Why Witch Sabrina Looks Thinner While Riding On Her Broom.

[Solitary]

Even dummies can understand an "explanation" that doesn't really explain the theory.

 :-k  #-o  Lets see, an explanation of the special theory of relativity doesn't really explain it if it doesn't have math. Makes sense to me.  8-)  Thanks! Does this mean if someone can't explain the special theory of relativity in a way that a dummy can understand it they are smarter than a dummy?

No, it just means that you can't explain math (which is what SR is) without using math.  And you can't understand math if you don't understand math.

No matter how many non-mathematical "explanations" of SR you can find, they don't actually explain SR, they just give you something that makes you think that you understand something that you don't actually understand.  (Christians used to think that they understood lightning - it was something God did.  It was an explanation, but it was about as close to reality as a non-mathematical "explanation" of SR is.)  It's like the "explanation" of e=mc[sup:1tk09dvh]2[/sup:1tk09dvh] that you posted.  It explains something, but it doesn't explain e=mc[sup:1tk09dvh]2[/sup:1tk09dvh].  It just claims that it does.

No matter how many mathematical "explanations" of SR you can find, they don't actually explain the Special theory either.  E=MC squared is a math formula and doesn't explain what it means without an explanation either. Just because one knows the math doesn't mean they understand what it actually is saying. Do you know what n squared plus n divided by 2 = means and understand if it isn't explained? Solitary

[Jason78]

If it was that obvious I didn't write it myself, how is that plagiarizing?  :P

It's not always obvious.  Yet you post it as if it was your own words and fail to attribute a source.

[Jason78]

The math in the special theory wasn't too hard was it?  :roll:  Solitary

You've copied and pasted that from //http://web.pdx.edu/~egertonr/ph311-12/relativ.htm.  Anybody can do that.

Care to explain that math in your own words?

How can I explain math in my own words when it requires abstract symbols? :roll:  

How about like this without complicating everything like JosephPallazzo does with many formulas that don't show the gist of the theory: Guv=8pituv.  :rollin:  :rollin:  Solitary

Those abstract symbols actually mean something!

Those formulas are the core of physics.   Instead of moaning about how hard maths is, why not actually try applying it?  Get a spreadsheet, feed in the formula for the lorentz factor and play with the numbers.  Try and get a feel for what these formulas mean, and maybe they'll stop looking like abstract symbols and end up actually meaning something to you.

[Icarus]

No matter how many mathematical "explanations" of SR you can find, they don't actually explain the Special theory either.  E=MC squared is a math formula and doesn't explain what it means without an explanation either. Just because one knows the math doesn't mean they understand what it actually is saying. Do you know what n squared plus n divided by 2 = means and understand if it isn't explained? Solitary

Energy = Mass x Speed of light[sup:1jqun6u9]2[/sup:1jqun6u9] and the other less know version  M = (E[sub:1jqun6u9]0[/sub:1jqun6u9] + pV[sub:1jqun6u9]0[/sub:1jqun6u9])/c[sup:1jqun6u9]2[/sup:1jqun6u9] show the relationship of energy and mass in a system. The actual meaning of the symbols is self evident to anyone who's done any calculations regarding thermodynamics in a system (or other energy - system calculations). As the case with special relativity, all the symbols are known and understood by those who actually have to use the equations. Your example is terrible because you aren't defining n, thus suggesting the symbols in special relativity are not defined (which they are).

[Solitary]

No matter how many mathematical "explanations" of SR you can find, they don't actually explain the Special theory either.  E=MC squared is a math formula and doesn't explain what it means without an explanation either. Just because one knows the math doesn't mean they understand what it actually is saying. Do you know what n squared plus n divided by 2 = means and understand if it isn't explained? Solitary

Energy = Mass x Speed of light[sup:i6508z30]2[/sup:i6508z30] and the other less know version  M = (E[sub:i6508z30]0[/sub:i6508z30] + pV[sub:i6508z30]0[/sub:i6508z30])/c[sup:i6508z30]2[/sup:i6508z30] show the relationship of energy and mass in a system. The actual meaning of the symbols is self evident to anyone who's done any calculations regarding thermodynamics in a system (or other energy - system calculations). As the case with special relativity, all the symbols are known and understood by those who actually have to use the equations. Your example is terrible because you aren't defining n, thus suggesting the symbols in special relativity are not defined (which they are).

n can be any number by definition. I had a mathematics teacher answer what this means at this same forum when I was here originally. Calculate it with any number you want and the answer is obvious. Like you said:

The actual meaning of the symbols is self evident to anyone who's done any calculations

Solitary

[Icarus]

n can be any number by definition. I had a mathematics teacher answer what this means at this same forum when I was here originally. Calculate it with any number you want and the answer is obvious. Like you said:

The actual meaning of the symbols is self evident to anyone who's done any calculations

Solitary

Well yes, but without knowing n before you use the calculation you can't possibly understand what it is you're trying to calculate. In reference to my quote, when you're learning how to do the calculations you're also learning the context of the calculations. Without context math is, for all practical purposes, useless.

[Solitary]

n can be any number by definition. I had a mathematics teacher answer what this means at this same forum when I was here originally. Calculate it with any number you want and the answer is obvious. Like you said:

The actual meaning of the symbols is self evident to anyone who's done any calculations

Solitary

Well yes, but without knowing n before you use the calculation you can't possibly understand what it is you're trying to calculate. In reference to my quote, when you're learning how to do the calculations you're also learning the context of the calculations. Without context math is, for all practical purposes, useless.

Please explain how the mathematics teacher could if what you say is true. Take any natural number you want and replace n with that number and calculate. If you start with one and work your way up the answer is obvious. Solitary

[Icarus]

Please explain how the mathematics teacher could if what you say is true. Take any natural number you want and replace n with that number and calculate. If you start with one and work your way up the answer is obvious. Solitary

If what I'm saying is true a mathematics teacher could do that easily. The problem is context, if I gave a mathematics teacher this equation: [P+a(n/v)[sup:117df7gi]2[/sup:117df7gi]]((V/n)-b) = RT (Van Der Waals equation)

The mathematics teacher would look at the formula and be stumped because (lets assume) he doesn't understand the context of the equation. He could spend any amount of time replacing values with different numbers but he would never discover how to use the formula without context.

[Colanth]

No matter how many mathematical "explanations" of SR you can find, they don't actually explain the Special theory either.

Since the theory IS math, that's not true.  1 + 1 = 2 completely and sufficiently explains 1 + 1 = 2.

E=MC squared is a math formula and doesn't explain what it means without an explanation either.

Unless you understand what E m and c are, in which case it does.

I'm not talking about a "pop-sci" "explanation" for the masses (which is usually incorrect, insufficient and explains nothing), but an explanation that mathematicians can understand.  Anything else is like explaining a French pun to someone who doesn't speak French.  You can explain the words, but that doesn't explain why they're funny.  And by the time you get to why they're funny, no one's listening any more.

Sure you can "explain" SR without math.  But it's not complete, it's not sufficient and it's not accurate.  "That blue fish floating above the ground" doesn't actually "explain" what a fish swimming under water is, but that's closer than most verbal explanations of SR (or GR).

Just because one knows the math doesn't mean they understand what it actually is saying.

Well ... "knowing the math" MEANS "understanding what it's saying".  Knowing how to reduce a formula isn't knowing the math, it's knowing some mechanical operations.

Do you know what n squared plus n divided by 2 = means and understand if it isn't explained?

In no context?  Of course not.  You don't know what "Red" means out of context either.  But "SR" is its own context.

[Colanth]

If you start with one and work your way up the answer is obvious.

The answer is obvious in context.  Unless you're discussing triangular numbers (which you probably had in that class), the answer is, at best, ambiguous.

[Solitary]

No matter how many mathematical "explanations" of SR you can find, they don't actually explain the Special theory either.

Since the theory IS math, that's not true.  1 + 1 = 2 completely and sufficiently explains 1 + 1 = 2.

So 1 apple + 1 apple is the same as 1 apple +1 pear?

E=MC squared is a math formula and doesn't explain what it means without an explanation either.

Unless you understand what E m and c are, in which case it does.

But that's my point, unless you are explained to what E m and c are you have no idea what it means.

I'm not talking about a "pop-sci" "explanation" for the masses (which is usually incorrect, insufficient and explains nothing), but an explanation that mathematicians can understand.  Anything else is like explaining a French pun to someone who doesn't speak French.  You can explain the words, but that doesn't explain why they're funny.  And by the time you get to why they're funny, no one's listening any more.

Sure you can "explain" SR without math.  But it's not complete, it's not sufficient and it's not accurate.  "That blue fish floating above the ground" doesn't actually "explain" what a fish swimming under water is, but that's closer than most verbal explanations of SR (or GR).

Explain how it is not complete in order to understand what the theory is about? I know red is a certain frequency of electromagnetic waves without the math.

Just because one knows the math doesn't mean they understand what it actually is saying.

Well ... "knowing the math" MEANS "understanding what it's saying".  Knowing how to reduce a formula isn't knowing the math, it's knowing some mechanical operations.

Again, you know the math for n squared + n divided by 2 is, but do you know what it means?

It's not out of context if you can provide the answer for what it means which you can.

The answer is any natural number for n gives you the addition of all the numbers up to n using that formula. Until this is explained or calculated you have no idea what it is saying. Solitary

[Colanth]

No matter how many mathematical "explanations" of SR you can find, they don't actually explain the Special theory either.

Since the theory IS math, that's not true.  1 + 1 = 2 completely and sufficiently explains 1 + 1 = 2.

So 1 apple + 1 apple is the same as 1 apple +1 pear?

No, that just demonstrates a lack of understanding of arithmetic (or an oversupply of wiseassery).

E=MC squared is a math formula and doesn't explain what it means without an explanation either.

Unless you understand what E m and c are, in which case it does.

But that's my point, unless you are explained to what E m and c are you have no idea what it means.

Or unless you understand math and physics.

Again, there's a difference between a complete and sufficient explanation (and don't confuse the two - complete and sufficient are completely different), and a pop-science "explanation" that doesn't actually explain anything, but it makes those too lazy or too stupid to actually learn enough to understand the subject think that they understand it.

Sure you can "explain" SR without math.  But it's not complete, it's not sufficient and it's not accurate.  "That blue fish floating above the ground" doesn't actually "explain" what a fish swimming under water is, but that's closer than most verbal explanations of SR (or GR).

Explain how it is not complete in order to understand what the theory is about? I know red is a certain frequency of electromagnetic waves without the math.

Now you're talking about linguistics, not physics.  "Red" is DEFINED as the name we give to a certain band of electromagnetic frequencies.  So you understand the definition.

Again, you know the math for n squared + n divided by 2 is, but do you know what it means?

It doesn't MEAN anything.  IT COULD BE referring to triangular numbers.  But it could also be referring to other things.  Out of context it's meaningless.

It's not out of context if you can provide the answer for what it means which you can.

It's totally out of context.  (Evidently you don't understand the concept of "context".)

The answer is any natural number for n gives you the addition of all the numbers up to n using that formula. Until this is explained or calculated you have no idea what it is saying.

It's actually "the sum" not "the addition" - and that description, "the sum of all integers from 1 to n", is math.  "All numbers up to n" gives you the sum of an infinite number of numbers, since "number" isn't limited to integers.  Describing an upper-case sigma, with an n on top, a k to the right and "k=1" on the bottom won't really tell you anything, but that's what the words are actually saying.  So you're just describing a formula in words.

SR is a special case of GR, and GR isn't simple enough to completely and sufficiently "describe" without using math.

I can describe beef stew without using genetics, but I can't fully and sufficiently describe "cow" without using genetics.  (Almost any "word" definition of "cow" that's not self-referential is ambiguous.)

(Oh, and it would make responding to you a lot easier if you used the quote tags properly.  Coloring text doesn't put quote tags around it.)

[entropy]

There's something that isn't clear to me in this discussion. It's about what "actually contracted" means in this context. If there were a an absolute, fixed length dimension, then I could readily see how a length could be contracted with reference to that absolute, fixed length dimension and thus what "actually contracted" means ("actually contracted" meaning contracted with reference to a fixed, absolute length of a spatial dimension). But if there is no absolute, fixed length dimension that is a reference, then what length is being referenced to say that a contraction is actual?

I am not trying to claim that people are mistaken in saying that such a contraction is actual; what I'm wondering is if what may be going on here is that different people mean different things when they use the term "actual" in this context. I ask the above question to see if it may help ferret out any such differences in conception of what an "actual contraction of length" means, if there are any such differences.

[josephpalazzo]

There's something that isn't clear to me in this discussion. It's about what "actually contracted" means in this context. If there were a an absolute, fixed length dimension, then I could readily see how a length could be contracted with reference to that absolute, fixed length dimension and thus what "actually contracted" means ("actually contracted" meaning contracted with reference to a fixed, absolute length of a spatial dimension). But if there is no absolute, fixed length dimension that is a reference, then what length is being referenced to say that a contraction is actual?

I am not trying to claim that people are mistaken in saying that such a contraction is actual; what I'm wondering is if what may be going on here is that different people mean different things when they use the term "actual" in this context. I ask the above question to see if it may help ferret out any such differences in conception of what an "actual contraction of length" means, if there are any such differences.

The best way to figure out things in SR is with graphics. You can represent one observer in a t-x graph, and a second one in a t' - x' axis.



In the case of length contraction, consider the ends of a meter stick that stand initially at the origin d(0,0) and at e(0,L). It is at rest in the unprimed frame of reference. And the two parallel lines in red indicate this. The dash line at 45° represents the speed of light ( t = x). The moving observer in the primed frame of reference will see a different meter stick. The moving observer will measure the meter stick along a synchronous time, which is the x'-axis, or t=vx, which will be the points d and f. But remember that df is really the proper time, a Lorentz invariant. What is the length that the moving observer measures? To find that, we must locate the x'-coordinate of the point f((0', L').

(1) t'[sup:1c2hvwb9]2[/sup:1c2hvwb9] – x'[sup:1c2hvwb9]2[/sup:1c2hvwb9]  =  t[sup:1c2hvwb9]2[/sup:1c2hvwb9] – x[sup:1c2hvwb9]2[/sup:1c2hvwb9]

Substituting,
(2) (0')[sup:1c2hvwb9]2[/sup:1c2hvwb9] – L'[sup:1c2hvwb9]2[/sup:1c2hvwb9] =  (vx)[sup:1c2hvwb9]2[/sup:1c2hvwb9] – x[sup:1c2hvwb9]2[/sup:1c2hvwb9]

(3) – L'[sup:1c2hvwb9]2[/sup:1c2hvwb9] =  v[sup:1c2hvwb9]2[/sup:1c2hvwb9]L[sup:1c2hvwb9]2[/sup:1c2hvwb9] – L[sup:1c2hvwb9]2[/sup:1c2hvwb9]
or L'[sup:1c2hvwb9]2[/sup:1c2hvwb9] =  – v[sup:1c2hvwb9]2[/sup:1c2hvwb9]L[sup:1c2hvwb9]2[/sup:1c2hvwb9]  +  L[sup:1c2hvwb9]2[/sup:1c2hvwb9]
                                                               
(4) L'[sup:1c2hvwb9]2[/sup:1c2hvwb9] =  (– v[sup:1c2hvwb9]2[/sup:1c2hvwb9]  +  1)L[sup:1c2hvwb9]2[/sup:1c2hvwb9]
 
(5) L'[sup:1c2hvwb9]2[/sup:1c2hvwb9] =  ( 1  –   v[sup:1c2hvwb9]2[/sup:1c2hvwb9] )L[sup:1c2hvwb9]2[/sup:1c2hvwb9]

Taking the square root and putting c back into the equation,
                                     
(6) moving ruler  =  stationary ruler (1  –  v[sup:1c2hvwb9]2[/sup:1c2hvwb9]/c[sup:1c2hvwb9]2[/sup:1c2hvwb9])[sup:1c2hvwb9]1/2[/sup:1c2hvwb9]
                                                               
We see that a moving meter will shrink.

[entropy]

There's something that isn't clear to me in this discussion. It's about what "actually contracted" means in this context. If there were a an absolute, fixed length dimension, then I could readily see how a length could be contracted with reference to that absolute, fixed length dimension and thus what "actually contracted" means ("actually contracted" meaning contracted with reference to a fixed, absolute length of a spatial dimension). But if there is no absolute, fixed length dimension that is a reference, then what length is being referenced to say that a contraction is actual?

I am not trying to claim that people are mistaken in saying that such a contraction is actual; what I'm wondering is if what may be going on here is that different people mean different things when they use the term "actual" in this context. I ask the above question to see if it may help ferret out any such differences in conception of what an "actual contraction of length" means, if there are any such differences.

The best way to figure out things in SR is with graphics. You can represent one observer in a t-x graph, and a second one in a t' - x' axis.

[ Image ]

In the case of length contraction, consider the ends of a meter stick that stand initially at the origin d(0,0) and at e(0,L). It is at rest in the unprimed frame of reference. And the two parallel lines in red indicate this. The dash line at 45° represents the speed of light ( t = x). The moving observer in the primed frame of reference will see a different meter stick. The moving observer will measure the meter stick along a synchronous time, which is the x'-axis, or t=vx, which will be the points d and f. But remember that df is really the proper time, a Lorentz invariant. What is the length that the moving observer measures? To find that, we must locate the x'-coordinate of the point f((0', L').

(1) t'[sup:2n49rp3n]2[/sup:2n49rp3n] – x'[sup:2n49rp3n]2[/sup:2n49rp3n]  =  t[sup:2n49rp3n]2[/sup:2n49rp3n] – x[sup:2n49rp3n]2[/sup:2n49rp3n]

Substituting,
(2) (0')[sup:2n49rp3n]2[/sup:2n49rp3n] – L'[sup:2n49rp3n]2[/sup:2n49rp3n] =  (vx)[sup:2n49rp3n]2[/sup:2n49rp3n] – x[sup:2n49rp3n]2[/sup:2n49rp3n]

(3) – L'[sup:2n49rp3n]2[/sup:2n49rp3n] =  v[sup:2n49rp3n]2[/sup:2n49rp3n]L[sup:2n49rp3n]2[/sup:2n49rp3n] – L[sup:2n49rp3n]2[/sup:2n49rp3n]
or L'[sup:2n49rp3n]2[/sup:2n49rp3n] =  – v[sup:2n49rp3n]2[/sup:2n49rp3n]L[sup:2n49rp3n]2[/sup:2n49rp3n]  +  L[sup:2n49rp3n]2[/sup:2n49rp3n]
                                                               
(4) L'[sup:2n49rp3n]2[/sup:2n49rp3n] =  (– v[sup:2n49rp3n]2[/sup:2n49rp3n]  +  1)L[sup:2n49rp3n]2[/sup:2n49rp3n]
 
(5) L'[sup:2n49rp3n]2[/sup:2n49rp3n] =  ( 1  –   v[sup:2n49rp3n]2[/sup:2n49rp3n] )L[sup:2n49rp3n]2[/sup:2n49rp3n]

Taking the square root and putting c back into the equation,
                                     
(6) moving ruler  =  stationary ruler (1  –  v[sup:2n49rp3n]2[/sup:2n49rp3n]/c[sup:2n49rp3n]2[/sup:2n49rp3n])[sup:2n49rp3n]1/2[/sup:2n49rp3n]
                                                               
We see that a moving meter will shrink.

I think I follow that, but it still isn't clear to me why this implies that the contraction is "actual" unless the stationary ruler is taken to be "the preferred" reference frame in terms of measurement of length. In a sense, it appears you want to treat the stationary ruler as though it were a fixed, absolute reference frame for length in terms of determining whether or not the moving ruler has "actually" contracted. Is there some reason to treat the stationary ruler as being preferred with respect to measuring length over the moving ruler? To put it another way, it's seems like you are saying that with respect to the stationary ruler, the moving ruler is contracted, therefore the contraction is 'actual'. But from the reference frame of the moving ruler, it is not contracted, therefore couldn't it be just as validly claimed that with respect to the reference frame of the moving ruler that there is no 'actual" contraction?