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This may be a trivial question, but I cannot find a good answer to it.

What would happen if the size of everything in the Universe is multiplied by some constant factor at the same time, let's say everything doubles its size for instance. People double their size, houses double their size, streets, towns, Earth... up to the whole known Universe.

The relative proportions and distance between objects would remain... If we measure our own size with a meter, the reading would be the usual one.

From current theories, it this something that can or cannot happen? that can or cannot be detected?

Would that change our perception of constants like c, gravity, or temperature?

Why? (in very simple terms...) Is there any reference, any previous study of this problem?

(This part has been added/edited to improve the question)

From this question, I went to this book by Benjamin Crowell, following Ben Crowell advice. This section describe in better words my idea. Citation:

8.2.6 Observability of expansion

[...] To organize our thoughts, let's consider the following hypotheses:

  • The distance between one galaxy and another increases at the rate given by a(t) (assuming the galaxies are sufficiently distant from one another that they are not gravitationally bound within the same galactic cluster, supercluster, etc.).
  • The wavelength of a photon increases according to a(t) as it travels cosmological distances.
  • The size of the solar system increases at this rate as well (i.e., gravitationally bound systems get bigger, including the earth and the Milky Way).
  • The size of Brooklyn increases at this rate (i.e., electromagnetically bound systems get bigger).
  • The size of a helium nucleus increases at this rate (i.e., systems bound by the strong nuclear force get bigger).

We can imagine that:

  • All the above hypotheses are true.
  • [...]

The author then propose to look at the first claim, all hypotheses are true...

If all five hypotheses were true, the expansion would be undetectable, because all available meter-sticks would be expanding together. Likewise if no sizes were increasing, there would be nothing to detect. These two possibilities are really the same cosmology, described in two different coordinate systems. But the Ricci and Einstein tensors were carefully constructed so as to be intrinsic. The fact that the expansion affects the Einstein tensor shows that it cannot interpreted as a mere coordinate expansion. Specifically, suppose someone tells you that the FRW metric can be made into a flat metric by a change of coordinates. (I have come across this claim on internet forums.) The linear structure of the tensor transformation equations guarantees that a nonzero tensor can never be made into a zero tensor by a change of coordinates. Since the Einstein tensor is nonzero for an FRW metric, and zero for a flat metric, the claim is false.

The author says this claim is impossible, the demonstration is not understandable for me as I'm not an expert in the domain, and don't know what are FRW or Ricci and Einstein tensors.


marked as duplicate by Qmechanic Jun 2 '15 at 4:53

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/47259/2451 , physics.stackexchange.com/q/2110/2451 , and links therein. $\endgroup$ – Qmechanic Jan 27 '14 at 20:50
  • $\begingroup$ Right, somehow similar, however I'm curious about the hypothesis of a full homothetic transformation of objects and the distance between them. Not sure homothetic is the correct adjective, English is not my mother tongue. $\endgroup$ – mins Jan 27 '14 at 21:00
  • $\begingroup$ Right out of The Great Eggplant (Halliday&Resnick); answer is naturally that one cannot double linear, areal, and volumetric sizes simultaneousl. $\endgroup$ – Carl Witthoft Jan 27 '14 at 21:06
  • $\begingroup$ "One cannot double linear, areal, and volumetric sizes simultaneous" My idea is about only linear size varying. For example Moon, Sun and Earth double their (linear size) and their distances is also doubled. Are Earth and Moon still orbiting the same way, or is there some perceptible change? $\endgroup$ – mins Jan 27 '14 at 21:18
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    $\begingroup$ Are fundamental constants keeping their current values? If they do, then atoms must retain the same size, and I guess your scheme involves adding more mass, and sothe number of atoms in things will scale up, adn this will be detectible. If they don't, then it's hard to see how this isn't equivalent to just redefining the meter. $\endgroup$ – Jerry Schirmer Jan 28 '14 at 0:13

Though I've not encountered any specific research into this, I ask how would you design such an experiment: Every form of measurement is calibrated against every other - our definition of spatial length, time, mass, inertia and energy in its various forms are all related to physical phenomena reproducible on this planet. If non arbitrary spatial distance were changed continuously, it would create no difficulty or even perceivable difference in the other measurements as they are all interdependent. A Plank length in any frame of reference would remain a Plank length.

That having been said, measurable change in spatial dimensions as derived from calculations of the Delta Doppler shift of far distant galaxies, I have not encountered any papers relating to such phenomena locally. And by locally I mean in our local cluster of galaxies. See here. It does not appear to be a phenomenon which will give you a noticeably bigger house or garden, as it is considered that local gravitational phenomena prevent expansion on this scale.

As to C, the gravitational constant and temperature should continue working just fine within whatever frame of reference you find yourself, see paragraph 1.

As to the "What if" question, that's for some alternate universe, perhaps you could yourself research what phenomena applied and write a Sci-Fi story based on it. (That's not meant to be as rude and insulting as it sounds -I only wish to assert that what ifs such as this, are not easy to answer in a Physics forum.)

  • $\begingroup$ Thanks, this is helpful. I need to study the linked article, it seems to be a good one to set a context to my question. $\endgroup$ – mins Jan 28 '14 at 7:15
  • $\begingroup$ I'm thinking about an analogy: one cannot determine from "internal" observation if we are moving at constant speed or we are just not moving. This can be determined only from "outside". Similarly if anything grows at the same rate... can we observe this growth? This is the idea behind my question. $\endgroup$ – mins Jan 28 '14 at 7:31

It seems that you in some sense are referring to inflation, that is commonly described as "expansion of the Universe" and sometimes incorrectly understood as "expansion of everything in the Universe".

Indeed, when everything doubles its size, including wavelength of radiation and all other possible lengths and masses and time, we are not able to detect anything. This is just equivalent to redefinition of a meter.

However, if only space lengths are changed, like size of a chair, then we can detect this by measuring how long does it take for light to pass the distance of 1 chair. If time is not rescaled, then this gives different answer. (Here one may comment on size of a pendulum clock, but lets think about number of oscillations of radiation emitted by Caesium atom.)

So, you see to make this undetectable you should balance all possible ways to measure distances. This balance effectively gives rescaling of a meter.

Obviously, this is NOT what happens in the cosmological inflation, where only space expands. I am personally not aware of any theories exploring expansion of objects, may be because this is not very interesting.

  • $\begingroup$ Thanks. I'm very interested in understanding if there is some general argument against the possibility that everything doubles its size and all laws of physics continue to appear valid (e.g. light now travels twice the distance in a the same time making impossible to detect the increase in size of the object). $\endgroup$ – mins Jan 27 '14 at 21:39
  • $\begingroup$ @Edvard: I don't think inflation applies to what he's talking about. Inflation doesn't happen at all scales. Due to the nonlinearity of gravity, inflation only happens on the scales of galaxies, while (say) a human or a chair are not expanding. $\endgroup$ – Siva Jan 27 '14 at 23:19
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    $\begingroup$ Careful about the use of the term "inflation". Astronomers/cosmologists mean something very specific when they use that term, and it's NOT the expansion of space that is currently ongoing (i.e. observation that galaxies are receding, etc.) Rather inflation refers to the postulated early exponential growth of the Universe, well before things like galaxies existed. There is some common ground (space is expanding) but VERY different context & specifics. $\endgroup$ – Kyle Oman Jan 28 '14 at 1:06
  • $\begingroup$ I mentioned inflation because there is often exactly this kind of misunderstanding of it's mechanism. At the very last sentence I explicitly write this. $\endgroup$ – Edvard Jan 28 '14 at 5:30

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