# Inflation and Mach

1. Jun 17, 2011

### Bob3141592

As I understand it, somewhere close to the beginning of the universe, the universe experienced an inflationary phase when the space 'underneath' object began to expand faster than c, the speed of light. Since it wasn't the objects themselves that were expanding, there was no violation of the principle that nothing can move faster than the speed of light, even though the separations between objects increased faster than c. Inflation only lasted for a brief moment, but in that time span the size of the universe increased by many orders of magnitude.

Therefore, when inflation ended, every object must have been isolated in it's own private realm. Since every other object in the universe was further away from it than light could travel, there was no exchange of forces or information or anything between objects. Each object was completely isolated, and would remain so for some time, until light from "nearby" objects could reach it. That's the same as saying until the light cone of the two objects intersected, right?

This strikes me to be a direct violation of Mach's principle, in which the inertia (and other intrinsic spatial properties like spin) of any particle is only in relation to the distribution of the rest of the mass in the universe. An alternate form of Mach's principle on Wikipedia says that "Mach2: An isolated body in otherwise empty space has no inertia." Then would a photon in a universe just come out of the inflation phase have momenta? Would an electron have spin? How could it? But if it doesn't how could it be an electron? (I presume there must have been electrons, even in the very high energy state early in the universe, since a blackbody always has a tail of low energy components, so everything couldn't have been higher energy particles, just most everything).

I'm confused about how this might work. Any help or thoughts would be appreciated.

2. Jun 17, 2011

### phinds

You've got one part of this wrong. Inflation did NOT separate EVERYTHING so much that after inflation stopped they were outside each others light cone. Think about it this way: you travel for an hour at mach 4 and then spend the next million years traveling at 1 mph. Sound from your starting point would have no trouble reaching you after a modest amount of time. Everything in our "observable universe" was acted on by inflation but we still see it. There IS stuff (and you can get into theological arguments about how much) that is beyond our observable universe that DOES have the characteristic you describe of being outside our realm.

3. Jun 17, 2011

### bcrowell

Staff Emeritus
We don't know whether inflation happened or not. As a theory, it has some successes and some major defects.

Mach's principle is false http://www.lightandmatter.com/html_books/genrel/ch08/ch08.html#Section8.3 [Broken] , so I wouldn't worry too much.

-Ben

Last edited by a moderator: May 5, 2017
4. Jun 17, 2011

### Bob3141592

Sure, we see it now. But we didn't always see it, just almost always. My question is about that short period, after inflation ends to just before any signal from any other part gets 'here.' For some short but real interval, every particle had to exist in complete isolation. Whatever details preceded or followed that period hardly matters. This utterly isolated state of the particles of the universe seems inevitable to me, yet it also seems contradictory.

Perhaps I don't understand how inflation works. Is it true that this 'utterly isolated' state must have existed? Given the size or age of the universe at the start of inflation, and the inflation rate and duration, you could calculate the duration of the isolation period. At least you could calculate the duration from some external frame - I can't imagine how you could measure time in a universe of only one particle.

So that's my question. Is it true that this 'utterly isolated' state must have existed? If so, then my second question is how long did it last? It has to be a nonzero positive value, and if it's longer than the Planck time, that would be interesting. I'd expect it would be much larger.

5. Jun 17, 2011

### bcrowell

Staff Emeritus
No, I don't think so (even assuming inflation did happen).

I think you're messing yourself up by assuming that the expansion of the universe can be measured in units of velocity. It can't. For example, Hubble observed that distant galaxies were receding from us at speeds proportional to their distance from us. Since the distances are all different, the speeds are all different.

6. Jun 18, 2011

### Jonathan Scott

That reference shows that a specific theory of gravitation (Brans-Dicke) which effectively incorporates Mach's Principle combined with GR is not compatible with experiment unless the strength of the Mach's Principle effect is set to something close to zero, leaving only the GR part.

The section title "Mach's Principle is false" quoted above is an extreme overstatement of that. Even in GR, local frame-dragging effects (linear and rotational) are entirely consistent with what might be expected from Mach's Principle. It can be shown that in trivial cases GR on its own is incompatible with Mach's Principle on the scale of the whole universe, but as we don't yet have a detailed understanding of the universe on that scale it seems premature to rule out some level of compatibility even at that level (even if it involves something new like "dark stress" or "dark angular momentum"!).

Last edited by a moderator: May 5, 2017
7. Jun 18, 2011

### phinds

My aplogies, I completely misread your point and I now see it as a REALLY interesting question. I am hesitant to say that Ben might be wrong about something but I don't find his belief that it didn't happen compelling and don't yet see how it can be that you are wrong. I CAN imagine that the time of isolation would be truely tiny since from what I have read, if expansion did happen then although it expanded the size of the U enormously in percentage of its pre-inflation size, it was starting from very close to zero, so even after expansion, the size was still very very small (estimates seem to vary quite a bit but I remember one of them being 1 meter)

8. Jun 18, 2011

### narrator

Interesting topic/question