# Red shift or blue shift?

#### nurica

In a hypothetical universe where mass of matter constantly increases, will we observe that distances also constantly increase?

This is not a new theory, I'm just asking what classic GM says about that.

If we are in a galaxy with constantly increasing mass, measuring distances to other galaxies, we must see that those distances are constantly increasing. Because when mass grows it slows down clocks (according to GM) so light takes longer to arrive and it indicates distance increase. So we must see more red shift.

On the other hand, gravitation blue shifts incoming light. Gravitation increase leads to even more blue shift.

Will we see red shift or blue shift in such situation?

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#### PeterDonis

Mentor
In a hypothetical universe where mass of matter constantly increases
What does this mean, exactly? If I take it literally, it's inconsistent with the laws of GR, so there's no way to formulate an answer to your question within GR.

#### AkInfinity

No of course your hypothetical question is extremely wrong in real physics; however because the mass continuasly increases (which would never happen) the velocity of each particle decreaes (conservation of energy and momentm) so after much time has passed (and all masses have incredibly increased) all will essencially stand still. Of course this is only mechanical as effects of magnetism and radiation are a different story

#### nurica

What does this mean, exactly? If I take it literally, it's inconsistent with the laws of GR, so there's no way to formulate an answer to your question within GR.
[Mentor's note: Link to unpublished article deleted.]

My question is not wrong in real physics.

It doesn't matter if mass is increasing or decreasing or constant. Other theories deal with it.
But if we research the case when mass is increasing, I'm asking what GR says about it.

My assumption is that an observation made inside such universe will find that distances are increasing.

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#### PeterDonis

Mentor
My question is not wrong in real physics.
You are assuming that the paper you linked to is "real physics". On a quick skim, I see a number of statements that look questionable to me, one of which is the idea that "the total mass of the universe" is something meaningful to begin with. The mass density of the universe is meaningful, but that doesn't necessarily mean it has a meaningful total mass. (For one thing, many viable cosmological models give the universe an infinite volume.)

My assumption is that an observation made inside such universe will find that distances are increasing.
If you mean the universe is expanding, that prediction doesn't depend on what the "total mass of the universe" is doing; in fact it doesn't even require that concept to have a well-defined meaning. Many standard cosmological models using GR do not even assign a well-defined "total mass" to the universe, since, as I said above, they assign it an infinite volume.

#### nurica

Many standard cosmological models using GR do not even assign a well-defined "total mass" to the universe, since, as I said above, they assign it an infinite volume.
Total mass is not important.
Assuming that each galaxy gained 1% in mass. Clocks slowed, light travels longer, so we see that galaxies recede from us.

#### PeterDonis

Mentor
Total mass is not important.
Well, that's the only thing the paper you linked to talks about. It doesn't talk about individual objects "gaining mass"; it only talks about the total mass of the universe.

Assuming that each galaxy gained 1% in mass.
This would violate the Einstein Field Equation; at least, I can't see a way to interpret this that doesn't. So again, I don't think your question can be answered in the context of GR.

#### nurica

How it would violate the Einstein Field Equation?

#### WannabeNewton

Peter, I agree with you as I'm not even sure how you would define a physically interpretable notion of total mass (e.g. Komar mass) for a non-stationary space-time such as the FLRW universe. As for nurica, it seems you are proposing a situation where galaxies suddenly gain mass out of nowhere. If so, this would violate local energy conservation.

#### PeterDonis

Mentor
How it would violate the Einstein Field Equation?
Where does the increased mass of a galaxy come from? The Einstein Field Equation says you can't just create mass out of nothing; it has to come from somewhere. You appear to be proposing that the increased mass of each individual galaxy comes from nowhere; it doesn't come from the galaxy attracting other objects, for example. The mass just magically increases. That violates the EFE.

#### PeterDonis

Mentor
I'm not even sure how you would define a physically interpretable notion of total mass (e.g. Komar mass) for a non-stationary space-time such as the FLRW universe.
I don't think there is any way to do that; AFAIK that is the standard view. One of the questionable things in the paper nurica linked to is that the author appears to believe there is some way of doing this.

#### nurica

that the increased mass of each individual galaxy comes from nowhere
I didn't say from nowhere. We might not know yet where it comes from, if it comes at all. It's the same situation as in the question where the universe came from, or dark energy. Can you claim that the universe doesn't exist just because you don't know where it came from?

The question is what will happen if additional mass came from somewhere and increased the masses of all galaxies by 1%.

#### PAllen

I didn't say from nowhere. We might not know yet where it comes from, if it comes at all. It's the same situation as in the question where the universe came from, or dark energy. Can you claim that the universe doesn't exist just because you don't know where it came from?

The question is what will happen if additional mass came from somewhere and increased the masses of all galaxies by 1%.
But the question cannot be answered in GR. The field equations are in terms of a tensor whose covariant divergence vanishes, by construction (i.e. inherent in mathematical definition, before even physics enters). This vanishing divergence rules out something like a galaxy gaining mass from nowhere. Your question cannot even be phrased in GR. So what mainstream theory are you proposing as the framework for answering your question?

#### nurica

But the question cannot be answered in GR
Why not? Just model the situation. Place several objects on a dinner table, measure distances, then replace objects with identical geometrically but heavier objects and measure distances again. Distances must change, according to GR.
Of course there is no reason to perform the actual experiment, just calculations.

I just want to confirm that distances will increase. Is that correct?

#### PeterDonis

Mentor
Place several objects on a dinner table, measure distances, then replace objects with identical geometrically but heavier objects
What does "identical geometrically" mean? Does it mean identical radius? How can you determine that when the measurement of the radius is affected by gravity? How do we define "identical radius" when we change the strength of the gravity field?

and measure distances again.
And how do we relate distances in the first scenario to distances in the second? What counts as distances "remaining the same"?

#### nurica

What does "identical geometrically" mean? Does it mean identical radius? How can you determine that when the measurement of the radius is affected by gravity? How do we define "identical radius" when we change the strength of the gravity field?
And how do we relate distances in the first scenario to distances in the second? What counts as distances "remaining the same"?
Lets simplify the experiment even more. Lets measure distances not "from surface to surface" but "from center to center". In this case relativistic change of radius will not affect distances, only the mass of the object will be important.

I'm not sure about "how do we relate distances". I assume we compare them. Distances will change. Will distances between more massive objects increase or decrease?