Stuff Explained

[Mr Skeptic]

Here I attempt to show how if you understand what distance *really is* then you understand what everything *really is*, in nice, mathematically precise terms. Oh, and you also need to understand some calculus. The explanation for the title is that it is a salute to another poster who likes to tell us what stuff really is.

 

Each definition is given in terms of previous definitions and physical laws, though I have occasionally added an alternative definition which doesn't, but serves more as clarification. Except, of course, for distance

 

distance [math]\vec{r}= ? [/math] Well, I don't actually understand distance, unless we are talking about a flat space (which doesn't correspond to the real world). Mathematicians and folks who understand general relativity would know this, though.

time [math]t=\frac{r_{light}}{c}=\int{\frac{1}{v}dr}[/math] Time is the distance light moves divided by its speed, which we know is c. You could also say that time is the ticks of a light clock. Or you could use the movement of something else if you really wanted to, but then you would have to know its speed. You already know the speed of light is c so you are better off using that.

velocity [math]\vec{v}=\frac{d\vec{r}}{dt}[/math] Velocity is the rate of change of distance with respect to time; that is, how quickly something moves.

acceleration [math]\vec{a}=\frac{d\vec{v}}{dt}=\frac{d^2\vec{r}}{dt^2}[/math] Acceleration is the rate of change of velocity with respect to time; that is, how quickly something changes its velocity.

momentum [math]\vec{p}=\int\vec{F} dt[/math] or [math]\vec{p}=\frac{h}{\lambda}[/math] If you knew what force was, you could integrate it with respect to time to get the momentum (that is, momentum is the amount of time a force is applied). Or you could calculate it by using the wavelength of the particle (since you know distance). Then the direction of the wave (and hence, of the wavelength) would give you the direction of the momentum. Then momentum is a measure of how small your particle's waveform is.

force [math]\vec{F}=\frac{d\vec{p}}{dt}[/math] Force is how quickly you change the momentum of a particle.

work [math]W=\int_{\vec{r}_i}^{\vec{r}_f}\vec{F} \cdot d\vec{r}[/math] Work (energy) is how much force a particle has moved away from. I think that work should be a vector in the direction of the force, but no one seems to do that (and it seems to be taken care of by momentum, anyhow).

potential energy [math]\Delta U=\int_{\vec{r}_f}^{\vec{r}_i}\vec{F} \cdot d\vec{r}[/math] (Change in) potential energy is how much force a particle has moved against. This is the opposite of work. The total potential energy is usually defined as being zero at infinity, so that it is always negative. This is a definition gimmick to avoid embarrassing infinity problems at [math]\vec{r}=0[/math] (which I take to mean that our usual concept of inverse square laws don't work at tiny distances).

power [math]P=\frac{d\vec{W}}{dt}=\int\vec{F} \cdot d\vec{v}[/math] Power is how quickly you can do work.

(relativistic) mass [math]m = \frac{E}{c^2} [/math] Mass is condensed energy. Dunno what kind of energy, just that it is energy. Or, it is the stuff that causes gravitation.

rest mass [math]m_0 = \sqrt{\frac{E^2}{c^4} - \frac{p^2}{c^2}}[/math] Derived from Einstein's other most famous equation. Uh, I think you should only use the positive root, though.

charge [math]e = \sqrt{\frac{F_{electric}r^2}{k}}[/math] Charge is the stuff that causes electrostatic attraction. (And yes, that is lame)

 

So what do people think of this? I don't understand the strong and weak forces nor particles, so I can't explain them.

[Martin]

 

So what do people think of this?

 

I think it's a neat sequence of explanations

skillfully presented

if you were doing a blackboard show of it you could use examples and some diagrams to make it more visual.

[NeonBlack]

I agree it was neat. Although the original "explained" series is entertaining, this is much more concise and coherent.

This is a problem I have considered many times. You don't have to use length as your starting point (although it might be the most intuitive- I don't know. This is something I haven't been able to decide on). You can use time. Take some arbitrary time interval. Then we can define length by ct, and you know the rest.

 

I don't want to distract from the main topic, but I suggest you forget you ever heard the words "relativistic mass." Then take "rest mass" and just call it mass.

[vincent]

Hi Mr Skeptic,

 

Here I attempt to show ...

 

I'm sorry but this is actually the wrong forum for this post. Try the classical physics forum.

 

Hi Martin,

 

I think it's a neat sequence of explanations

skillfully presented

if you were doing a blackboard show of it you could use examples and some diagrams to make it more visual.

 

This response is inappropriate. As a moderator you're responsibility was to tell Mr Skeptic what I just did and then move his post to a more appropriate forum.

[Mr Skeptic]

I agree it was neat. Although the original "explained" series is entertaining, this is much more concise and coherent.

This is a problem I have considered many times. You don't have to use length as your starting point (although it might be the most intuitive- I don't know. This is something I haven't been able to decide on). You can use time. Take some arbitrary time interval. Then we can define length by ct, and you know the rest.

 

I don't want to distract from the main topic, but I suggest you forget you ever heard the words "relativistic mass." Then take "rest mass" and just call it mass.

 

Well, the original "explained" series had some interesting if vague ideas, but the reaction to scrutiny was pure entertainment.

 

The reason I did not choose time is because more people do not understand it (or is it that people know that they do not understand it?) . I might be able to derive everything else from a starting point other than distance and time, but it would look ... different. And more complicated. Perhaps that is reason enough to try it. The derivatives and integrals with respect to something other than distance and time might be impossible, though.

 

I'm pretty sure that we want a distinction between rest mass and relativistic mass (or we could say rest energy and energy). Otherwise you would end up with massive photons or somesuch. Do photons have a gravitational field?

 

Hi Mr Skeptic,

 

 

 

I'm sorry but this is actually the wrong forum for this post. Try the classical physics forum.

 

Well, I thought that figuring out what all that stuff is was theoretical. And since explanation for momentum and everything past it uses the de Broglie wavelength and mass uses relativity, it is not very classical. That said, I don't mind if it gets moved elsewhere.

[Martin]

... I don't understand the strong and weak forces nor particles, so I can't explain them.

 

So what is your idea? Would you like people to try to EXTEND your chain of explanations into areas like particle physics?

 

I gathered you were starting a process and might want to challenge others to continue it. Or do you want it to stop here, basically at E = mc²

or thereabouts?

 

 

what about continuing with Planck's constant----energy/frequency relation or something of the sort?

[Sisyphus]

I agree it was neat. Although the original "explained" series is entertaining, this is much more concise and coherent.

This is a problem I have considered many times. You don't have to use length as your starting point (although it might be the most intuitive- I don't know. This is something I haven't been able to decide on). You can use time. Take some arbitrary time interval. Then we can define length by ct, and you know the rest.

 

Classically, you really have three starting points. Distance, time, and velocity. You can't really give a definition of any one of those without the other two that isn't simply tautological. So traditionally we just start assuming we have an idea of what distance and time are (since they are slightly more intuitive than velocity) and go from there. Then you add mass, and pretty much everything follows from that.

[NeonBlack]

The reason I did not choose time is because more people do not understand it (or is it that people know that they do not understand it?) .

 

You're right. Length is something that we can understand with our primary sense, sight. On the other hand, time is completely abstract. We think we know what time is, but if you ask someone "What is time?" I don't think anybody (expect FS, of course) would be able to give you an answer.

 

SI defines time first as something completely arbitrary- the frequency of cesium-133, and uses this definition, with c to define length.

 

There's no reason we couldn't do it the other way, in principle. We could define length as the wavelength of a certain element's emission line- maybe something a little more common than cesium-133, but again, this is completely arbitrary.

 

(As far as I know, the kilogram is still defined by a hunk of metal locked in a vault in France.)

 

As for mass, looking at your definitions again, what you call relativistic mass is not what is normally thought of as such. I think when most people hear relativistic mass, they think

[math]m(v)=\frac{m_0}{\sqrt{1-v^2/c^2}}[/math], where m0 is the "rest mass"

This is completely unneccessary. You only need one mass. mass is mass is mass.

 

Under Newtonian gravity, photons do not create a gravitional field as they have no mass, but I believe that in General Relativity, (I am only beginning to study GR) photons do create "curvature" (GR's way of describing g-fields).

[Mr Skeptic]

So what is your idea? Would you like people to try to EXTEND your chain of explanations into areas like particle physics?

 

I gathered you were starting a process and might want to challenge others to continue it. Or do you want it to stop here, basically at E = mc²

or thereabouts?

 

 

what about continuing with Planck's constant----energy/freqency relation or something of the sort?

 

Definitely. I don't know how to continue, but I was hoping that some people here who know more physics might be able to add something.

 

 

Classically, you really have three starting points. Distance, time, and velocity. You can't really give a definition of any one of those without the other two that isn't simply tautological. So traditionally we just start assuming we have an idea of what distance and time are (since they are slightly more intuitive than velocity) and go from there. Then you add mass, and pretty much everything follows from that.

 

I thought I got around that by using the speed of light. Since we know the speed of light, [math]\frac{d\vec{r}_{light}}{dt}=c[/math], then solving the differential equation to get t seems reasonable.

[Martin]

If you'd like others to contribute to the idea-chain then I'll add "frequency", as a suggestion. Change the wording around to suit yourself.

 

 

Each definition is given in terms of previous definitions and physical laws, though I have occasionally added an alternative definition which doesn't, but serves more as clarification...

...

time [math]t=\frac{r_{light}}{c}=\int{\frac{1}{v}dr}[/math] Time is the distance light moves divided by its speed, which we know is c. You could also say that time is the ticks of a light clock...

 

 

frequency [math]f=\frac{cycles}{t}= \frac{events}{t}[/math]

 

The events are whatever you are counting---with a frequency it has to be clear what you are counting the frequency of. It could be a unit of angle or rotation per unit time, like "radians per second", or it could be cycles. And for example in the case of a quantum of light,

Planck's constant h gives [math]E = hf[/math], the photon's energy related to its frequency.

 

BTW I see you already introduced Planck's constant in your starter post---with corresponding the relation of momentum and wavelength.

 

Mr Skeptic, I see you don't have anything with temperature in the list so far. I like this thread idea. It could almost be a "sticky". Mr Skeptic's Brief Dictionary of General Physics (that reminds me, if all right with you, I might eventually move the thread to General Physics since it seems like it could intersect with several different areas.)

[Klaynos]

Hi Mr Skeptic,

 

 

 

I'm sorry but this is actually the wrong forum for this post. Try the classical physics forum.

 

Hi Martin,

 

 

 

This response is inappropriate. As a moderator you're responsibility was to tell Mr Skeptic what I just did and then move his post to a more appropriate forum.

 

You've got to respect this back seat moderation... you REALLY do... esspecailly as Martin is not infact a mod... But oh well....

 

Vincent if you REALLY feel this strongly you should use the report post button.

 

Now back on topic, it's a nice concise list....

 

Personally I'd have liked it to start with time, because time is the thing that we can measure most accurately...

[Martin]

 

Personally I'd have liked it to start with time, because time is the thing that we can measure most accurately...

 

That's a really good point!

To an increasing extent, since the mid 20th century, units have been ultimately based on the atomic clock.

 

time is the fundamental measurable thing. e.g. 1 meter is defined as distance lite goes in vacuum in a certain definite timeperiod.

so measuring distance is based on measuring time, comes down to it in the end.

 

this is even true about the de facto Voltage standard in place since 1990 (based on josephson junction frequency, measured by atomic clock) and the 1990 Current standard (quantum hall effect, based on voltage, in turn based on the atomic clock frequency standard)

 

eventually even mass will probably be based on frequency---with a declared exact value of h.

 

Mr Skeptic take note

if we were really making a sticky of physics definitions and superbrief explanations (which might not be a bad idea), I think it would probably start with time

[Sisyphus]

I thought I got around that by using the speed of light. Since we know the speed of light, [math]\frac{d\vec{r}_{light}}{dt}=c[/math], then solving the differential equation to get t seems reasonable.

 

It seems to me you've just used distance and velocity instead of distance and time.

[Mr Skeptic]

If you'd like others to contribute to the idea-chain then I'll add "frequency", as a suggestion. Change the wording around to suit yourself.

 

frequency [math]f=\frac{cycles}{t}= \frac{events}{t}[/math]

 

The events are whatever you are counting---with a frequency it has to be clear what you are counting the frequency of. It could be a unit of angle or rotation per unit time, like "radians per second", or it could be cycles. And for example in the case of a quantum of light,

Planck's constant h gives [math]E = hf[/math], the photon's energy related to its frequency.

 

BTW I see you already introduced Planck's constant in your starter post---with corresponding the relation of momentum and wavelength.

 

Thanks for the contribution It seems that we also need to understand what a cycle/event is (same with my use of wavelength, which would make no sense without a wave, to define momentum). Events are invariants in relativity, yes?

 

I just realized that I changed my definition of energy to that of work and potential energy, but forgot about it. Also, that work definition should have been for change in work. Reason I changed it is because I had a bit of uncertatinty about energy. I think total energy (which includes relativistic) should be a sum of positive potential energy and positive total work energy, where the work might come from a different force than the potential energy. But trying to get positive potential energy has infinity problems, and it would also ASS-U-ME (useful mnemonic) that rest energy is potential energy. That seems like a reasonable enough assumption, given matter-antimatter annihilation, but I dunno if it still works if we have more matter than antimatter. More on that later, after I think a bit about it. Until it is fixed, all my definitions based on energy are suspect.

 

Mr Skeptic, I see you don't have anything with temperature in the list so far.

 

I like this thread idea. It could almost be a "sticky". Mr Skeptic's Brief Dictionary of General Physics (that reminds me, if all right with you, I might eventually move the thread to General Physics since it seems like it could intersect with several different areas.)

 

You're probably right that this should go in general physics. the subject doesn't really fit in any particular area. And I think I pissed off some people in the theoretics section by using relatively simple (for them) math and then explaining it besides What are the requirements to make this a sticky? I'd still like to venture a little out of accepted definitions, like where I defined momentum in terms of wavelength rather than mass and velocity. Or should we condense it after we figure everything out?

 

 

That's a really good point!

To an increasing extent, since the mid 20th century, units have been ultimately based on the atomic clock.

 

time is the fundamental measurable thing. e.g. 1 meter is defined as distance lite goes in vacuum in a certain definite timeperiod.

 

do measuring distance is based on measuring time.

 

this is even true about the de facto Voltage standary since 1990 (based on josephson junction frequency, measured by atomic clock) and the 1990 Current standard (quantum hall effect, based on voltage, in turn based on the atomic clock frequency standard)

 

eventually mass will probably be based on a frequency with a declared exact value of h.

 

Mr Skeptic take note

if we were really making a sticky of physics definitions and superbrief explanations, it

 

would probably start with time

 

I still like the distance idea better, but due to popular demand, I had better start from time, or do both. I thought distance would be more intuitive, and preferred turning a vector into a scalar than a scalar into a vector. Since my first step is to define time and distance in terms of the other, it doesn't make a difference to past the second step anyhow.

distance [math]\vec{r} = \vec{c} t[/math]

Hmm, it does look simpler that way, but we need to know the direction the light is travelling, and knowing direction without knowing distance seems weird.

 

Eventually, I will see if we can't define time/distance from various other starting points as well, and let people choose their favorite.

[math]\lambda = \frac{h}{\vec{p}}[/math] etc.

 

It seems to me that we are working with a system of n equations and n+1 unkowns. I think we are missing one more law of physics to tie all of these together (eg it seems to me that the period of an electron about an atom should be deriveable from basic principles).

 

 

It seems to me you've just used distance and velocity instead of distance and time.

 

You are right about that: v = dr/dt was already defined; it is not my own definition, rather what (instantaneous) velocity means and has always meant. However, we didn't *know* what it was, because we did not know t. But we *know* that the speed of light is c (because we know light is an electromagnetic wave as defined by Maxwell's Equations), and we can use that to solve for t. Then we *know* both distance (which I said at the start you needed to know to know the rest) and time, so we now *know* velocity.

 

In fact, most everything I wrote was already defined like that, with the exception of the few places I plugged a law of physics in instead, and the places I replaced some things with others.

[Klaynos]

period of an electron about an atom

 

Unless I'm missing something, I think what you're referring to here (the time of one orbit) does not infact exist.

[Sisyphus]

You are right about that: v = dr/dt was already defined; it is not my own definition, rather what (instantaneous) velocity means and has always meant. However, we didn't *know* what it was, because we did not know t. But we *know* that the speed of light is c (because we know light is an electromagnetic wave as defined by Maxwell's Equations), and we can use that to solve for t. Then we *know* both distance (which I said at the start you needed to know to know the rest) and time, so we now *know* velocity.

 

In fact, most everything I wrote was already defined like that, with the exception of the few places I plugged a law of physics in instead, and the places I replaced some things with others.

 

You don't know what the speed of light is without knowing what velocity is. Maxwell's equations are not magical (though they certainly seem to be!). I'm not saying you're doing anything wrong, I'm just saying that's how it has to be.

[Mr Skeptic]

If you'd like others to contribute to the idea-chain then I'll add "frequency", as a suggestion. Change the wording around to suit yourself.

frequency [math]f=\frac{cycles}{t}= \frac{events}{t}[/math]

 

The events are whatever you are counting---with a frequency it has to be clear what you are counting the frequency of. It could be a unit of angle or rotation per unit time, like "radians per second", or it could be cycles. And for example in the case of a quantum of light,

Planck's constant h gives [math]E = hf[/math], the photon's energy related to its frequency.

 

After considering what Klaynos and Martin have said, it does seem clear that I should change my starting point. However, I think I should change it to period or frequency, not time. It may seem like splitting hairs, but exactness is important in definitions. Besides, people might not know what time is, but they are very familiar with period -- the changes in time per event/cycle -- the ticks of a clock. And as Martin has pointed out, this is what we currently use to measure both time and distance. Atomic clocks are insanely accurate, so much so that they make light look slow

 

So, here we go:

wavelength [math]\lambda_{light} = \vec{c} T [/math] I wonder what would happen if I tried to replace distance with wavelengths...

Period [math]T = \frac{1}{f} = \frac{h}{E_{photon}} = \frac{h}{\vec{p}c} = \frac{\lambda_{light}}{c}[/math] Period is a change in time per event or cycle.

 

So now we can also start from knowing frequency, the energy of a photon, momentum of a photon, or the wavelength of light. Lots of stuff to think about.

[Mr Skeptic]

Mr Skeptic, I see you don't have anything with temperature in the list so far.

 

Well, since I had some trouble with energy I couldn't very well go defining temperature at the time. Sorry it took me this long to add it.

 

rest energy [math]E_0 = \sqrt{E^2 + (pc)^2}[/math] rest energy is the portion of energy that is not due to movement. I think it would also be equivalent to the potential energy of a particle (which is released when it annihilates with its antiparticle).

 

kinetic energy [math]E_K = E - E_0 [/math] Kinetic energy is the portion of a particle's energy that is due to movement.

 

pressure [math] P = \frac{F}{A}[/math] Pressure is the force per area. I think it might better be modeled as a derivative, though.

 

temperature Temperature is an illusion. It is just the portion of the kinetic energy of an object that is not due to the object's movement as a whole. That is, it is the random movements of molecules within an object. Imagine perfectly elastic spheres bouncing around, then the temperature is related to the speed at which they move. In a real object, the molecules have shapes so they can rotate and wiggle as well as move, making this incredibly chaotic (which is why it is a major component of entropy).

 

I need an equation for temperature, though I don't think I can model it as described above. Perhaps a modification of the gas law, [math] Temperature = \frac{PV}{nR}[/math], where P is pressure, V is volume, n is the number of moles (just a convenient way to count huge number of molecules), and R is the gas constant. Ugh.

 

Uh, by this definition, a bunch of photons would have an insanely high temperature. Is that a bad thing?

[Martin]

...

Uh, by this definition, a bunch of photons would have an insanely high temperature. Is that a bad thing?

 

Not a bad thing in my opinion. I think it is customary to say that the temperature of sunlight is 5000-6000 kelvin---essentially the temperature of the surface of the sun.

 

the black body law (Max Planck 1900) is one of the most beautiful things in all of physics IMHO----it relates the thermal mix of energies of photons to the temperature of the radiating surface.

 

the fit to the black body law is why one says that the temperature of the universe's microwave background is 2.7 kelvin. same story as with sunlight, just a different temperature.

 

Again I want to thank you for assembling these definitions and concise statements of natural laws and stuff. It's great. Hope others will help out.

[Klaynos]

You could consider using the van der walls equation of state...

 

http://en.wikipedia.org/wiki/Van_der_Waals_equation

[Martin]

Klaynos, should we move this to General Physics---to indicate that it is comprehensive: touching on any/all Phizzy subject areas?

 

Should we try to assemble a concise "Physics Cheat Sheet" of Everybody's Favorite Laws and Definitions? (EFLAD)

 

If it was good enough it could be made sticky. If not, no harm done.

Also I think better get some input from Swansont.

[Klaynos]

Yeah I think that would be good.

 

I actually have on my desk a cheat sheet that I had for my A-Level physics exams (it was printed at the front of all exams I wasn't actually cheating), that's aged 16-18. I still refer to it now. Although after many years of looking at it I do now know alot of it without having to refer to it:) But it's nice to know I can check I've got the kinimatic equations correct when I answer a thread about them!

[Mr Skeptic]

I've recently realized that we can get a photon of known energy, frequency, and wavelength using the emission spectrum of Hydrogen. Really, pretty much anything that involves particles could be used as the initial measure to measure everything else. However, I don't know how to derive particles and their interactions.

 

Also, I'm not sure my definition of acceleration plays nice with gravity, or maybe its because I don't really understand curved spacetime.

[Mr Skeptic]

I suppose I should add some electromagnetic definitions too. I will need some help here people if I'm ever going to finish this...

Charge [math]Q = \sqrt{\frac{F_{electric}r^2}{k}}[/math] Charge is the stuff that causes electrostatic attraction. (And yes, that is lame)

Electric Field [math]\vec{E} = \frac{F_{elecric}}{q}[/math] The electric field at a point is the electric force per unit charge. (there may be a better definition)

Electric Flux [math]\Phi_e = \int \vec{E} \cdot dA[/math] The electric flux is the amount of electric field flowing through an area.

Electric Charge Density [math]\rho = \frac{dQ}{ds}[/math] or [math]\frac{dQ}{dA}[/math] or [math]\frac{dQ}{dV}[/math] Electric charge density is the amount of charge per unit length, area, or volume as needed.

Electric Current Density [math]\vec{J} = \rho\vec{v}[/math] Electric current density is the flow of charge density.

Electric Current [math]I = \frac{dQ}{dt} = \int \vec{J} \cdot d\vec{A} = - \int_V{\Big( \frac{\partial \rho}{\partial t} \Big) dV}[/math] Electric current is the charge flow, or the flux of the electric current density.

Electric Dipole Moment [math]\vec{p} = q\vec{r}[/math] The electric dipole moment is the product of the charge of a dipole and the separation vector of the charges. Not to be confused with the p for momentum.

 

I need some sleep. Please correct any mistakes you might find.

[Fred56]

Um, just a thought, could (or might) you explain some of the EM phenomena, like current and charge density, like water in a pipe? Would it make the concepts easier for say, high-school types? The analogy would be tricky to extend to the frequency domain, but...