# B Have H and/or c ever changed?

1. Nov 15, 2016

### Chris Miller

If H, estimated to be ~71/km/s/Mpc, were unchanged since the Biog Bang, then it seems the universe would be smaller than a ping-pong ball, if not a lepton. Could H have slowed/be slowing? If so, could this change affect the constant, c?

2. Nov 15, 2016

### phyzguy

According to our current model of cosmology, the Hubble constant H definitely changes as the universe evolves. Since $H = \frac{\dot a}{a}$, only exponential expansion has a constant H, and the presence of matter has caused the universe to expand slower than exponentially. It may approach exponential expansion in the future as the universe becomes dominated by the cosmological constant Λ. The speed of light, c, does not change.

3. Nov 15, 2016

### Chris Miller

Thanks very much, physguy. I suppose c doesn't mean a lot in a walnut-sized u?

4. Nov 15, 2016

### Bandersnatch

Why do you think c depends on the size of the observable universe, or on whether or not H is constant in time?

5. Nov 15, 2016

### Staff: Mentor

You can make c change as much as you like simply by picking units that make it change the way you want. In the current SI units c cannot change.

6. Nov 15, 2016

### Chris Miller

I hypothesize (not so much think) c relates to the size of u and on H (whether or not it's consistent), and have twice posted my "reasoning" on that, and twice had my post deleted for violating the "No personal theories" rule.

7. Nov 15, 2016

### Chris Miller

Not sure I understand. You mean miles vs. kilometers? That would seem to go without saying. Perhaps an example of an alternative unit?

8. Nov 15, 2016

### Staff: Mentor

No, I mean how you define a mile or a kilometer or whatever unit you choose to use. For instance in SI units the speed of light is fixed. But suppose I used units where the unit length (in SI units) was a function of time e.g. 1 m * .005 t. Where t is the number of years from Jan 1, 2000. The speed of light would change in such units, but not in SI units.

9. Nov 15, 2016

### Chris Miller

Thanks, okay, I think I see. The units of measurement change so your definition of c changes, but not the actual velocity itself.

10. Nov 15, 2016

### Staff: Mentor

What is "the actual velocity itself"? The underlying point is that only dimensionless ratios are typically meaningful. The velocity only is meaningful when compared dimensionlessly to other velocities.

11. Nov 15, 2016

### Chris Miller

c is a velocity? what other velocity is needed to give c meaning? I think I'm either in over my head or getting lost in semantics.

12. Nov 15, 2016

### Staff: Mentor

If there is no other velocity then what would it mean for c to change. Compared to what would it be changing?

13. Nov 16, 2016

### Chris Miller

To meaningfully express v requires only the measure of distance and time, not the existence another v (i.e., d/t)?

Surely, by "dimensionless" you don't mean 0D, a point on which motion is not possible.

I'm still confused by your vernacular here.

14. Nov 16, 2016

### phyzguy

What Dale is explaining is the difference between a number like c, which has units or dimensions, and a unitless or dimensionless number like pi or the fine structure constant. The number c will depend on the units you use to measure it. It is a different number in meters/second than it is in miles/hour. By contrast, a number like the α, the fine structure constant, has a value of about 1/137, and this number has no units, so we say it is "dimensionless". I will get the same number regardless of the system of units I use to measure it. Another example is the mass of the electron, which has units and depends on what units you use. However, the ratio of the mass of the proton to the mass of the electron is about 1836, and is independent of the units you use.

15. Nov 16, 2016

### Chris Miller

Thanks for explaining "dimensionless," phyzguy. I'd go with "unitless" or something, but I understand.

16. Nov 16, 2016

### Staff: Mentor

In such a system of units (not SI) then you would need reference standards for time and distance. You would then make dimensionless comparisons to those reference standards.

Note that the SI is not such a system of units. In SI distances are measured from a time standard and a velocity standard. Since the velocity of light is the standard it cannot possibly change in SI units.

This is standard terminology. I submit to you that the issues raised by a question like changing c are subtle and have been well discussed in the professional literature by many scientists over many years. Frankly, you are not qualified to be making your own hypotheses on the topic, you clearly have not even recognized that the relevant issues exist.

Here are a few good starting references on the topic.
http://math.ucr.edu/home/baez/constants.html
https://en.m.wikipedia.org/wiki/Fine-structure_constant
https://en.m.wikipedia.org/wiki/International_System_of_Units
https://en.m.wikipedia.org/wiki/Lorentz–Heaviside_units
https://en.m.wikipedia.org/wiki/Planck_units
https://en.m.wikipedia.org/wiki/Geometrized_unit_system

17. Nov 16, 2016

### Chris Miller

Thanks, Dale. I suffer no such illusions (although even a blind squirrel sometimes finds a nut) of ever making any meaningful contribution to science. Although I'd submit that the guy who discovered SR did so moonlighting in the Swiss patent office, after doing poorly academically, failing to land a teaching position in academia, and that after his discovery was recognized and he was welcomed into academia with open arms, accomplished little.

18. Nov 16, 2016

### Mister T

That won't work because dimension and unit already have separate meanings. For example something like the meter is both a unit and a dimension, but something like the radian is a unit but not a dimension. So a radian is a dimensionless unit.

19. Nov 16, 2016

### Mister T

There's a difference between making a contribution and achieving an understanding. There are many cases where people have done one but not the other, both, or neither; in any given area of science.

That's not my understanding. Einstein had an accomplished academic record, even though it was not flawless. When he found instructors who were poor he made no bones about telling them that, and he paid for that professionally. And even after his greatest discoveries his theories were not by any means accepted. Those open arms were hard to find at first.

20. Nov 16, 2016

### Staff: Mentor

You may make a meaningful contribution at some point in the future, but your approach here is backwards. You need to learn the current body of knowledge first, and then seek to expand it. Not the other way around. Even Einstein had to do it in that order.

21. Nov 17, 2016

### newjerseyrunner

pi has no dimensions, but it certainly doesn't start that way, it's a ratio between two lengths, so it is somewhat dependent on 2D, even though by itself it doesn't care.

c I like to think of as a translation between space and time. The faster you go in space, the slower you go in time and the slower you go in space you approach a proper time. In that way, it can be thought of sort of like little, can't it?

You can't formulate pi without being dependent on at least 2D, regardless of whether the final value has units or not. Pi also isn't just the ratio of cicumfrance and diameter, that's still actually meaningless without one more bit of information that's usually assumed: the curvature of space.

22. Nov 17, 2016

### Chris Miller

Thanks so much E=Mc^^2 and Dale for your patience, encouragements and understanding. I believe that in math alone, the "current body of knowledge" has far surpassed any individual's ability (longevity) to understand. So I'd be a little surprised if this weren't also true of physics. Though I agree, the more you know, the more informed your imagination, curiosity, and even confusion, and without which your knowledge is no better than a computer's, as you are just another repository for the information.

I'll have to read Einstein's bio sometime. Not sure where I gleaned my current understanding. Just finished John Nash's bio, liked where he met with and tried to convince Einstein that the universes wasn't expanding. Einstein entertained his math and hypotheses, then advised he study physics.

As an admittedly lazy autodidact, for whom the educational system has never worked well, my interest, and probably ability, in math and science and SR in particular, doesn't extend much past that of a SF (Carl Sagan wrote one of my favorite SF novels, "Contact") writer/reader, but which I'm beginning to see has hugely misinformed me.

E.g., Like this staple from almost every SF novel (e.g., The Forever War, The Three-body Problem, etc., etc.) I've ever read:

Q: I pass earth at ~c on my way to 100 lightyear distant (by earth measurement) star. Surely by earth's clock it takes me 100 years. How long, by my clock?

23. Nov 17, 2016

### phyzguy

It depends how close to c you are.

24. Nov 17, 2016

### Ibix

Edit: As @jbriggs444 points out below, I misread this. How long it takes in the Earth frame is dependent on synchronisation convention; your own time depends only on your speed relative to the two planets and can be arbitrarily low.

Last edited: Nov 17, 2016
25. Nov 17, 2016

### jbriggs444

On the earth's synchronization convention, rather. Which should be a given. You are using a single stopwatch and have no synchronization convention to worry about.