Ask a physicist anything. (6)

[TheReasoner]

A physics question for you:

Show that the intensity of sound waves can be written as:
I=(1/2)*ρvω^2A^2

 

[GrowingSmaller]

The bus I need to catch arrives at the stop every 10 minutes. I am walking there through some side streets, not from a regular time each day but as random time in relation to the regular arival of the bus. I guess that when I arrive my average waiting time will be 5 minutes. But what if I run through the side streets to the bus stop? Will my average waiting time go down, or will it (as I believe) remain at 5 minutes? Anyway, whats the math to this...

 

[Wiccan_Child]

The bus I need to catch arrives at the stop every 10 minutes. I am walking there through some side streets, not from a regular time each day but as random time in relation to the regular arival of the bus. I guess that when I arrive my average waiting time will be 5 minutes. But what if I run through the side streets to the bus stop? Will my average waiting time go down, or will it (as I believe) remain at 5 minutes? Anyway, whats the math to this assuming I have it ALL wrong...

So, buses arrive regularly every ten minutes, and you arrive at the bus station with between 0 and 10 minutes to wait (average 5 minutes). If you don't care which bus you get, then running won't improve anything, as your waiting is indeed still 5 minutes (you may catch the next bus, but you may overshoot and have to wait longer at the station than if you had walked).

However, if we factor in transit time as well, then running is more logical. Though your time waiting at the bus station remains an average of 5 minutes, your transit time is obviously lower when you run. So, running lowers the total time you spend catching a bus (walking/running + waiting).

More realistically, if you need to get a certain bus, running is even more preferable, as it not only decreases your total time spent catching the bus, but it also improves your odds of catching a particular bus.

So, I'd favour running everywhere for everything

 

[GrowingSmaller]

Thanks for that!

Ok IIRC Bertran Russel tried to derive math (arithmetic) from logic. This view is called logicism, and I think also that Godel said that it was not possible to derive all of it in such a way. Anyway is there any possibility that physics (e.g. e=mc^2) could be derived from logic or maths? I mean not in theory logically possible, like a turquoise flying pig is merely because it doen not entail a contradiction in terms, but in any way achieveable knowing what we do about maths, physics and logic? Could physics be a branch of maths, and could it (if it is) be derived from basic axioms? If so, are there any theoreticians working on this?

 

[Wiccan_Child]

Thanks for that!

Ok IIRC Bertran Russel tried to derive math (arithmetic) from logic. This view is called logicism, and I think also that Godel said that it was not possible to derive all of it in such a way. Anyway is there any possibility that physics (e.g. e=mc^2) could be derived from logic or maths? I mean not in theory logically possible, like a turquoise flying pig is merely because it doen not entail a contradiction in terms, but in any way achieveable knowing what we do about maths, physics and logic? Could physics be a branch of maths, and could it (if it is) be derived from basic axioms? If so, are there any theoreticians working on this?

Arguably, it's already been done. Everything in physics, including the 'end-user' equations like E = mc[sup]2[/sup], is derived from other, more basic stuff. The mathematics is all built upon the logic of numbers, and so all the physics that is derived from mathematics already has a solid basis in axiomatic logic. However, physics makes fundamental assumptions and then uses mathematics to derive necessary conclusions. For example, Relativity is a necesssary by-product of the assumption that the speed of light is constant in all inertial frames. That assumption can't be derived from logic, it is an observation of reality.

So all the in-between steps are founded in good old-fashioned axiomatic logic, but the starting points, the premises and assumptions, are based on empirical observation. Unfortunately for Aristotle, we can't sit down and work out everything from first principles.

 

[mzungu]

What beautiful and grand beasts they are:

NASA - NASA's Chandra Finds Nearest Pair of Supermassive Black Holes

 

[GrowingSmaller]

Abouth the assupmptions (e.g. speed of light being constant). Are they necessary in order to have a working physics? I mean, there might be infinite models with different a priori assumptions about the speed of light, and although we might need data to determine which model is correct in this universe, there must at least be an assumption or two to get the whole thing off the ground and working. So any physical model is not pure math and logic, but needs certain physical principles to be assumed in order for it to be a theoretical physical model in the first place? I mean, there might be a model with different constants etc to the ones in our working model, but all models must have certain non-derivable constants. ETA Then again I suppose that the same could be argued about math and logic, you need axioms and definitions of operators, geometries etc in order to float the boat. So are there any domain specific assumptions needed for physics which distinguish it from maths, or is that a posteriori matter such that our physics is just an arbitrary type of maths, a subset of an infinite potential variety, except it has certain arbitrary constants based on observation and thats what makes it "physical"?

 

[Wiccan_Child]

Abouth the assupmptions (e.g. speed of light being constant). Are they necessary in order to have a working physics? I mean, there might be infinite models with different a priori assumptions about the speed of light, and although we might need data to determine which model is correct in this universe, there must at least be an assumption or two to get the whole thing off the ground and working. So any physical model is not pure math and logic, but needs certain physical principles to be assumed in order for it to be a theoretical physical model in the first place? I mean, there might be a model with different constants etc to the ones in our working model, but all models must have certain non-derivable constants.

Pretty much. As far as we can tell, the speed of light doesn't have to be constant in all inertial frames - it just so happens that it is. But, perhaps, pure logic can indeed be used to derive physical constants and suchlike, and we just don't know it yet!

 

[chris4243]

So are there any domain specific assumptions needed for physics which distinguish it from maths, or is that a posteriori matter such that our physics is just an arbitrary type of maths, a subset of an infinite potential variety, except it has certain arbitrary constants based on observation and thats what makes it "physical"?

That's pretty much it -- physics is the maths of the real world, whatever that may be. As for the speed of light being constant, that's not a separate assumption but what results from Maxwell's equations. And Maxwell's equations are similar to equations for fluids, and I'd heard it is so because of similar conservation laws. You'd have to mess with a whole lot of stuff if you didn't want the speed of light to be constant.

As for physical constants, the most interesting ones are the dimensionless constants, since those don't depend on our choice of units. So far, we've not figured how to calculate them based on first principles, and some hypotheses claim that those are randomly fixed when a new universe is made.

 

[TheReasoner]

What is your favorite - and least favorite - branch of physics?

 

[Chalnoth]

Abouth the assupmptions (e.g. speed of light being constant). Are they necessary in order to have a working physics? I mean, there might be infinite models with different a priori assumptions about the speed of light, and although we might need data to determine which model is correct in this universe, there must at least be an assumption or two to get the whole thing off the ground and working. So any physical model is not pure math and logic, but needs certain physical principles to be assumed in order for it to be a theoretical physical model in the first place? I mean, there might be a model with different constants etc to the ones in our working model, but all models must have certain non-derivable constants. ETA Then again I suppose that the same could be argued about math and logic, you need axioms and definitions of operators, geometries etc in order to float the boat. So are there any domain specific assumptions needed for physics which distinguish it from maths, or is that a posteriori matter such that our physics is just an arbitrary type of maths, a subset of an infinite potential variety, except it has certain arbitrary constants based on observation and thats what makes it "physical"?

My suspicion is that if we knew more, we would discover that there are many potential ways to build a consistent universe, but only some of those ways would correspond to the universe we observe.

I'm a bit partial to Tegmark's idea here:
The Universes of Max Tegmark

The basic idea, at its core, is that as long as we believe our universe is consistent (which seem to me an obvious assumption), then there exists some mathematical structure which describes our universe. That means that there is a mathematical structure that has real existence. If one kind of mathematical structure exists, why not all of them?

 

[mzungu]

My suspicion is that if we knew more, we would discover that there are many potential ways to build a consistent universe, but only some of those ways would correspond to the universe we observe.

I'm a bit partial to Tegmark's idea here:
The Universes of Max Tegmark

The basic idea, at its core, is that as long as we believe our universe is consistent (which seem to me an obvious assumption), then there exists some mathematical structure which describes our universe. That means that there is a mathematical structure that has real existence. If one kind of mathematical structure exists, why not all of them?

Logically speaking; if the universe had a single point of beginning then suffice it to say that the universe will be consistent. The constants must apply to the whole else a paradox is created where differing constants cannot occupy the same spacetime. That is why C is constant in any part of the universe!

 

[Tuddrussell]

Let's say that I, hypothetically, drop my watch into a black hole. Would there be any way to get it back? If not, could there ever be such a thing, and would it be likely that I could get my watch back at that time?

Assuming I'm immortal, which I like doing.

 

[Chalnoth]

Logically speaking; if the universe had a single point of beginning then suffice it to say that the universe will be consistent.

You don't even need to assume that that much. All that consistency demands is that the answer to any sufficiently-specific question about the universe be definitively either true or false.

The constants must apply to the whole else a paradox is created where differing constants cannot occupy the same spacetime. That is why C is constant in any part of the universe!

It is conceivable that the parameters we believe to be constant could potentially vary. But since no deviation from these constants has yet been found, if they vary, they vary very slowly.

 

[Chalnoth]

Let's say that I, hypothetically, drop my watch into a black hole. Would there be any way to get it back? If not, could there ever be such a thing, and would it be likely that I could get my watch back at that time?

Assuming I'm immortal, which I like doing.

Nope. It's gone. You will always be able to come back and check to see what time you dropped it in, though.

 

[Tuddrussell]

What if a ghost fell into a black hole, do they work on ghosts?

 

[Chalnoth]

What if a ghost fell into a black hole, do they work on ghosts?

It wouldn't exist as much after as it doesn't exist before it falls in...

 

[Tuddrussell]

Say I invented a ghost in a lab, then threw it into a black hole. What heppens?

 

[pgp_protector]

Say I invented a ghost in a lab, then threw it into a black hole. What heppens?

What do you make the Ghost out of?

 

[Tuddrussell]

Maybe some sort of energy, a gel, nanaomachine cloud, or light.