Expected rate of change, if at all, of nature's constants

[hideelo]

I am reading gravitation and spacetime by Hans Ohanian and he is discussing the possibility of the constants, such as proton mass, fine structure constant, etc, actually changing over time. He makes the claim that since the universe is ~10^10 years old the expected change should be ~10^(-10)/year. I don't see why that should be the case. Can anyone justify it for me?

 

[mfb]

The expected change is zero.

If something changes, and the change is not completely weird, it cannot be more than 10^-10/year, otherwise the universe would have started with completely different laws of physics, which does not agree with observations. In other words, if you can rule out a 10% change in the last 100 years for some constant, that does not tell you anything new.

 

[hideelo]

The expected change is zero.

Lemme correct that, IF there is a change, then the expected...

Other than that, I didnt really understand the rest of what you said, can you try explaining it again?

 

[mfb]

Let's imagine the electron to proton mass ratio decreases by 10^-8 per year today (ruled out by experiments long ago, just a hypothetical situation). One year ago, the electron was 10^-8 heavier relative to the proton. If this absolute rate of change is constant, 1000 years ago, the electron was 10^-5 heavier relative to the proton, 100 million years ago the electron to proton mass ratio had twice its current value and at the time of the big bang it had more than 100 times its current value. This is clearly not right, the cosmic microwave background and early stars would look completely different then.
To make this work, the rate of change has to change itself over time. This is not impossible, but it sounds much more improbable - why should the ratio have been quite constant over billions of years, just to quickly change today?

A change of 10^-13 per year today is easier to get in agreement with observations - if this rate has been constant the last 13.7 billion years, it just leads to a 0.1% change of the ratio since the big bang. This is still four orders of magnitude above limits from astronomy, but the electron to proton ratio is one of the most well-measured constants.

 

[Nugatory]

Other than that, I didnt really understand the rest of what you said, can you try explaining it again?

Observations tell us that the laws of physics, including the values of these constants, have not changed noticeably over the 10¹⁰ years that the universe has existed. Therefore, if the value of these constants is changing, the rate of change has to be small enough that it doesn't build up to something noticeable even over a period of 10¹⁰ years. Clearly any change greater than one part in 10¹⁰ per year is going to build up to something noticeable over that time, so we know the rate of change must be lower than that.

Most likely it is zero, but that's not something that we can ever prove - no matter how many observations we make, we can never exclude the possibility that there's been a change smaller than our measurements could detect over the period of measurement.