# Height Issues of the Time Traveler [duplicate]

A person from the year 2250 goes back in time. They go back 60 Million years, because they want to observe dinosaurs. Imagine their surprise when they see T-Rex's running around like little chickens!!

That's because they neglected the Hubble Expansion that had occurred in the last 60 Million years. So they are much larger than anything that existed so far in the past.

Is this correct?

## marked as duplicate by John Rennie, David Z♦Jan 19 '16 at 14:34

• So it sounds like the time traveler would be larger, just not very much larger. Like only infinitesimally larger. – Jiminion Jan 18 '16 at 19:19
• exactly. However, this would be a non-trivial calculation to determine the exact expansion, and my guess is that it would be less than an atom's diameter. – Sam Blitz Jan 18 '16 at 19:26
• – rob Jan 18 '16 at 23:51
• I find some of the answers unclear. It is unclear whether matter (or galaxies, for that matter) do not expand, or they expand so little as to be impossible to discern. Subtle, but very different answers. – Jiminion Jan 19 '16 at 15:19
• I don't find the answers in the referenced question responsive. – Jiminion Jan 19 '16 at 22:02

No, because Hubble expansion has negligible effects on very small systems (such as human beings).

Here is an answer which explains the maths behind it : Can the Hubble constant be measured locally??

Shortly, no, this is not correct.

Here's why. Hubble's law gives us that for a distance of one megaparsec, that space expands by approximately 70 km/s (the data varies, but it's somewhere between 60-80 km/s - it doesn't matter, and you'll see why). Now, how tall is your average human? Let's be generous and say your time traveler is 2m tall. Now, how many MPc is that? Oh, about $6.4 \times 10^{-23} \text{ MPc}$. So, even naively neglecting the fact that the expansion of the universe does not affect gravitationally, electromagnetically, chemically, or otherwise bound bodies (see mlg's answer above, i.e. the earth does not expand with the universe), if we assumed it did, then we would find that your 2m tall person has grown about a centimeter. Not dwarfing anything!

• But this seems even more serious. How can we have atoms of two different conflicting sizes in the same space? The quantum laws dictate the size of atoms, they must all be the same size at a given time, no? – The_Sympathizer Mar 11 '17 at 5:08
• @mike4ty4 So you're right, there should be some conflict, but as far as I can tell, Hubble's law would apply on all scales. That said, GR affects at the quantum scale is not understood - that's the domain of quantum gravity. – Sam Blitz Mar 12 '17 at 5:58

I think I should go from another direction.

Yes, obviously the Hubble constant refers to intergalactic motion, and cannot be properly applied to intragalactic effects. That does not necessarily mean that such effects do not exist (it just means that they are too minor to measure, and/or usually overshadowed by other effects; that said, I believe that GPS is precise enough that Hubble drift would've affected it if it worked on these scales, but I hadn't done the calculation, and for all I know perhaps it does and it's just brushed off as another easy correction).

But that aside, consider what the Hubble constant means: it is (roughly, due to complicated inflationary models, but it works as a first approximation) the inverse of the time since Big Bang. Everyone knows how much it had been since Big Bang: 13 billion years (give or take a bit).

That means that the fraction of the Hubble expansion that had occurred over the last X million years is about X/13000. (Well, more like 13600 really, but whatever.)
For x=70 (an appropriate value for seeing T-Rex - 60 would put the traveller in the early Paleogene*), this would be 70/13000, or about 1/200. Yes, Sam Blitz's estimation is correct: about half a percent, or, for typical human height, about a centimeter.
If they wanted to visit the Triassic period instead, the time gap would roughly triple, so they would instead be about three centimeters taller. Still not significant (and probably not noticeable).

*) Which might be the reason he's seeing chickens instead of dinosaurs: because all the big dinosaurs have gone extinct, and the few that still remain (mainly ancestors of modern birds) are tiny and look like chickens! Since they also happen to be fairly close relatives of T-Rex (and even closer, IIRC, of Velociraptor), the result is a lot similar to a chicken-sized T-Rex (except with feathers, obviously - though perhaps the actual T-Rex also had them).

• GPS has been in operation less than 40 years, and has an accuracy of a few centimeters if you use really fancy techniques and equipment that didn't exist for most of those 40 years; more like 1m at best without them. Given the Hubble figure of 70km/s/MPc, that's a change in the Earth's diameter of 3.6 cm in 40 years. A close thing, but I'm going to call a "not quite" on your GPS verification theory. – hobbs Jan 19 '16 at 14:07
• A maybe more practical concern — plate tectonics adds a confounding motion of multiple cm/year to any given point on the Earth's surface, making it tricky to measure an effect on the order of 1 mm/year. – hobbs Jan 19 '16 at 14:14
• GPS works by triangulating distance of multiple satellites, I don't know how the Earth's diameter plays a role. Maybe you are referring to the tables involved. I suppose expanding space changes the freq. slightly of the radio waves used? (Again, not sure what expanding space really means.) – Jiminion Jan 19 '16 at 19:37