What course would explain why c is a hard limit?

[ibkev]

So far in my reading of SR, we explore various consequences of c being a constant in a vacuum and frame invariant, etc. At what point in a physics education do you learn why a universal speed limit is necessary at all? Is that the sort of thing that is revealed in an intro to GR course? Or is this just something we have to accept?

 

[PeterDonis]

At what point in a physics education do you learn why a universal speed limit is necessary at all?

At no point. There is nothing logically "necessary" about a finite universal speed limit. Newtonian physics, with no finite speed limit, is a logically consistent theory. It just doesn't describe our actual universe. The universal speed limit is a contingent fact about our actual universe, not a "necessary" one.

 

[ibkev]

Bummer! Though somehow I had a feeling that might be the case.

What about why c has the value it does (putting aside the arbitrariness of units). Like why not double what it is or half? Is that something physicists understand? Maybe that's just a variation of my original question and the answer is "because all our other relativistic experiments rely on it."

 

[PeterDonis]

What about why c has the value it does (putting aside the arbitrariness of units).

The value of $c$, like the value of any constant with units, is not really the right thing to focus on. The right thing to focus on is dimensionless constants. In the case of light, the primary such constant is the fine structure constant $\alpha$. We don't know why that constant has the particular value it has.

 

[rootone]

Another constant that simply is what it is for no particular reason is Pi.
It could be a bit different and if it was, a Universe would probably still exist.

 

[ibkev]

Thanks for the answers and for pointing me to fine structure constant! The idea that c can be derived from it is pretty neat

 

[haushofer]

The value of $c$, like the value of any constant with units, is not really the right thing to focus on. The right thing to focus on is dimensionless constants. In the case of light, the primary such constant is the fine structure constant $\alpha$. We don't know why that constant has the particular value it has.

Is that a sensible question, regarding renormalisation?

 

[PeterDonis]

Is that a sensible question, regarding renormalisation?

Taking renormalization group flow into account would just mean rephrasing the statement as "we don't understand why $\alpha$ has the specific renormalization group flow curve that it has". Still basically the same thing: we have this dimensionless thing that we can measure, but we don't have a theory that explains why the measurement gives the particular results that it does.

 

[jbriggs444]

Another constant that simply is what it is for no particular reason is Pi.
It could be a bit different and if it was, a Universe would probably still exist.

Pi is a dimensionless constant dictated by mathematics. It is what it is regardless of the features of the universe we happen to live in. It can be computed without measurement of any sort.

Edit: The ratio of a circle's circumference to its radius could fail to be a constant in some universes (e.g. those with intrinsic curvature). The ratio of a "circle's" circumference to its radius could fail to be equal to 2pi in some universes (e.g. ones with a "taxicab" metric).

 

[vanhees71]

Bummer! Though somehow I had a feeling that might be the case.

What about why c has the value it does (putting aside the arbitrariness of units). Like why not double what it is or half? Is that something physicists understand? Maybe that's just a variation of my original question and the answer is "because all our other relativistic experiments rely on it."

The value of $c=1$. Changing the value of $c$ within special relativity doesn't change anything but the units of time and/or length.

 

[ibkev]

The value of $c=1$. Changing the value of $c$ within special relativity doesn't change anything but the units of time and/or length.

I've thought about this more and I think I see what you guys are saying. I could choose units for time/length that would make c any value I want and the math would all still work out. I think I briefly tripped over "if c=1 then c^2 = 1 also and something is lost then" but that's not a problem, that's one of the benefits of choosing c=1. So, my understanding now is that it's the ratio of speed to the maximum possible speed (aka c) that's important, not the specific values.

Also, if I chose to work in units that make c=1, then E=mc^2 literally becomes E=m which is seems very cool and elegant.

Ok so given that the length and time units we use came from fairly arbitrary things like the length of a king's foot, or a rod in Paris - does this imply that there are other units that would have been chosen instead had the physicists of today defined them? Heck I guess even our base 10 number system comes from counting on our fingers.

 

[vanhees71]

Today the second is defined by a certain hyperfine structure transition in Cs.

"The second is "the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom".

Time measurements are among the most accurate measurements one can do, and that's why nowadays the metre is determined by defining $c$:

"The metre is the length of the path traveled by light in vacuum during a time interval of 1/299792458 of a second."

For details on the very interesting history of definitions of the second and the metre see the Wikipedia articles:

https://en.wikipedia.org/wiki/Second
https://en.wikipedia.org/wiki/Metre

 

[SlowThinker]

Ok so given that the length and time units we use came from fairly arbitrary things like the length of a king's foot, or a rod in Paris - does this imply that there are other units that would have been chosen instead had the physicists of today defined them?

There is the Boltzmann constant that converts Kelvins into Joules, but then, Joules are arbitrary too.
Electric charge should obviously be counted in elementary charges.
You can also give Geometrized Unit System a read, although there must be a better page about this somewhere. The idea is to measure everything in, e.g., meters (charge, energy, temperature etc.)

 

[Vitro]

There is the Boltzmann constant that converts Kelvins into Joules, but then, Joules are arbitrary too.
Electric charge should obviously be counted in elementary charges.
You can also give Geometrized Unit System a read, although there must be a better page about this somewhere. The idea is to measure everything in, e.g., meters (charge, energy, temperature etc.)

Here's another one: https://en.m.wikipedia.org/wiki/Natural_units

 

[ibkev]

Thanks for these links everyone. This idea of "natural units" was what I was trying to get at in my earlier post but the history of how seconds and meters have been defined is pretty interesting too.

 

[haushofer]

Taking renormalization group flow into account would just mean rephrasing the statement as "we don't understand why $\alpha$ has the specific renormalization group flow curve that it has". Still basically the same thing: we have this dimensionless thing that we can measure, but we don't have a theory that explains why the measurement gives the particular results that it does.

Yes. As such it sounds less like numerology :P

 

[stoomart]

we have this dimensionless thing that we can measure, but we don't have a theory that explains why the measurement gives the particular results that it does.

Is time also a dimensionless thing we can measure? I'm trying to figure out if time and c are directly related or dependent on each other (assuming EM waves don't oscillate without time, and time doesn't pass without EM waves oscillating).

 

[PeterDonis]

Is time also a dimensionless thing we can measure?

No, time has units.

 

[brainierthaneinstein]

Would be an interesting world if c was something like 60kmh - twins paradox commuting to work!

 

[rootone]

In think all the same principles would apply, but we could forget about things like exploring Mars.
Typically we can a get a craft to Mars in less than a year and once it arrives. signals can be sent to Earth with a delay of 15-30 minutes.
You need to replace that with journey time around a million years, and transmission time delay of a few centuries.