Time variable of space-time at the end of universe

[VaibhavP]

Time variable of space-time at the end of universe...

As universe is continuously expanding at the accelerating speed...expansion of the universe causes Redshift...the whole universe is made up of the tiny particles and the material. Because of this all the material particles of the universe must be continuously accelerating, causing redshift...in redshift wavelength decreases and the frequency increases..means time increases...and the end of the expansion the wavelength will be almost flat...and time will be infinite...I am not wrong then what that infinite time indicates?

 

[Chronos]

No. Exansion is universal, not local. Objects at the limit of observation are not moving any faster in their local reference frames than the local cluster. No special relativistic effects apply.

 

[VaibhavP]

But if we look mathematically wavelength, frequency and time relationship...anyway it is also getting applied to all the universe combinedly (as you said) then, time comes into picture...we cannot neglect it...

 

[Chalnoth]

But if we look mathematically wavelength, frequency and time relationship...anyway it is also getting applied to all the universe combinedly (as you said) then, time comes into picture...we cannot neglect it...

The short of it is that special relativity only applies in flat space-time. The expansion amounts to a significant curvature of space-time that cannot be ignored if you're talking about objects at high redshift. Because of this curvature, you just can't use special relativity to get the right answer. You have to use General Relativity.

 

[VaibhavP]

Thanks Chalnoth...can you please briefly explain, the way to approach the conclusion...

 

[Chalnoth]

Thanks Chalnoth...can you please briefly explain, the way to approach the conclusion...

I'm not entirely sure what you're asking, so I'll answer what I think you're asking...

A sort of intuitive way of approaching the question of why gravitational potential energy is negative is to consider simple, Newtonian gravity. If you have two masses very far away from one another at rest, then they have no kinetic energy. And generally, we also consider them to have zero potential energy. If you then let the system move in time, no matter how far these masses are, they will slowly be attracted to one another, falling towards one another. As they do so, they will pick up speed. Meaning that their kinetic energy increases.

And where does this extra kinetic energy come from? One easy way to describe it is to say that it comes from gravitational potential energy. The gravitational potential energy that was once zero is now some negative number, equal in magnitude to the amount of kinetic energy gained by the two masses. So it is normal to think of gravitational potential energy as being negative.

To see why the gravitational potential energy perfectly cancels all of the mass energy once you consider a closed universe in General Relativity, well, that takes a lot of work. If you really want to look into the details, look up the Hamiltonian formulation of General Relativity.

 

[VaibhavP]

Yeah that's right about gravitational potential...my basic question was why time variable remains unchanged as expansion of universe continues...the thing I am not getting is that during big bang what would have value of this variable and what it will be at the end of expansion, if we consider the expansion to be of flat type or of closed type...logically...are you getting now what I am asking about?

 

[Chalnoth]

Yeah that's right about gravitational potential...my basic question was why time variable remains unchanged as expansion of universe continues...the thing I am not getting is that during big bang what would have value of this variable and what it will be at the end of expansion, if we consider the expansion to be of flat type or of closed type...logically...are you getting now what I am asking about?

Well, a sort of glib answer to this is that there is no answer. Basically, the specific time at any point is whatever we want it to be. All that we can measure, really, are differences in time. And even then, the difference in time depends upon the motion of the clock. So if you want to say how long something takes, you first have to define your clock.

In cosmology, we usually take a clock that is stationary with respect to the expansion (that is, a clock that sees the expansion as being the same in all directions). Such a clock, it turns out, isn't affected by the rate of expansion at all. Nor is it affected by the average matter density.

But no matter how you slice it, it looks like our universe will expand forever, so that there is no maximum limit to the difference in time starting from when our universe began.