# Does the size of the Universe change with motion?

## Main Question or Discussion Point

This is a question I was looking at based on Relativity and John Wheeler's one-electron universe theory.

The one-electron universe postulate, proposed by John Wheeler in a telephone call to Richard Feynman in the spring of 1940, hypothesises that all electrons and positrons are actually manifestations of a single entity moving backwards and forwards in time. According to Feynman:

“ I received a telephone call one day at the graduate college at Princeton from Professor Wheeler, in which he said, "Feynman, I know why all electrons have the same charge and the same mass" "Why?" "Because, they are all the same electron!"[1]
https://en.wikipedia.org/wiki/One-electron_universe

My question is this. The faster you move towards the speed of light, wouldn't everything in the universe contract to a single particle or singularity?

As you move below the speed of light, wouldn't you see that singular particle from many different perspectives? These different perspectives would be separated by more and more space the slower you move below c.

The earth rotates around the sun at 67,000 mph and the speed of light is over 670,000,000 mph which is about .0001 or .01% of the speed of light in mph.

So, is there any evidence that an observer on earth and an observer moving at say 80% of the speed of light would measure the size of the universe and get the same size?

Related Special and General Relativity News on Phys.org
Ibix
My question is this. The faster you move towards the speed of light, wouldn't everything in the universe contract to a single particle or singularity?
No. The distance between things may be unmeasurably small in the coordinate system you use, but things remain separate. There can be no physical consequence to travelling very fast, or the mere existence of high-energy cosmic rays would imply that the universe would be different from how it is.

It's also not as simple as length contraction, because this scenario requires general relativity, not special relativity. Furthermore, cosmologists typically don't assign a size to the observable universe (the whole thing is modelled as spatially infinite), since it's a coordinate dependent quantity and therefore a matter of choice.
So, is there any evidence that an observer on earth and an observer moving at say 80% of the speed of light would measure the size of the universe and get the same size?
As noted, cosmologists don't typically assign a size to the observable universe. If they do they have to pick a coordinate system, and different coordinate systems do yield different sizes. Of course, most people observe that coordinate systems are arbitrary, so the only sensible one to use is the one that maximises symmetry - the one in which the CMB is isotropic (we certainly use that system, instead of a system which regards the Earth/Sun/Milky Way as stationary). In which case their measurements will all agree, regardless of the state of motion, because they choose to interpret them that way.

Nugatory
Mentor
The earth rotates around the sun at 67,000 mph and the speed of light is over 670,000,000 mph which is about .0001 or .01% of the speed of light in mph.
These statements but both true.... but have you considered how fast the sun is moving? And the galaxy of which the sun is a member?

No. The distance between things may be unmeasurably small in the coordinate system you use, but things remain separate. There can be no physical consequence to travelling very fast, or the mere existence of high-energy cosmic rays would imply that the universe would be different from how it is.

It's also not as simple as length contraction, because this scenario requires general relativity, not special relativity. Furthermore, cosmologists typically don't assign a size to the observable universe (the whole thing is modelled as spatially infinite), since it's a coordinate dependent quantity and therefore a matter of choice.
As noted, cosmologists don't typically assign a size to the observable universe. If they do they have to pick a coordinate system, and different coordinate systems do yield different sizes. Of course, most people observe that coordinate systems are arbitrary, so the only sensible one to use is the one that maximises symmetry - the one in which the CMB is isotropic (we certainly use that system, instead of a system which regards the Earth/Sun/Milky Way as stationary). In which case their measurements will all agree, regardless of the state of motion, because they choose to interpret them that way.
Thanks for the response.

I do think the observable universe has a size. Here's Astronomers, Physicist and others talking about it.

How Big is the Universe?

But though the sphere appears almost 28 billion light-years in diameter, it is far larger. Scientists know that the universe is expanding. Thus, while scientists might see a spot that lay 13.8 billion light-years from Earth at the time of the Big Bang, the universe has continued to expand over its lifetime. If inflation occurred at a constant rate through the life of the universe, that same spot is 46 billion light-years away today, making the diameter of the observable universe a sphere around 92 billion light-years.
https://www.space.com/24073-how-big-is-the-universe.html

It took centuries, but we now know the size of the Universe

Caitlin Casey, an astronomer at the University of Texas at Austin, studies the Universe as we know it. As she points out, astronomers have developed an ingenious array of tools and measuring systems to calculate not just the distance from Earth to other bodies in our Solar System, but the spans between galaxies and the journey to the edge of the observable Universe itself.

The steps to measuring all these things are known as the "cosmic distance ladder". The first rung of the ladder is easy enough for us to get onto and these days it relies on modern technology.
http://www.bbc.com/earth/story/20160610-it-took-centuries-but-we-now-know-the-size-of-the-universe

There's like a million articles and papers that reach the same conclusion.

Here's a paper from 2016.

Size of the Observable Universe

We have updated the 2005 estimates of Gott et al. for the size of the observable universe in accordance with the revised cosmological parameters published by the Planck team in 2013. The value we obtained of 14,200 Mpc for the radius of the observable universe is 0.7% less than the prior estimate of 14,300 Mpc. Similarly, the value we obtained for the radius of the horizon determined by photons emitted during the recombination era is 13,900 Mpc, also 0.7% less than the prior estimate of 14,000 Mpc. Therefore, the observable universe is slightly smaller than previously calculated.

I'm not trying to debate the size of the universe though. I wanted to know is there any evidence that shows an observer on earth and and observer moving close to the speed of light will have these same measurements.

Most of these articles and papers that talk about the diameter of the observable universe all say 92-93 billion light years. Will an observer traveling at 80% of the speed of light say the observable universe is 93 billion light years in diameter?

Here's a video from Fermilab presented by Dr. Lincoln about length contraction. He compares a stick seen by a stationary observer vs. a moving observer and he says the observer that's moving will see a shorter stick than the one that's stationary. He gives a very good technical review of length contraction.

Here's an example using the twin paradox.

In 1911, Paul Langevin gave a "striking example" by describing the story of a traveler making a trip at a Lorentz factor of γ = 100 (99.995% the speed of light). The traveler remains in a projectile for one year of his time, and then reverses direction. Upon return, the traveler will find that he has aged two years, while 200 years have passed on Earth.

Let's say the ship didn't come back for 100 million years. When he leaves, both observers agree the age of the universe is 13.8 billion years old. When the ship returns 100 million years later, observers on earth would say the universe is 13.9 billion years old. The observer on the ship would say the universe is 13.801 billion years old. This will mean the diameter of the universe is smaller when they're traveling near c and larger when they're on earth.

phinds
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2019 Award
Let's say the ship didn't come back for 100 million years. When he leaves, both observers agree the age of the universe is 13.8 billion years old. When the ship returns 100 million years later, observers on earth would say the universe is 13.9 billion years old. The observer on the ship would say the universe is 13.801 billion years old.
No, when the traveler returns to Earth, he is in the same reference frame as the other observer so they both see the same thing. The universe will be 13.9 billion years old. The fact that the traveler has taken to different path through space-time to get back to Earth only has an impact on HIS age relative to a stay-at-home, not to the age of the universe.

Nugatory
Mentor
i'm not trying to debate the size of the universe though. I wanted to know is there any evidence that shows an observer on earth and and observer moving close to the speed of light will have these same measurements.
You are missing an important point: an observer on earth is just as much moving as any other observer. It is meaningless to speak of an observer "moving at close to the speed of light" without saying what that speed is relative to - everything is at rest relative to something, moving at near the speed of light relative to something else, and at any speed in between relative to something somewhere.

What is called "the age of the universe" is the proper time along the worldline of an observer for which the cosmic microwave background is the same in all directions. That's something we calculate, and as with any calculation the answer has to be the same for everyone - whether the CMB is isotropic or not for me is irrelevant when I'm calculating something about an observer for whom it is.
Let's say the ship didn't come back for 100 million years. When he leaves, both observers agree the age of the universe is 13.8 billion years old. When the ship returns 100 million years later, observers on earth would say the universe is 13.9 billion years old. The observer on the ship would say the universe is 13.801 billion years old. This will mean the diameter of the universe is smaller when they're traveling near c and larger when they're on earth.
The twin paradox does say that a clock on the ship will tick off more time between the start and the end of the ship's journey than a clock on the earth. However, this fact has no bearing at all on their calculation of the age of the universe; the age of the universe at the end of the journey is not in general equal to the age of the universe at the start of the journey plus the time elapsed on the journey.

There are many subtleties in the relationship between relative motion and the passage of time, and you will have to understand these before you take on questions of cosmology. A good start, college-level but accessible to a determined high school student, would be Taylor and Wheeler's "Spacetime Physics".

Last edited:
Ibix
I do think the observable universe has a size. Here's Astronomers, Physicist and others talking about it.
You'll notice I said "typically". You'll also notice that I said "[i]f they do they have to pick a coordinate system, and different coordinate systems do yield different sizes." The Halpern and Tomasello paper you cite explicitly specifies which coordinate system they are using - they refer to the co-moving radius, so are using the exact coordinate system I specified, the one where the CMB is isotropic.

The point I was trying to make is that if you pick a different coordinate system then you will get different answers (some coordinate systems, probably most, won't give you a uniquely defined radius, though). The choice of coordinate system is always free, whatever your state of motion. You always have to take your measurements and interpret them in light of your coordinate system if you want to come up with a radius of the universe. We already correct our observations for the movement of the Earth relative to a co-moving observer in order to get the radius you are citing. So yes, you probably will get a different radius of the universe if you choose to define "radius" differently from everyone else.

However, none of this means that all electrons are the same electron. Not dissing Wheeler, just saying it doesn't follow from your argument. As I noted, distinct objects are always distinct, even if you adopt a silly coordinate system in which you need billions of digits of precision to see that two galaxies aren't in the same location.

phinds
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2019 Award
The twin paradox does say that a clock on the ship will tick off more time between the start and the end of the ship's journey than a clock on the earth.
I know that you know what you are talking about but this is, at best, confusingly stated.

Nugatory
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I know that you know what you are talking about but this is, at best, confusingly stated.
How would you state it? Or maybe I should ask what part you find confusing?

phinds
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2019 Award
How would you state it? Or maybe I should ask what part you find confusing?
Since the traveler is younger than the stay-at-home when he returns, his clock ticks less time than the stay-at-home. You seem to have stated it the opposite

Nugatory
Mentor
Since the traveler is younger than the stay-at-home when he returns, his clock ticks less time than the stay-at-home. You seem to have stated it the opposite
Oh - Oooops - I changed the operative clause while I was rewriting that sentence and forgot to switch the adjectives. Fixing it now. You want a job as "Nugatory's proofreader"? Same pay as the mentors receive.

No, when the traveler returns to Earth, he is in the same reference frame as the other observer so they both see the same thing. The universe will be 13.9 billion years old. The fact that the traveler has taken to different path through space-time to get back to Earth only has an impact on HIS age relative to a stay-at-home, not to the age of the universe.
Sure it does.

Say that observer never returns to earth and stays in that reference frame. A million years would have passed for him on the ship while 100 million years passed for observers on earth. Observers on earth will say the universe is 13.9 billion years old while the moving observer will say the universe is 13.801 billion years old.

This is because the universe will contract for the moving observer just like Dr. Lincoln showed in the Fermilab video. Distance between objects will shrink for the moving observer.

Here's an example. Our solar system is 122 AU long or 11,346,000,000 miles long.

Say we had a ship that traveled at 50,000 mph. It would take 226,920 hours or around 26 years to travel to the end of our solar system.

Traveling at 60% of the speed of light would be 28 hours or a little over a day traveling at 402,000,000 mph.

So from the frame of reference at 60% the speed of light, the planets will contract and the distance between planets will be reduced.

phinds
Gold Member
2019 Award
Sure it does.
you need to reread post #6. If you don't understand it say so, but making the same incorrect argument over and over does not make it correct.

Nugatory
Mentor
This is because the universe will contract for the moving observer just like Dr. Lincoln showed in the Fermilab video. Distance between objects will shrink for the moving observer.
That video is accurate, but you are drawing a wrong conclusion from it - the universe does not contract the way the stick of length $L$ in the video does.

At the beginning of the video Lincoln reminds us that he is talking about special relativity not general relativity, and his discussion of length contraction is based on the Lorentz transformations of special relativity. However, special relativity only works within local regions of spacetime with no tidal gravitational effects (and that's why it's called "special" relativity - it applies only to these special cases). The universe as a whole is clearly not one of these special cases, so we have to use general relativity here instead.