Relativity, speed of light and stuff

[ricmat]

Hi guys!

this is my first post here, and I would like to ask a few questions concerning relativity, speed of light and concerning stuff.
I know that a lot has already been talked around here about this areas, but I have not found one thread that puts this issue in the way I would like to put it.

First, I would like to make just a few points about my background:
-I am not a physic, nor I have some background in physics, apart from school teaching, obviously
-I've read some books, threads, posts and articles about physics, but that is pretty much my background!
-So, please, if you mind to answer this thread be critic. If I'll say something very stupid, please state so! just let me know. I really love to learn and discuss this topics.





So, my issues:

My very first doubt urged when I read about einstein. I am a strong fan of Newton, but I have to admit I do not "like" the way Einstein aproaches all concepts in his theories.

My point is just a simple one: I do not understand why do physics consider light so much special! Why is its speed the limit!

I have read a lot about this, and how the very nature of light (not a wave, but a wave-particle) is so important to define speed of light as the limit. or even as it is calculated from the relations within universe laws.

My point is just this one - if we are sublight beings (we work tops at light speed minus chemicals relations in our neurons), if all our creations are sublight (a computer can't work at light speed) ... ... ...

how can we measure light speed if we work, tops, at sublight? how can we say that there is nothing that can travel faster than speed of light if we can't "see" at over speed of light?


this is - if we had no eyes, and only ears, wouldn't we think that sound speed would be the greatest speed ever? wouldn't Einstein put "c" as the speed of sound?

of course we never experienced for sure faster than light experiences. but is that possible? we have no machines working at that speed! Is there a flaw in my reasoning?

and i even can't understand that argument people usually say, that if one travels that speed of light it would almost like we do something before it occurs - how is that?

yes, we would do something and then travel faster than the speed of light, but that's not time travel. It is just like making a sound and then traveling at mach 3, only multiplied many times, but not even close to "change" time line

This is not so obvious for me, and I have never read anything that answered this question clearly.


I have also read something stating that it actually makes sense once we are the ones to "analyse" all this phenomena, and it makes sense to the actual observer (us, humans) but for me physics is the study of nature rules, and not nature rules as seen by humans. At least, that's the way I see it!


Hope to discuss this further with you!


Cheers,
ricmat

 

[berkeman]

This article should answer most of your questions, including how the speed of light is measured, and the issues concerning FTL.

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


.

 

[JesseM]

The "specialness" of the speed of light basically has to do with the way the laws of physics look in different coordinate systems. If you know something about Newtonian physics you may be familiar with the idea of inertial coordinate systems, where different inertial (non-accelerating) observers can construct coordinate systems to assign position and time coordinates to different events, and each observer's own rest frame is the one where his own position coordinate isn't changing with time. In Newtonian coordinate systems, if you have two observers in motion relative to one another, then naturally they will get different values for the speed of some object in their own coordinate systems. This means that in Newtonian coordinate systems, if Maxwell's equations of electromagnetism work in one observer's coordinate system they can't work in the coordinate system of a different observer moving relative to the first, since Maxwell's equations predict that the speed of light is c, and if they were c in the coordinate system of the first observer and the second observer was moving at speed v relative to the first, then the second observer would measure the light to be moving at v+c or v-c. So Einstein's work was in part an attempt to construct a different set of coordinate systems than the Newtonian ones, such that Maxwell's laws could work correctly in every observer's coordinate system. The set of coordinate systems he found are related to one another by a set of equations called the "Lorentz transformation", which is different from the "Galilei transformation" which relates the coordinates of different inertial observers in Newtonian physics. Einstein also made the postulate that if we use such coordinates, all the fundamental laws of physics (not just Maxwell's laws) will turn out to obey the same equations in all these coordinate systems, a property known as "Lorentz-invariance". This postulate has shown to be correct as more fundamental laws continued to be discovered (asking why all the laws of physics obey this symmetry is not really something that physicists can answer, their job is only to discover what the laws of nature are like, not why the laws have the particular form they do and not some other). You could indeed construct a different set of coordinate systems where the speed of sound waves (or some other object) was the same in each coordinate system, the difference is that the known laws of physics would not show the same sort of symmetry with respect to these coordinate systems.

 

[rbj]

it's not just visible light.
nor is it just electromagnetic interaction (of which light is).

all fundamental interactions (caused by a generating agent) have their effect (on the responding agent) delayed by a time (as observed by a third party equal distant from the two agents) that is proportional to the distance between the cause and effect agent. whether the two of us are holding charges that are attracted (by the E&M action) to each other or the two of us are much bigger and holding planets that are attracted (by gravitation) to each other, if i wave my charge (or planet) around, your charge (or planet) will be disturbed accordingly. the time between my agitation and the disturbance you detect will be longer (as observed by the third party) if the distance between you and me is longer. that implies a speed of interaction. that speed is the same whether it's E&M (light), gravity, or the nuclear forces. and there aren't any other interactions that we know about. it's a property of space and time (and the relationship betwixt the two), not specifically of light, nuclear forces, or gravitational attraction.

 

[Dale]

if we had no eyes, and only ears, wouldn't we think that sound speed would be the greatest speed ever? wouldn't Einstein put "c" as the speed of sound?

Hi ricmat, welcome to PF

I have to admit that I didn't understand special relativity for several years using exactly this same line of reasoning. The key difference between sound and light is that sound requires a medium in which to propagate and light does not.

The speed of sound is only constant wrt its medium, and can be measured faster or slower depending on the speed of the medium wrt the measuring apparatus. We can detect the motion of the medium with many other techniques (e.g. finger in the wind) and accurately determine what the speed of sound should be in our reference frame.

By contrast, since there is no medium for light, the speed of light is never measured faster or slower than c regardless of the speed of the measuring apparatus. We cannot in any way detect the motion of empty space (this is essentially what M&M were trying to do), and so the speed of light is always c in any reference frame.

I hope this helps, because I understand your reasoning since I used it too for many years.

 

[atyy]

Although we are sublight beings, we can measure the speed of light by making it go over a very great distance, so that the time interval measured is very long.

But this is not so relevant. The constancy of the speed of light actually comes from the Newtonian idea that if you are in a car, the cars going in the same direction will seem to move more slowly, and cars going in the opposite direction will seem to approach more quickly than if you were standing by the road.

In the Michelson-Morley experiment, the car is the Earth going round the sun. At different times of the year, the Earth is going in different directions, and so if light is moving with respect to some external medium, it should change its speed according to the time of the year. The change should be around 15 m/s, which perhaps you will more readily believe sublight beings can detect?

 

[ricmat]

Thank you guys for your quick answers.

a lot of food for thought to digest, and little time to do so! so sorry for not being able to address all points, but i'll do soon.


just a quick answer to DaleSpam:

Hi ricmat, welcome to PF

I have to admit that I didn't understand special relativity for several years using exactly this same line of reasoning. The key difference between sound and light is that sound requires a medium in which to propagate and light does not.

The speed of sound is only constant wrt its medium, and can be measured faster or slower depending on the speed of the medium wrt the measuring apparatus. We can detect the motion of the medium with many other techniques (e.g. finger in the wind) and accurately determine what the speed of sound should be in our reference frame.

By contrast, since there is no medium for light, the speed of light is never measured faster or slower than c regardless of the speed of the measuring apparatus. We cannot in any way detect the motion of empty space (this is essentially what M&M were trying to do), and so the speed of light is always c in any reference frame.

I hope this helps, because I understand your reasoning since I used it too for many years.

so great i find a person who has already thought the same way. I just have one question, as I seem to find a flaw in your reasoning: light does not travel the same way in each mean! as we can find in the link above mentioned:

"Light traveling through a medium such as air (for example, this laser) travels slower than light through a vacuum."


my question is - yes, sound do not travels in vacuum, but they are different kind of waves! one is mechanic the other one is electromagnetic, so that maybe the reason!
I would just like to recall that before einstein we thought that there was no vacuum, and light traveled through ether... i have a phd friend in cosmology, who told me very recently that this very same thesis as come up more and more in present days again... it seem that there is no consensus among today scientist that there is no "something" like ether as opposite to vacuum...

 

[granpa]

The speed of sound is only constant wrt its medium, and can be measured faster or slower depending on the speed of the medium wrt the measuring apparatus. We can detect the motion of the medium with many other techniques (e.g. finger in the wind) and accurately determine what the speed of sound should be in our reference frame.
.

thats perfectly true, but if you became length contracted, time dilated, and experienced loss of simultaneity as you approached mach one then you would not be able to detect any change in the speed of sound.

 

[FeynmanMH42]

I just have one question, as I seem to find a flaw in your reasoning: light does not travel the same way in each mean! as we can find in the link above mentioned:

"Light traveling through a medium such as air (for example, this laser) travels slower than light through a vacuum."


my question is - yes, sound do not travels in vacuum, but they are different kind of waves! one is mechanic the other one is electromagnetic, so that maybe the reason!

Ahh, but the speed of light in a medium is irrelevant. There's no law saying that the speed of light in glass is a universal constant - in fact it's perfectly okay to travel faster than the speed of light passing through a medium, and this can produce http://en.wikipedia.org/wiki/Cherenkov_radiation"
Special relativity is based upon the speed of light in a vacuum only. There is something special about this speed BECAUSE then light is traveling only through a vaccuum... get me?

 

[Dale]

I seem to find a flaw in your reasoning: light does not travel the same way in each mean! as we can find in the link above mentioned

The constant, c, refers to the speed of light exclusively in vacuum, which is the same for all inertial observers. I agree with FeynmanMH42's comments above.

 

[Dale]

thats perfectly true, but if you became length contracted, time dilated, and experienced loss of simultaneity as you approached mach one then you would not be able to detect any change in the speed of sound.

Yes, and if such things happened then the invariant speed would be mach one, light would travel at the speed of sound, and tornados would be relativistic phenomena.

 

[granpa]

Yes, and if such things happened then the invariant speed would be mach one, light would travel at the speed of sound, and tornados would be relativistic phenomena.

of course. but nobody would be claiming that because its velocity is the same for all observers that sound doesn't have a medium.

 

[Dale]

nobody would be claiming that because its velocity is the same for all observers that sound doesn't have a medium.

Of course not. But think about it. Why not?

 

[granpa]

I imagine that you mean that we can't stick our hand out the window and feel the breeze of the aether going by. but particles are waves too. If we are also waves in the aether then we should hardly expect to be able to do so.

 

[Dale]

Precisely, there are many physical experiments that we can do to measure the velocity of air. There are no experiments that we can do to measure the velocity of the vacuum.

 

[rbj]

of course. but nobody would be claiming that because its velocity is the same for all observers that sound doesn't have a medium.

i might claim that, given the premise (which we don't believe).

 

[Doc Al]

but nobody would be claiming that because its velocity is the same for all observers that sound doesn't have a medium.

The speed of sound is not the same for all observers.

 

[granpa]

The speed of sound is not the same for all observers.

you seem to have missed the 'would' in my post.

read post 8

 

[Doc Al]

you seem to have missed the 'would' in my post.

read post 8

Oops. My bad.

 

[granpa]

i might claim that, given the premise.

An engineer, a mathematician, and a physicist were traveling through Scotland when they saw a black sheep through the window of the train.
"Aha," says the engineer, "I see that Scottish sheep are black."
"no," says the mathematician, "You mean that some Scottish sheep are black."
unable to agree, they asked the physicist to decide which was the correct statement.
The physicist thought for a moment then said "there is one sheep in Scotland and it is black on one side".

 

[rbj]

of course. but nobody would be claiming that because its velocity is the same for all observers that sound doesn't have a medium.

i might claim that, given the premise (which we don't believe).

An engineer, a mathematician, and a physicist were traveling through Scotland when they saw a black sheep through the window of the train.
"Aha," says the engineer, "I see that Scottish sheep are black."
"no," says the mathematician, "You mean that some Scottish sheep are black."
unable to agree, they asked the physicist to decide which was the correct statement.
The physicist thought for a moment then said "there is one sheep in Scotland and it is black on one side".

... if you became length contracted, time dilated, and experienced loss of simultaneity as you approached mach one then you would not be able to detect any change in the speed of sound.

i don't know gramps, the observer approaching c (from the perspective of some other observer) does not, from his/her own POV, become length contracted, time dilated, etc. life is perfectly normal for him or her yet he/she still observes no variance in c. if we measured the speed of sound (whatever that could be if it wasn't the compressions and rarefractions of air) to be invariant no matter which direction or how fast we were moving (w.r.t. something, perhaps the ground), then we can conclude that either the medium that sound propagates in is smart enough to move along with us at whatever velocity we move, or there isn't such a medium.

 

[granpa]

i don't know gramps, the observer approaching c (from the perspective of some other observer) does not, from his/her own POV, become length contracted, time dilated, etc. life is perfectly normal for him or her

so? what's your point?

if we measured the speed of sound (whatever that could be if it wasn't the compressions and rarefractions of air) to be invariant no matter which direction or how fast we were moving (w.r.t. something, perhaps the ground), then we can conclude that either the medium that sound propagates in is smart enough to move along with us at whatever velocity we move, or there isn't such a medium.

the premise of this whole hypothetical argument was a person becoming length contracted, time dilated, and experiencing loss of simultaneity as they approach mach one. this would cause the speed of sound to be the same for all observers and it certainly wouldn't cause the medium of sound to magically disappear.

 

[granpa]

of course. but nobody would be claiming that because its velocity is the same for all observers that sound doesn't have a medium.

i might claim that, given the premise (which we don't believe).

An engineer, a mathematician, and a physicist were traveling through Scotland when they saw a black sheep through the window of the train.
"Aha," says the engineer, "I see that Scottish sheep are black."
"No," says the mathematician, "You mean that some Scottish sheep are black."
Unable to agree, they asked the physicist to decide which was the correct statement.
The physicist thought for a moment then said "there is one sheep in Scotland and it is black on one side".

I messed it up. My memory isn't what it should be.

An engineer, a mathematician, and a physicist were traveling through Scotland when they saw a flock of black sheep through the window of the train.
The engineer says "From this observation we can deduce that Scottish sheep are black."
"no," says the mathematician, "We can only deduce that some Scottish sheep are black."
Unable to agree, they asked the physicist to decide which was the correct statement.
The physicist thought for a moment then said "there is one flock of sheep in Scotland and they are black on one side".[/QUOTE]

 

[Primordial]

The constant, c, refers to the speed of light exclusively in vacuum, which is the same for all inertial observers. I agree with FeynmanMH42's comments above.

Is this true , where the electromagnetic interaction is exiting the event horizon of a black hole, or is the event horizon considered to be something other than vacuum?

 

[JesseM]

Is this true , where the electromagnetic interaction is exiting the event horizon of a black hole, or is the event horizon considered to be something other than vacuum?

When physicists say the speed of light in a vacuum is always c, they are talking either about an inertial coordinate system in the flat spacetime of special relativity, or a "locally inertial" coordinate system of a freefalling observer in the curved spacetime of general relativity ('locally' because the coordinate system only covers a very small region in the neighborhood of the observer, small enough that the curvature of spacetime is negligible). A freefalling observer passing by a light beam leaving a black hole will still measure the speed of that beam to be c in his own local neighborhood, even if he crosses paths with the light beam at the same moment he reaches the event horizon (from his perspective at that moment, the event horizon also seems to be moving outward at exactly c). On the other hand, in the Schwarzschild coordinate system which is often used to describe the entire black hole, light may move at different speeds at different distances from the black hole, but that's OK because this is not an inertial coordinate system (even in flat SR spacetime you can use non-inertial coordinate systems where the speed of light may be different at different points in space).

 

[rbj]

the premise of this whole hypothetical argument was a person becoming length contracted, time dilated, and experiencing loss of simultaneity as they approach mach one. this would cause the speed of sound to be the same for all observers and it certainly wouldn't cause the medium of sound to magically disappear.

just that it would have no measureable properties.

if the aether exists but has no measureable or perceivable properties whatsoever, what difference does it make if it exists or not? it may as well be pixie-dust or The Force or whatever it is in anyone's religion. if some hypothesized something is utterly unmeasureable, that's a pretty good indicator that it's non-existant.

that's the point. (that you should instead be mindful about it magically appearing rather than it magically disappearing. it never appeared in the first place.)

 

[rbj]

oh, and the other point is that the time dilation and length contraction are the effect and the invariancy of c is the cause.

 

[JesseM]

just that it would have no measureable properties.

if the aether exists but has no measureable or perceivable properties whatsoever, what difference does it make if it exists or not? it may as well be pixie-dust or The Force or whatever it is in anyone's religion? if some hypothesized something is utterly unmeasureable, that's a pretty good indicator that it's non-existant.

But in the thought-experiment where the speed of sound is the ultimate limit, air would still have measurable properties--it would be made of molecules, for example, and so any given region of air would have a specific average rest frame. If you had two air-filled ships passing by one another, and in each ship the air was at rest with respect to its own ship, it would be true that if people on board each ship clapped at the moment their positions lined up, then each would measure the sound wave on the other ship to move at the same speed as their own sound wave in spite of the fact that the two sound waves would be traveling through regions of air with different rest frames. Of course this wouldn't be true in our universe because clocks don't approach a rate of zero ticking as you approach the speed of sound, and rulers don't approach being compressed to zero length as you approach the speed of sound. But as a thought-experiment I don't see anything inherently impossible about a universe where the above was true.

 

[JesseM]

oh, and the other point is that the time dilation and length contraction are the effect and the invariancy of c is the cause.

Only if you choose to derive length contraction and time dilation from the two postulates that Einstein used. But nothing would stop you from taking length contraction and time dilation as postulates, and deriving the fact that anything moving at c in one inertial frame will be measured to move at c in all other inertial frames; there aren't really any fundamental physical concerns that force you to conclude which of these is a postulate and which is a conclusion, it's more of an aesthetic choice (sort of like how there are multiple different sets of theorems you might use to constitute the axioms of geometry or arithmetic, which would be equivalent in the sense that they wouldn't give different answers to whether or not a given theorem is true or false).

 

[rbj]

Precisely, there are many physical experiments that we can do to measure the velocity of air. There are no experiments that we can do to measure the velocity of the vacuum.

that (the meaninglessness of a moving vacuum) is why, i believe, Einstein, though he was likely knowledgeable of the Michaelson-Morley experiment and null result, was never surprized by that null result. when asked about some of the properties of nature, he was quoted as questioning if God had any other choice (in how nature had come out). not implying that Einstein was a theist in the traditional sense, he said he "believe[d] in Spinoza's God, who reveals Himself in the lawful harmony of the world,..."

 

[rbj]

Only if you choose to derive length contraction and time dilation from the two postulates that Einstein used. But nothing would stop you from taking length contraction and time dilation as postulates, ...

Occam's razor.

 

[rbj]

But in the thought-experiment where the speed of sound is the ultimate limit, air would still have measurable properties--it would be made of molecules, for example, and so any given region of air would have a specific average rest frame. If you had two air-filled ships passing by one another, and in each ship the air was at rest with respect to its own ship,

again, Occam's razor. sure, somehow the aether which really exists is smart enough to move around the Sun along with the Earth because it knows that Michaelson and Morley are set out to measure our speed through it. the aether sticks to the planet's surface no matter what time of day or what season of the year. so that's why the experiment had a null result.

it would be true that if people on board each ship clapped at the moment their positions lined up, then each would measure the sound wave on the other ship to move at the same speed as their own sound wave in spite of the fact that the two sound waves would be traveling through regions of air with different rest frames. Of course this wouldn't be true in our universe because clocks don't approach a rate of zero ticking as you approach the speed of sound, and rulers don't approach being compressed to zero length as you approach the speed of sound. But as a thought-experiment I don't see anything inherently impossible about a universe where the above was true.

but silly and complicated explanations of observed phenomena are deprecated in favor of concise explanations. sure, you can say that it's because of the length contraction and time dilation that we measure c to be invariant, but you offer no mechanism for why such length contraction and time dilation would happen in the first place.

 

[granpa]

If you had two air-filled ships passing by one another, and in each ship the air was at rest with respect to its own ship, it would be true that if people on board each ship clapped at the moment their positions lined up, then each would measure the sound wave on the other ship to move at the same speed as their own sound wave .

I don't agree with that.

 

[JesseM]

I don't agree with that.

I think you missed the point, I was speaking in the context of your own thought-experiment where, if mach 1 is represented by the symbol s, then moving clocks slow down by a factor of \sqrt{1 - v^2/s^2} and moving rulers shrink by the same factor. This would apply to things like the distance between air molecules in the direction of motion too, I'm assuming that all the laws of physics are invariant under the equivalent of a Lorentz Transformation with c replaced by s. In this case it would certainly be true that sound waves on the two ships would stay in line with one another as they moved.

 

[JesseM]

Occam's razor.

I'd say Occam's razor only applies to empirically different theories, not to different sets of logically equivalent axioms to be used in some formal proof.

 

[JesseM]

again, Occam's razor. sure, somehow the aether which really exists is smart enough to move around the Sun along with the Earth because it knows that Michaelson and Morley are set out to measure our speed through it. the aether sticks to the planet's surface no matter what time of day or what season of the year. so that's why the experiment had a null result.

Since when were we discussing the aether? Of course I don't believe in such a thing. I was discussing granpa's thought-experiment where length contraction and time dilation depend on the speed of sound, and I understood the point of this thought-experiment to be a pedagogical point about why in the real universe the speed of light is "special" in the way the speed of sound is not (essentially because the laws of physics are Lorentz-symmetric and the Lorentz transformation has c as its speed constant...if the laws of physics were symmetric under a transform that had the speed of sound as its speed constant, then the speed of sound would be 'special' in the same way the speed of light is in our universe, but they don't so it isn't).

sure, you can say that it's because of the length contraction and time dilation that we measure c to be invariant, but you offer no mechanism for why such length contraction and time dilation would happen in the first place.

No theory of physics offers a "mechanism" to explain why the fundamental laws of physics take the form they do. The goal of physics is just to discover what the fundamental equations are, not "why" they are.

 

[granpa]

I think you missed the point, I was speaking in the context of your own thought-experiment where, if mach 1 is represented by the symbol s, then moving clocks slow down by a factor of \sqrt{1 - v^2/s^2} and moving rulers shrink by the same factor. This would apply to things like the distance between air molecules in the direction of motion too, I'm assuming that all the laws of physics are invariant under the equivalent of a Lorentz Transformation with c replaced by s. In this case it would certainly be true that sound waves on the two ships would stay in line with one another as they moved.

ok. I guess you are right but what on Earth is your point? why would you want to move the air with the planes? its completely unnecessary. it adds nothing and distracts from the point I was making.

 

[granpa]

No theory of physics offers a "mechanism" to explain why the fundamental laws of physics take the form they do. The goal of physics is just to discover what the fundamental equations are not "why" they are.

excellent point.

 

[JesseM]

ok. I guess you are right but what on Earth is your point? why would you want to move the air with the planes? its completely unnecessary. it adds nothing and distracts from the point I was making.

What was the point you were making? As I said to rbj, I interpreted your point like this:

I understood the point of this thought-experiment to be a pedagogical point about why in the real universe the speed of light is "special" in the way the speed of sound is not (essentially because the laws of physics are Lorentz-symmetric and the Lorentz Transformation has c as its speed constant...if the laws of physics were symmetric under a transform that had the speed of sound as its speed constant, then the speed of sound would be 'special' in the same way the speed of light is in our universe, but they don't so it isn't).

So, showing that the speed of sound would remain constant in a universe with such a symmetry even if the medium it was traveling in moved at different speeds is quite relevant to this point, which is that it is symmetries in the laws of physics that determine what speed is special (and if these symmetries have picked out a particular speed as special then other issues, like whether or not some wave moving at that speed has a medium or not, become irrelevant, since the speed will be invariant regardless).

 

[granpa]

So, showing that the speed of sound would remain constant in a universe with such a symmetry even if the medium it was traveling in moved at different speeds is quite relevant to this point

NO. the point isn't that the speed of sound would be constant when the medium was moving. the point is that the speed of sound would be constant even when the observer was moving. why would the aether move?

 

[rbj]

I'd say Occam's razor only applies to empirically different theories, not to different sets of logically equivalent axioms to be used in some formal proof.

i'd say that Occam's razor applies to "explanation of any phenomenon [and prefers those that] make as few assumptions as possible, eliminating those [assumptions] that make no difference in the observable predictions of the explanatory hypothesis or theory."

you have one explanation that the laws of physics are identical for any inertial observer, independent of how these observers are passing through the vacuum (or that the concept of a moving vacuum, a moving nothing is meaningless). from that single postulate, many relativistic consequences can be predicted to be observed.

or you can set up a world of make-believe where time dilation and length contraction occur to fast moving objects for no apparent reason. it's just magic. and then a consequence of that time dilation and length contraction (which is inexplicable) is that the speed of the electromagnetic interaction (as well as gravity and nuclear interactions) are measured to be constant. Occam's razor perfectly applies to these two explanations.

 

[rbj]

No theory of physics offers a "mechanism" to explain why the fundamental laws of physics take the form they do. The goal of physics is just to discover what the fundamental equations are, not "why" they are.

excellent point.

to each his own, i guess.

i think the goal of physics is to discover what the fundamental causes and interactions are. that means discovering why some (less fundamental) phenomena occur as a consequence of more fundamental phenomena. John Baez wrote this in Wikipedia regarding fundamental physical constants:

The list of fundamental physical constants increases when experiments measure new relationships between physical phenomena. The list decreases when physical theory advances and shows how some previously fundamental constant can be computed in terms of others.

i don't think that I'm extrapolating too far to say that physical theory advances when it shows how some previously fundamental phenomenon can be derived or predicted in terms of other fundamental phenomena, thereby removing the first phenomenon from the list of fundamental interactions. that's what holy grails (GUTs) are supposed to be about.

the invariancy of the laws of physics (for inertial observers) is the fundamental principle, resulting in the constancy of c, and time dilation and length contraction are consequences of that. these are not fundamentally equivalent.

 

[atyy]

but silly and complicated explanations of observed phenomena are deprecated in favor of concise explanations. sure, you can say that it's because of the length contraction and time dilation that we measure c to be invariant, but you offer no mechanism for why such length contraction and time dilation would happen in the first place.

How about thinking about it this way:

1) We get Maxwell's equations from experiments done with currents, magnets, metal plates, metal wires, iron filings etc.

2) Maxwell's equations describe how the electromagnetic field changes when you move charges, magnets etc. These changes in the electromagnetic field provide a mechanism for length contraction, which can actually break things:

http://en.wikipedia.org/wiki/Bell's_spaceship_paradox

A good and entertaining reference is John Bell's "Speakable and Unspeakable in Quantum Mechanics".

 

[Al68]

No theory of physics offers a "mechanism" to explain why the fundamental laws of physics take the form they do. The goal of physics is just to discover what the fundamental equations are, not "why" they are.

I hate to disagree, but science is (from American Heritage Dictionary) the observation, identification, description, experimental investigation, and theoretical explanation of phenomena. I would say that length contraction and time dilation are "phenomena".

Of course the last part of that definition is not emphasized the way it used to be in science.

Al

 

[atyy]

BTW, the whole discussion about the speed of sound being the ultimately limit, and sound still having a medium. Wouldn't that seriously change our formulation of the laws of physics? Under the present formulation of special relativity, anything traveling with constant speed in any special relativistic inertial reference frame must have zero rest mass. So if experiments suggested that the thing with constant speed in any reference frame had mass, we might have to rethink how mass-energy transforms in a frame change. Or would we have to ditch the Principle of Special Relativity?

Actually, is this discussion equivalent to: What would the consequences be for our formulation of the laws of physics if the photon were measured to have mass?

I guess the photon would be demoted to a neutrino, and the Principle of Special Relativity would remain intact?

 

[granpa]

I think you mean 'anything moving at the speed of light must have zero rest mass'. is that right?

bear in mind that space itself expanded much faster than light shortly after the big bang.

 

[JesseM]

i think the goal of physics is to discover what the fundamental causes and interactions are. that means discovering why some (less fundamental) phenomena occur as a consequence of more fundamental phenomena.

Well, I agree in general, but you weren't talking about deriving some higher-level laws from more fundamental laws, instead you were just talking about different sets of logically equivalent sets of axioms for deriving precisely the same general laws of SR.

the invariancy of the laws of physics (for inertial observers) is the fundamental principle, resulting in the constancy of c, and time dilation and length contraction are consequences of that. these are not fundamentally equivalent.

But you were talking about different sets of axioms which could be used to derive Lorentz-symmetry, which presumably is what you mean by "the invariancy of the laws of physics (for inertial observers)". But a key point here is that this description is overly vague, since without some additional assumptions it could also describe Galilei symmetry in Newtonian physics. To derive Lorentz-symmetry, you can start from the axiom that all fundamental laws of physics are the same in every inertial frame, plus the axiom that the speed of light is the same in every inertial frame; or you can start from the axiom that all the fundamental laws of physics are the same in every inertial frame, plus the axiom that in each frame rulers moving at v are measured to shrink by \sqrt{1 - v^2/c^2} and that in each frame clocks moving at v are measured to have the time between ticks lengthened by 1 / \sqrt{1 - v^2/c^2}. These two possible sets of axioms are completely equivalent in terms of their physical implications.

 

[atyy]

I think you mean 'anything moving at the speed of light must have zero rest mass'. is that right?

bear in mind that space itself expanded much faster than light shortly after the big bang.

No, I meant what I wrote. I don't think the Principle of Special Relativity and the Lorentz transformations would work with 2 invariant speeds. At least one of them must give. I'm only thinking within SR, no GR, inflation etc.

 

[JesseM]

I hate to disagree, but science is (from American Heritage Dictionary) the observation, identification, description, experimental investigation, and theoretical explanation of phenomena. I would say that length contraction and time dilation are "phenomena".

Of course the last part of that definition is not emphasized the way it used to be in science.

Al

I don't think it's a good idea to approach questions in philosophy of science by appealing to dictionary definitions. The definition is good enough to cover most situations in science, where you're explaining some high-level laws governing a system by appealing to more fundamental laws which govern the basic parts of that system (reductionism); but when you reach the level of the most fundamental laws, what exactly would it mean to have a "theoretical explanation" of these laws?

Here is Feynman writing about this topic in The Character of Physical Law, using gravitation as an example:

On the other hand, take Newton's law for gravitation, which has the aspects I discussed last time. I gave you the equation:

F=Gmm'/r^2

just to impress you with the speed with which mathematical symbols can convey information. I said that the force was proportional to the product of the masses of two objects, and inversely as the square of the distance between them, and also that bodies react to forces by changing their speeds, or changing their motions, in the direction of the force by amounts proportional to the force and inversely proportional to their masses. Those are words all right, and I did not necessarily have to write the equation. Nevertheless it is kind of mathematical, and we wonder how this can be a fundamental law. What does the planet do? Does it look at the sun, see how far away it is, and decide to calculate on its internal adding machine the inverse of the square of the distance, which tells it how much to move? This is certainly no explanation of the machinery of gravitation! You might want to look further, and various people have tried to look further. Newton was originally asked about his theory--'But it doesn't mean anything--it doesn't tell us anything'. He said, 'It tells you how it moves. That should be enough. I have told you how it moves, not why.' But people are often unsatisfied without a mechanism, and I would like to describe one theory which has been invented, among others, of the type you migh want. This theory suggests that this effect is the result of large numbers of actions, which would explain why it is mathematical.

Suppose that in the world everywhere there are a lot of particles, flying through us at very high speed. They come equally in all directions--just shooting by--and once in a while they hit us in a bombardment. We, and the sun, are practically transparent for them, practically but not completely, and some of them hit. ... If the sun were not there, particles would be bombarding the Earth from all sides, giving little impuleses by the rattle, bang, bang of the few that hit. This will not shake the Earth in any particular direction, because there are as many coming from one side as from the other, from top as from bottom. However, when the sun is there the particles which are coming from that direction are partially absorbed by the sun, because some of them hit the sun and do not go through. Therefore the number coming from the sun's direction towards the Earth is less than the number coming from the other sides, because they meet an obstacle, the sun. It is easy to see that the farther the sun is away, of all the possible directions in which particles can come, a smaller proportion of the particles are being taken out. The sun will appear smaller--in fact inversely as the square of the distance. Therefore there will be an impulse on the Earth towards the sun that varies inversely as the square of the distance. And this will be the result of a large number of very simple operations, just hits, one after the other, from all directions. Therefore the strangeness of the mathematical relation will be very much reduced, because the fundamental operation is much simpler than calculating the inverse of the square of the distance. This design, with the particles bouncing, does the calculation.

The only trouble with this scheme is that it does not work, for other reasons. Every theory that you make up has to be analysed against all possible consequences, to see if it predicts anything else. And this does predict something else. If the Earth is moving, more particles will hit it from in front than from behind. (If you are running in the rain, more rain hits you in the front of the face than in the back of the head, because you are running into the rain.) So, if the Earth is moving it is running into the particles coming towards it and away from the ones that are chasing it from behind. So more particles will hit it from the front than from the back, and there will be a force opposing any motion. This force would slow the Earth up in its orbit, and it certainly would not have lasted the three of four billion years (at least) that it has been going around the sun. So that is the end of that theory. 'Well,' you say, 'it was a good one, and I got rid of the mathematics for a while. Maybe I could invent a better one.' Maybe you can, because nobody knows the ultimate. But up to today, from the time of Newton, no one has invented another theoretical description of the mathematical machinery behind this law which does not either say the same thing over again, or make the mathematics harder, or predict some wrong phenomena. So there is no model of the theory of gravity today, other than the mathematical form.

If this were the only law of this character it would be interesting and rather annoying. But what turns out to be true is that the more we investigate, the more laws we find, and the deeper we penetrate nature, the more this disease persists. Every one of our laws is a purely mathematical statement in rather complex and abstruse mathematics.

...[A] question is whether, when trying to guess new laws, we should use seat-of-the-pants feelings and philosophical principles--'I don't like the minimum principle', or 'I do like the minimum principle', 'I don't like action at a distance', or 'I do like action at a distance'. To what extent do models help? It is interesting that very often models do help, and most physics teachers try to teach how to use models and to get a good physical feel for how things are going to work out. But it always turns out that the greatest discoveries abstract away from the model and the model never does any good. Maxwell's discovery of electrodynamics was made with a lot of imaginary wheels and idlers in space. But when you get rid of all the idlers and things in space the thing is O.K. Dirac discovered the correct laws for relativity quantum mechanics simply by guessing the equation. The method of guessing the equation seems to be a pretty effective way of guessing new laws. This shows again that mathematics is a deep way of expressing nature, and any attempt to express nature in philosophical principles, or in seat-of-the-pants mechanical feelings, is not an efficient way.

It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities. But this speculation is of the same nature as those other people make--'I like it', 'I don't like it',--and it is not good to be too prejudiced about these things.

 

[Fredrik]

I hate to disagree, but science is (from American Heritage Dictionary) the observation, identification, description, experimental investigation, and theoretical explanation of phenomena. I would say that length contraction and time dilation are "phenomena".

I agree with both of you, even though you say you disagree with him. I agree with you because if we can't say e.g. that GR explains Newton's law of gravity, then we might as well remove the word "explain" from the English language since there are no better explanations than that. However, I also agree with Jesse, because he just said that science doesn't explain the fundamental laws. Newton's law of gravity isn't fundamental in GR, but Einstein's equation is. So what he said is consistent with my view, which is that GR explains Newton's law of gravity but not Einstein's equation, just like Newton's theory of gravity explains the elliptical orbits and falling apples but not the inverse square law.

Edit: Lol, you guys wrote a whole bunch of posts while I wrote this.