in universe expansion. Due to the T^4 magnitude, our universe is expanding accelerately. Radiation pressure has greater impact on space-time dimension than gravity. Gravity is a force to cause space-time distortion. It is not a pure inward force to cause space-time contraction. Thus, we dont need to balance gravity with radiation pressure. We believe that radiation pressure is actually the dark energy.

Machs principle pointed out there is no absolute time and space. Substance in space-time will affect the surrounding space-time. Einstein was inspired by Machs principle and developed general relativity. There must be an outward force to cause universe expansion. Radiation pressure is the best candidate. The other fundamental forces cannot account for the large dimensional universe expansion. Strong force and weak force are mediated from particles and only work in a very short range inside the atom. Electromagnetism can be transmitted from a long distance. However, almost all the large substances are neutralized in electricity in our universe. Electrostatic force is from rest charges and magnetic force is from moving and spinning charges. However, when there is no net charge in stars or planets, there is no electromagnetism. Thus, electromagnetism cannot be the cause of universe expansion. Radiation (Heat and Light) becomes the best candidate of the force of dark energy.

Due to the second law of thermodynamics, heat has a very close relationship with time. Entropy is always increasing from high temperature to low temperature to achieve the maximal magnitude of randomness when time is moving ahead. In addition, lightspeed is very important in space and time due to relativity. Radiative wave can cause entrophy increase, and convergent wave can cause entrophy decrease. Thus, we think heat and light play dominant roles in our four dimensional universe. The heats moving arrow is very correlated with the space-time moving arrow(universe expansion arrow or comsmological arrow). It means that heat and light decides the moving of space-time. Radiation pressure is actually from heat and light. Thus, heat and light can cause space-time movement due to the mediation of radiation pressure. Radiation is from the central substance and radiating to all the outward direction. Thus, radiation from stars or from galaxy can expend the space-time outwardly and evenly in every direction. It is very important to synchronize all the time arrows in universe. All the time arrows must be the same and have only one meaning. If radiation pressure is dark energy, then entrophy arrow=radiation wave arrow=cosmological universe expansion arrow=time arrow=causal arrow. Thus, there is no contradicts in these time arrows. They can be well synchronized. Only when dark energy is radiation pressure, all the time arrows can be synchronized. Thus, radiation pressure is the best candidate of dark energy. It is also important to know that universe will cease to expand if the whole universe reaches heat death(maximal entrophy). In addition, universe wont contract when it reaches heat death because radiation wave wont become convergent wave to let universe contraction and to let time arrow fly back. This concept is very important. It means that the time arrow wont be reversed to disobey the causal-effect relationship.

In order to test if radiation pressure is the dark energy, we tried to derive Hubbles law from radiation pressure. We found that Hubbles law can be derived from assuming radiation pressure is dark energy. Below is our deduction:

In this deduction, we need to assume that observable universe is the actual universe. We can imagine this from the following example. When a light is emitted from our solar system to the actual universe boundary to cause universe expansion, the time it spends is the same as a light emitted from the observable universe boundary to travel to our solar system. Thus, observable universe is the actual universe. The volume of observable universe is given by Hubble volume:

Hubble Volume V=(c^3/v^3)R^3 (c=lightspeed, R=distance, v=recession velocity)
Hubble Length R=cR/v

Thus, we can derive the relation between heat and distance first:

Universe entropy per comoving volume(Hubble Volume) is:
s=(2pi^2/45)GsT^3
There is conservation of total entropy:
Thus, S=(2pi^2/45)GsT^3*c^3R^3/v^3=constant
Thus, T -> (v/c)R
temperature(T) is inverse proportional to cR/v

Second, we assume the whole universe is a close system. Based on the conservation of energy, the total energy of the universe is constant.

Radiation outward pressure=uT^4/c,
Thus, Total E=P*V=(uT^4/c)*V=constant
Applying the concept of Hubble Volume and Hubble Length
And, T is inverse proportional to cR/v
Total E={kv^4/(c^4R^4)}* [(c^3/v^3)R^3]=constant
Total E=(k)v/cR=constant (k, c are both constants)
Thus, v is direct proportional to R
That is Hubbles law : v=HR (H: Hubbles constant)

In the second part of this article, we will derive why our universe is accelerated expanding. There is a relation between temperature and acceleration which is called Unruh effect. The formula is:

T=ha/2pi*k*c (T=absolute temperature. h'=reduced planck constant, a=acceleration, k=Boltzman constant, c=lightspeed)

This formula can be derived by Lorentz transformation, Plancks law, and Doppler shift. This formula is a natural consequence of time dependent Doppler shift seen by the accelerated observer. Originally, the formula is explained, A observer undergoing uniform acceleration a in vacuum responds as though it were immersed in thermal radiation T (T=ha/2pi*k*c).[1] However, we can also explain that temperature can cause uniform acceleration in vacuum.

In one spatial dimension, T is in direct proportion to a. Thus, it means that absolute temperature T can cause vacuum to expand at a acceleration in X-axis. In addition, the radiation pressure is:

P=(uT^4)/c, (T=ha/2pi*k*c)
Thus, P=(u/c)*(h^4*a^4/16pi^4*k^4*c^4)

Radiation pressure P is in direct proportion to acceleration a^4. It means that radiation pressure can cause accelerated universe expansion in 4 dimensional space-time. Based on current observation, our universe is accelerated expanding. If radiation pressure is dark energy, it can perfectly fulfill our observation.

Then, we introduce u=(pi^2/60)k^4/h'^3c^2 into the above equation, then we get:

P=(pi^2/60)h'a^4/16pi^4*c^7

We know c=at, then a=c/t (t=time,x=space distance),

P=(1/pi^2*960)(h'/t^4c^3), let x=ct

Thus, P=(1/pi^2*960)(h'/t*x^3)=(1/pi^2*960)(h'c/x^4)

Compared to the Casimir effect F=P/A=(pi^2/240)(h'c/x^4)

There is only a difference of factor 4pi^4, thus we can infer that radiation pressure is the cause of Casamir force

In Carnot cycle, we find out that it disobeys energy conservation. Small amount work can produce higher amount of heat. That is heat pump. By using the above equation, we can know that heat is a function of spacetime. In the initial universe, space-time is so small with greatest amount of heat(temperature). In addition, we can expain why friction can induce heat. It is because heat production is from spacetime compression movement. Thus, we can solve the paradox of energy conservation problem in Carnot cycle.

Then, we let  P=(1/pi^2*960)(h'/t^4*c^3)==(uT^4)/c==(pi^2/60)k^4T^4/h'^3c^3

Then, h'^4/16pi^4*t^4=k^4T^4

Thus, h'/2pi*t=KT, since h'=h/2pi and t=1/f and w=2pi/t,

Then, we get hf/4pi^2=h'w/4pi^2=kT that is temeprature=time equation

Time is a function of temperature

In summary, we believe radiation pressure is the best candidate of dark energy. It can be well correlated with space-time movement. We suggest further experiments and observations to confirm this hypothesis.

Reference
1. Alsing P. M. and Milonni P. W. Simplified derivation of the Hawking-Unruh temperature for an accelerated observer in vacuum arXiv:quant-ph/0401170v2 Aug27,2004


 

Offline Mr. Scientist

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« Reply #1 on: 13/11/2009 12:42:15 »
It can't be radiation pressure, Mr Wanchung. The reason why is because there is more negative energy in the vacuum which counteracts this. This is known as the zero-point energy field. It far outweighs the pressure of the natural CMB. If anything, you'd be better off resorting to answering acceleration using zero-point energy, since it has a magnitude of around 10^120 times larger than that of all the visible electromagnetic energy in the universe.
 

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« Reply #2 on: 13/11/2009 12:49:11 »
Thus, P=(1/pi^2*960)(h'/t*x^3)=(1/pi^2*960)(h'c/x^4)

Compared to the Casimir effect F=P/A=(pi^2/240)(h'c/x^4)

you'v made some mistakes here.
 

Offline wanchung

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« Reply #3 on: 14/11/2009 15:18:46 »
Hello,

What is the mistake?
 

Offline Mr. Scientist

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« Reply #4 on: 15/11/2009 01:00:26 »
Well, why have you got a factor of (x^3) on one side and then compare it to he casimir force which has factor of x^4? Maybe its just me, but i struggle to follow much of what you talk about.

 

Offline wanchung

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« Reply #5 on: 16/11/2009 09:59:10 »
We can also use the concept of zero point energy(Vacuum energy) to explain the temperature-time eqaution:

The zero-point energy(vacuum energy) is 1/2hf

The volume of 3-sphere is 4 dimentional space time is 2pi^2

The heat energy of unit space-time volume is KT

Then, (1/2hf)/2pi^2=KT

That is hf/4pi^2=KT

which is time-temperature equation!



Hi, because the universe is expanding due to light pressure.

Thus, the distance in universe X=ct

Put this relation into Casamir force, we can get the above formula!
 

Offline Mr. Scientist

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« Reply #6 on: 16/11/2009 17:28:58 »
We can also use the concept of zero point energy(Vacuum energy) to explain the temperature-time eqaution:

The zero-point energy(vacuum energy) is 1/2hf

The volume of 3-sphere is 4 dimentional space time is 2pi^2

The heat energy of unit space-time volume is KT

Then, (1/2hf)/2pi^2=KT

That is hf/4pi^2=KT

which is time-temperature equation!
Better worded, and yes it is a new equation. Well done Wanchung!
 

Offline wanchung

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« Reply #7 on: 17/11/2009 10:16:36 »
Hi, Mr. Scientist,

Thanks a lot!
 

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« Reply #8 on: 19/11/2009 08:19:37 »
Wangchung,

may i have your permission to unify your temperature-equation derivationally-wise into my new Lorentz Invariant force law for Gravitation given as

vћ(c/G)=μ_gν X G'(∂A*/∂t)−F_g

where v<c
 

Offline wanchung

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« Reply #9 on: 19/11/2009 11:57:08 »
Hi, Mr Scientist,

Are you using the equation in scientific paper or book? Would you please tell me your true name? Is it okay you cite my name in your paper or book? Please email me at lukluk73_2006@yahoo.com.tw
 

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« Reply #10 on: 19/11/2009 13:02:42 »
My name is Gareth Lee. Nice to meet you :) formally at once.

I will not communicate over the e-mail system, as it;s filled to the brim, and would take a good hour to delete them -

Are you using the equation in scientific paper or book? Would you please tell me your true name?

and

Is it okay you cite my name in your paper or book?

Of course it is, but there is a second counterpart who needs your permission. This is the man we all know as vern.

The mathematical formalities so far arisen, are given a sub-published group: http://www.scribd.com/documents

The article which interests this discussion is called ''A New Unified Theory Studied Under Luxon Theory '' - this an attempt to unfiy verns grand vision with some mathematics.

 

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« Reply #11 on: 19/11/2009 13:05:05 »
Oh and hoperfully, we will publish it academically rather than the usage i have been using, as helpful as it is when keeping copy-right issues.

I've heard you have had problems like that yourself. I think it be only fair thought that if[/b[ we manage to recreate physics into a new form worthy of publication, we all give equal shares into the money side of things, whilst profits are equally shared. :)
 

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« Reply #12 on: 19/11/2009 13:06:48 »
A guestimate of the price, of a publication of our (vern, you and myself, and anyone else who wishes to integrate work within) would be no less than 500 in UK money. That would mean i think around 200 dollars per authors.
 

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« Reply #13 on: 19/11/2009 13:36:09 »
Hi, Gareth,

Nice to meet you. The price is ok to me. But, I would still like to read the whole deduction. Would you please email me your book or article? Thank you very much.
 

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« Reply #14 on: 20/11/2009 02:49:36 »
Hi, Gareth,

Nice to meet you. The price is ok to me. But, I would still like to read the whole deduction. Would you please email me your book or article? Thank you very much.

It's not even finished. Not have myself or Vern confirme on how to present the work ina book title. Nor have we even finished completing a confirmation bwteen both our ideologies/theories. Until this is done, then we can present the thesis to a PhD theorist as a New Unified Theory Paper, involving the integration of lawyers of course :)
 

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« Reply #15 on: 20/11/2009 02:52:14 »
And the link is (in indepence from vern, even though i give Him absoute credit for his theory), is found at

http://www.scribd.com/documents
 

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« Reply #16 on: 22/11/2009 23:08:55 »
Right wangchung, what i have done is modified one of the important linear tensor of rank zero in the gravitational-force due to energy equation, which was:

|(∫F_g vt)_<A_k>|=∫-▼φ(ћ(c/G))_g βt(e^i ∫d^4 δ(x-x')([ξ√g'_0((∂/∂δt-Δ + M)ψ-(∂/∂δt-Δ + M)ψ)]+[ξ√g'_g((∂/∂δt-Δ + M)ψ*-(∂/∂δt-Δ + M)ψ*]) (20)

Any actions that can come from this are restricted by the presence of d^4 δ(x-x').

What interested me most is how you quite rightly applied it to the zero-point field when i questioned you about it... If we take our attentions to ∫d^4 δ(x-x') this can be such a mathematical arguement to be made to support the dimensions of your time-temperature equation. It seemed so odd how the two worked so well together, if i might be so bold.

where from now on x=KT

|(∫F_g vt)_<A_k>|=∫-▼φ(ћ(c/G))_g βt(e^i ∫d^4 δ(KT-KT')([ξ√g'_0((∂/∂δt-Δ + M)ψ-(∂/∂δt-Δ + M)ψ)]+[ξ√g'_g((∂/∂δt-Δ + M)ψ*-(∂/∂δt-Δ + M)ψ*]) (B)

Very convincing as an equation which can calculate the zero-rank linear tensor to measure the temperature and the time i would say, within a planck time since δ is very small. Alterations of the algbebra will obviously lead to different results. A quick demonstration is:

∫d^4 δ(KT+KT')=∫d^4δΔE

Note that in the equation marked (B) not mistake d'Alembert operators use of the delta symbol, and that in this different usage ΔE as the total energy.
 

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« Reply #17 on: 25/05/2010 11:12:50 »
Dear All,

I think I have found out the reason of thermal expansion.

The reason is universal lightity(radiation pressure).

If there is more heat, there will be more photons between two atoms.

More photons will elongate the space between two atoms(forming the substance), then the volume of the substance will enlarge

Thus, it can explain why there is thermal expansion.

It can also explain cold contraction since there will be photons removed out during cold.

The current mechanism of thermal expansion is wrong!

Wrong theory1: Heat causes atoms vibration or kinetic movement, then vibration or kinetic movement will enlarge the volume since atoms will need larger space.

This theory is wrong! If atoms in a substance is rigorously randomly vibrating or moving, the actual of this substance will be changeable. All solid will be like Ameba worm to have randomly changeable volume/shape. It won't let continously thermal expansion.

Wrong theory2: Heat will cause atomes to kinetically move. Then, moving atoms will bump each other. Because of these collisions, atomes will tend to repulse each other. Then, the volume is enlarged.

This theory is still wrong. We can see the example of a solid. Say a gold. The atoms(nuclear) inside the gold have fixed position. They are not freely movable. However, gold can still suffer from thermal expansion. The second theory is still wrong.

I am very confident that universal lightity(radiation pressure) is the actual cause of thermal expansion. A common puzzled phenomenon with long long history is solved!
 

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