- #1
sami_m
- 16
- 0
Expanding universe or contracting matter?
this may look very weird question, but what if instead of that the universe is expanding, all matter is contracting as a function of its (proper) time?
[itex] Δs' = Δs_0 /F(t) [/itex]
The contraction of matter would effect on the length unit what we use.
I am posting this as thought experiment and i am just interested to know where does this kind of thinking crash down and hit the wall of reality.
If it is assumed that any structure in cosmological length scale do not contract when the matter in small length scales is contracting, we would measure that cosmological distances would appear to grow as a function of time.
We would get the usual Robertson-Walker metric:
[itex] ds^2 = dt^2 - a(t) dr^2 [/itex]
as in expanding space, but the underlying reason for this metric would now be not the expansion of space,
but contraction of the unit length we use.
This kind of weird possibility has to explain all cosmological observations to be a valid explanation. In addition to produce robertson-Walker metric, It should be able to explain The following two basic observations:
(i) Cosmological time dilation
(ii) Cosmological redshift and energy loss of the photon
and yes, contracting matter does not support these observations. So, is it worth of a throwing to rubbish bin?
-maybe not yet, there is still one thing what might make it look at least somewhat sensible.(i) First, It should be able to explain cosmological time dilation - that is, that distant objects appears to have time dilation.
Cosmological time dilation is explained by expanding universe by the expansion of the photons that travel through expanding space.
If it is thought that there is no expanding universe, but that there is contracting matter, there would not be observation of cosmological time dilation.
I think the only sensible solution for this problem is that if the matter were contracting, the time unit of the matter should be contracting also. Otherwise it just does not make sense. :
[itex] Δt' = Δt0 /F(t) [/itex]
where F(t) is some function.
So The change of the length unit and time unit would be together:
[itex] Δt'= Δt_0 /F(t) [/itex]
[itex] Δs'= Δs_0 /F(t) [/itex]
and the formula for scale factor a(t) in the metric equation has to be linear relative to the time unit the observer uses:
[itex] a(t') = 1 + H t'[/itex]
[itex] a(t) = F(t) [/itex]
assuming that all matter in the universe share exactly same proper time.
(ii) Secondly, this kind of hypothesis should also explain cosmological redshift and cosmological energy loss of the photon.
Again the only sensible solution for this would be that as the matter contracts, and observers own unit length and unit time contracts, it has to be that the observers measurement of the energy and momenta, must change such that:
[itex] ΔE'_{measured in photon}= ΔE_0 / F(t) [/itex]
[itex] dp'_{measured in photon} = dp_0 / F(t) [/itex]
The changes in the units of which the observer uses would be the opposite.
To put these four equations together, the changes of the time, lengt, energy and momentum are :
[itex] Δt' = Δt_0 / F(t) [/itex]
[itex] Δs' = Δs_0 / F(t) [/itex]
[itex] ΔE' = ΔE_0 * F(t) [/itex]
[itex] Δp' = Δp_0 * F(t) [/itex]
There is a theoretical fact In physics that it is possible to determine any kind of unit system by defining only three different kind of units - length unit, time unit and energy or momentum unit. All other units can be then derived from these 3 units by dimensional analysis.
Here i am not talking about just unit conversion of length, time and energy /momentum, but real, actual changes. But similarly as in unit conversion, from three equations, it is possible to derive the contraction or expansion equations for all physical measurables from these three or four equations.
Example : a mass
[itex] p'/p = m'/m , v'/v = 1 ⇒ m' = m0 * F(t) [/itex]
example : A local force
[itex] F' / F = m'/m a'/a = m'/m (1/dt'/dt) = F(t)^2 [/itex]
example: A local charge
[itex] q'/q = F'/F * (s'/s)^2 ⇒ q' = q_0 * F(t) [/itex]
example: Coulomb's constant
[itex] k'/k = F'/F * (s'/s)^2 * (1/ e'/e)^2 = 1/ F(t)^2 [/itex]
Key problem: What happens to energy conservation principle?
So the mass of the matter would be increasing according to these equations.
Due to the mass-energy equivalence, E = mc^2, it seems that increase of the mass would mean that the energy content of the matter should increase.
But If we look for example contraction of hydrogen atom, if we do not care of the mass-energy content, the change of the energy in this system is negative, because the matter-wavelength of the electron decreases. (The change in coulomb constant is canceled by the changes in electrons and protons charges if the distance r stays constant during the change. you can do this by evaluating by dimensional analysis how k and e changes and end up that k'/k (e'/e)^2 = 1) And for the same reason the electron should emit the energy difference in the form of radiation when it goes more near to nucleus.
Similarly, by similar deduction, all bounded Quantum mechanical systems should lose their system energy.
Another key problem: weird predictions:
IF the contraction of matter depends on the proper time, the hypothesis that the matter is contracting would make different prediction than expanding space.
1) The assumption that all matter share common proper time cannot be true in the following cases:
-in Compact objects like neutron stars and Black Holes
-In relativistic jets like in quasar jets
-In ultrarelativistic cosmic rays
If the contraction of the matter is dependent to the proper time of the matter, then this kind of idea would predict that in relativistic phenomenom that extends to cosmological time scales, there should exist differently contracted matter. But this kind of thing has never been observed in nature.
example: ultrarelativistic jet appear to have redshift and cross section expansion as a function of its distance from the source.
2) for same reason, if the contraction of matter depends on its proper time, the black hole event horizon shouldn't be contracting. This would give prediction that the radius of black holes should appear to increase at the same rate than the space appears to be expanding. And this would mean that Black holes appear to gain mass from nowhere.
this may look very weird question, but what if instead of that the universe is expanding, all matter is contracting as a function of its (proper) time?
[itex] Δs' = Δs_0 /F(t) [/itex]
The contraction of matter would effect on the length unit what we use.
I am posting this as thought experiment and i am just interested to know where does this kind of thinking crash down and hit the wall of reality.
If it is assumed that any structure in cosmological length scale do not contract when the matter in small length scales is contracting, we would measure that cosmological distances would appear to grow as a function of time.
We would get the usual Robertson-Walker metric:
[itex] ds^2 = dt^2 - a(t) dr^2 [/itex]
as in expanding space, but the underlying reason for this metric would now be not the expansion of space,
but contraction of the unit length we use.
This kind of weird possibility has to explain all cosmological observations to be a valid explanation. In addition to produce robertson-Walker metric, It should be able to explain The following two basic observations:
(i) Cosmological time dilation
(ii) Cosmological redshift and energy loss of the photon
and yes, contracting matter does not support these observations. So, is it worth of a throwing to rubbish bin?
-maybe not yet, there is still one thing what might make it look at least somewhat sensible.(i) First, It should be able to explain cosmological time dilation - that is, that distant objects appears to have time dilation.
Cosmological time dilation is explained by expanding universe by the expansion of the photons that travel through expanding space.
If it is thought that there is no expanding universe, but that there is contracting matter, there would not be observation of cosmological time dilation.
I think the only sensible solution for this problem is that if the matter were contracting, the time unit of the matter should be contracting also. Otherwise it just does not make sense. :
[itex] Δt' = Δt0 /F(t) [/itex]
where F(t) is some function.
So The change of the length unit and time unit would be together:
[itex] Δt'= Δt_0 /F(t) [/itex]
[itex] Δs'= Δs_0 /F(t) [/itex]
and the formula for scale factor a(t) in the metric equation has to be linear relative to the time unit the observer uses:
[itex] a(t') = 1 + H t'[/itex]
[itex] a(t) = F(t) [/itex]
assuming that all matter in the universe share exactly same proper time.
(ii) Secondly, this kind of hypothesis should also explain cosmological redshift and cosmological energy loss of the photon.
Again the only sensible solution for this would be that as the matter contracts, and observers own unit length and unit time contracts, it has to be that the observers measurement of the energy and momenta, must change such that:
[itex] ΔE'_{measured in photon}= ΔE_0 / F(t) [/itex]
[itex] dp'_{measured in photon} = dp_0 / F(t) [/itex]
The changes in the units of which the observer uses would be the opposite.
To put these four equations together, the changes of the time, lengt, energy and momentum are :
[itex] Δt' = Δt_0 / F(t) [/itex]
[itex] Δs' = Δs_0 / F(t) [/itex]
[itex] ΔE' = ΔE_0 * F(t) [/itex]
[itex] Δp' = Δp_0 * F(t) [/itex]
There is a theoretical fact In physics that it is possible to determine any kind of unit system by defining only three different kind of units - length unit, time unit and energy or momentum unit. All other units can be then derived from these 3 units by dimensional analysis.
Here i am not talking about just unit conversion of length, time and energy /momentum, but real, actual changes. But similarly as in unit conversion, from three equations, it is possible to derive the contraction or expansion equations for all physical measurables from these three or four equations.
Example : a mass
[itex] p'/p = m'/m , v'/v = 1 ⇒ m' = m0 * F(t) [/itex]
example : A local force
[itex] F' / F = m'/m a'/a = m'/m (1/dt'/dt) = F(t)^2 [/itex]
example: A local charge
[itex] q'/q = F'/F * (s'/s)^2 ⇒ q' = q_0 * F(t) [/itex]
example: Coulomb's constant
[itex] k'/k = F'/F * (s'/s)^2 * (1/ e'/e)^2 = 1/ F(t)^2 [/itex]
Key problem: What happens to energy conservation principle?
So the mass of the matter would be increasing according to these equations.
Due to the mass-energy equivalence, E = mc^2, it seems that increase of the mass would mean that the energy content of the matter should increase.
But If we look for example contraction of hydrogen atom, if we do not care of the mass-energy content, the change of the energy in this system is negative, because the matter-wavelength of the electron decreases. (The change in coulomb constant is canceled by the changes in electrons and protons charges if the distance r stays constant during the change. you can do this by evaluating by dimensional analysis how k and e changes and end up that k'/k (e'/e)^2 = 1) And for the same reason the electron should emit the energy difference in the form of radiation when it goes more near to nucleus.
Similarly, by similar deduction, all bounded Quantum mechanical systems should lose their system energy.
Another key problem: weird predictions:
IF the contraction of matter depends on the proper time, the hypothesis that the matter is contracting would make different prediction than expanding space.
1) The assumption that all matter share common proper time cannot be true in the following cases:
-in Compact objects like neutron stars and Black Holes
-In relativistic jets like in quasar jets
-In ultrarelativistic cosmic rays
If the contraction of the matter is dependent to the proper time of the matter, then this kind of idea would predict that in relativistic phenomenom that extends to cosmological time scales, there should exist differently contracted matter. But this kind of thing has never been observed in nature.
example: ultrarelativistic jet appear to have redshift and cross section expansion as a function of its distance from the source.
2) for same reason, if the contraction of matter depends on its proper time, the black hole event horizon shouldn't be contracting. This would give prediction that the radius of black holes should appear to increase at the same rate than the space appears to be expanding. And this would mean that Black holes appear to gain mass from nowhere.
Last edited: