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Modern And Classical Physics Questions

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I'm a college student taking modern physics (or Quantum Topics, as my university calls it) and there are some things I'd like cleared up, if anyone cares to help me.

First, my classical physics question: why is potential energy held to be something that actually exists (according to the conservation of energy principle)? I can directly percieve various other forms of energy with my senses (kinetic by catching a ball, thermal by putting my hand in a fire, electric by touching an exposed live wire), but not potential.

The only justification for assuming the existence of it seems to be the conservation principle, but the conservation principle only survives because the existence of potential energy is assumed in order to make the math work (a circular arguement). I can't shake the feeling that potential energy is like the imaginary number; a useful conceptual tool, but not something that is actually found in nature.

Am I missing something?

As for modern physics...

Einstein's two postulates are that:

a) the laws of physics (Newton's laws and Maxwell's equations) must be identical in any two frames of referance which are moving at a constant velocity relative to each other and

all observers will measure the speed of light to be the same (the constant "c") regardless of their frames of referance.

So, my modern physics questions are:

1) My textbook claims that b can be derived from a, but hasn't given any details yet. How? I don't see how to derive it using *only* a. What other pieces of information are involved here?

2) Suppose I declare a particular photon to be the origin of a frame of referance. Wouldn't the speed of that particular light particle be 0 rather than c in that referance frame, no matter how fast it was measured to be moving in any other frame? If so, doesn't that destroy Einstein's second claim? And if not, how on Earth could a photon still be considered to have a speed of c in a frame in which the origin travels with it?

3) I understand that time dilation has been demonstrated experimentally, and if I can accept that then I can accept the existance of length contraction as well. But has it been determined experimentally whether these phenomenon are solely the result of relative motion or matter itself being affected somehow?

A thought experiment to clarify what I mean: take a perfect sphere and set up some measuring/recording device like a camera (the "observer") next to it. Put this setup on a spaceship and have the ship accelerate along a straight line until length contraction becomes significant. Now, stop acceleration and rotate the sphere along an axis perpindicular to the direction of acceleration.

Does the sphere appear deformed (compressed along the axis it was being accelerated in) to the observer or not? If it does, that would suggest to me that time and space don't actually dilate or contract, but that the matter itself is being changed in such a way as to give that illusion. But if the sphere still appears perfect, then that would suggest that it is, in fact, relative motion that is the culprit.

Have any such experiments been done?

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The energy types you've mentioned here are expressed. The ball's kinetic energy hits a brick; the burning stick's thermal energy warms us up, etc. Potential energy, is by definition, not expressed. Furthermore, what kind of energy is waiting to be expressed? Kinetic (I think). So Kinetic and Potential energies are two sides of the same coin. You can't have Kinetic energy without having a source that it comes from. If that source is stifled and cannot express its kinetic energy immediately (a loaded spring), we say that it has potential energy, implying that as soon as the impediments are removed (the lock on the spring is open), the potential energy will express itself as a kinetic one (the spring expands).

There are no alternatives to thermal energy, it just IS. Kinetic energy, on the other hand, is just one half, and needs potential by its very definition.

Think of it this way: we are technically exerting kinetic energy on the ground when we stand upon it. Yet we don't fall, though the energy urges us downward. So we have the potential to fall downward, which is yet unexpressed to us due to the limitations (rigidity) of what supports us. If that limitation is removed, the potential energy stored within us is released.

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First, my classical physics question: why is potential energy held to be something that actually exists (according to the conservation of energy principle)? I can directly percieve various other forms of energy with my senses (kinetic by catching a ball, thermal by putting my hand in a fire, electric by touching an exposed live wire), but not potential.
What do you mean by "actually exists?" Is energy a physical thing, a substance?

Einstein's two postulates are that:

a) the laws of physics (Newton's laws and Maxwell's equations) must be identical in any two frames of referance which are moving at a constant velocity relative to each other and

all observers will measure the speed of light to be the same (the constant "c") regardless of their frames of referance.

Note that these formulations are not the actual postulates which Einstein indentified when presenting, in 1905, what was eventually called special relativity. But let's just accept them for now.

So, my modern physics questions are:

1) My textbook claims that b can be derived from a, but hasn't given any details yet. How? I don't see how to derive it using *only* a. What other pieces of information are involved here?

Sometimes beginning texts tell little lies which texts later on are supposed to correct. Some do so out of incompetence while others do so because of expediency. Using "a)" and demanding causality invariance one can derive both the Galilean transformations of classical physics and the Lorentz transformation of relativity. If a least upper bound for particle speeds exists, then, via a bit of reasoning, one is led to the conclusion that there exists a quantity which transforms to itself, and that uniquely singles out the Lorentz transformation. So it is not quite "" which is derived, but rather, that in relativity there is some speed that is invariant across all inertial frames. One then needs certain physical facts, from observation or experiment, to discover that that invariant speed is the speed of light.

2) Suppose I declare a particular photon to be the origin of a frame of referance.
There does not exist a valid inertial reference frame where a photon is at rest.

3) I understand that time dilation has been demonstrated experimentally, and if I can accept that then I can accept the existance of length contraction as well. But has it been determined experimentally whether these phenomenon are solely the result of relative motion or matter itself being affected somehow?

Time dilation and length contraction are consequences of measurement and there is no physical change in the clocks or rods being measured.

A thought experiment to clarify what I mean: take a perfect sphere and set up some measuring/recording device like a camera (the "observer") next to it. Put this setup on a spaceship and have the ship accelerate along a straight line until length contraction becomes significant.
Time dilataion has been measurable for decades, but length contraction is too small an effect for current technology to detect.

If it does, that would suggest to me that time and space don't actually dilate or contract, but that the matter itself is being changed ...
These are false alternatives. Neither is true. Time itself does not dilate and space itself does not contract, and neither does matter change. Time dilation is a relationship between the tick rate of a clock and the measurement of such by an observer in uniform relative motion to the clock. Length contraction is a relationship between the length of an object and the measurement of such by an observer in uniform relative to the object. Both of these measurements differ among observers because, in general, there is no simultaneity of events between observers in uniform relative motion to each other.

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What do you mean by "actually exists?" Is energy a physical thing, a substance?

In a sense, that second question is what I'm asking you. It's possible that I'm inappropriately mixing philosophy and science, so let me try and clarify.

Philosophically, I'm thinking that entities (chunks of matter, gravitational fields, etc.) don't just exist, they exist in a certain state (here as opposed to there, having a temperatue of 100 Kelvin as opposed to 200 Kelvin, etc.). "Entity" and "identity," nothing new to you I'm sure. But the exact identity of entities (their location, temperature, etc.) is changing all the time. I call the transition from any one state to a differant state "action."

Passing from philosophy to physics, I understand "energy" to be a quantitative measure of action (change of state). The various types of energy (kinetic, thermal, etc.) refer to various types of changes.

But potential energy doesn't seem to fit. It doesn't measure change that's actually occuring, but only change that *could* occur under differant conditions. Now having a measure of unacheived potential is fine, but when you call it energy (a term which I associate with *actual* change-in-progress) and then use it to support the claim that energy is never created or destroyed, then I start having conceptual issues.

Does that clear it up?

Â

Note that these formulations are not the actual postulates which Einstein indentified when presenting, in 1905, what was eventually called special relativity.

What were his actual postulates?

There does not exist a valid inertial reference frame where a photon is at rest.

I'd really like some explination to that.

As I understand it the motion of anything can only be measured relative to something else, and except for simplifying the math involved there is no prefered frame of referance. In other words, there's no reason I can't make a car going down the highway my point of origin and measure the rest of the world as moving relative to it.

So why can't I replace the car with a photon and see what happens?

Both of these measurements differ among observers because, in general, there is no simultaneity of events between observers in uniform relative motion to each other.

I'm not sure I grasp this. Is this something that has to be treated as a basic principle (basic as in, it can't be broken down and explained in terms of anything else)?

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Philosophically, I'm thinking that entities (chunks of matter, fields of energy, etc.)

I think I know what "chunks of matter" are, but what are "fields of energy?" Can you give me an example? That, in essence, is part of the question I asked. Do you think of energy as a thing, as an independent substance?

But potential energy doesn't seem to fit.Â  It doesn't measure change that's actually occuring ...
Then the rest energy of a particle would also not fit.

What were his actual postulates?

"1. The laws governing the changes of the state of any physical system do not depend on which one of the two coordinate systems in uniform translational motion relative to each other these changes of the state are referred to.

"2. Each ray of light moves in a coordinate system 'at rest' with the definite velocity V independent of whether this ray of light is emitted by a body at rest or a body in motion. Here, velocity = light path/time interval..."

--Albert Einstein, On the Electrodynamics of Moving Bodies, Annalen der Physik, 17, 1905, reprinted in The Collected Papers of Albert Einstein: Volume 2, The Swiss Years: Writings, 1900-1909, Anna Beck, Translator, pp. 143-144, Princeton University Press_, 1989.

Note that the "postulate" you labeled as "" in your prior post is really a deduction made from Einstein's "1." based on Einstein's "2."

There does not exist a valid inertial reference frame where a photon is at rest.

I'd really like some explination to that.
The photon always travels at c, and if you calculate the gamma factor of the Lorentz transformation you will see that the value is infinite. You cannot transform into a rest frame for the photon. Another way to see this, more physically, is that the relativistic Maxwell equations have only a single speed, c, for electromagnetic radiation. If you could transform to a rest frame the radiation would vanish, which, among other things, would contradict the first postulate.

Both of these measurements differ among observers because, in general, there is no simultaneity of events between observers in uniform relative motion to each other.

I'm not sure I grasp this.Â  Is this something that has to be treated as a basic principle (basic as in, it can't be broken down and explained in terms of anything else)?

The relativity of simultaneity is a feature of the Lorentz transformation, so when you derive time dilation the lack of simultaneity is built in. And, since measuring the length of an object requires you to mark the end points simultaneously, such measurement will vary for different observers.

p.s. What is the title of the course you are taking and what is the title of the text?

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I think I know what "chunks of matter" are, but what are "fields of energy?" Can you give me an example? That, in essence, is part of the question I asked. Do you think of energy as a thing, as an independent substance?

Argh. I caught that mistake shortly after I posted and changed it to say "gravitational fields" instead, but you must have grabbed a copy to work with offline too quickly. That's also why I made the accidental double-post; I hit the wrong button the first time I tried to change it. Sorry about all of that.

To answer your questions, no. Entities are independent substances, energy is a quantitative measure of change in entities and as such by definition can't exist independently of them. Not in my book, anyway.

Examples are gravitational fields, magnetic fields, etc. I'll just call them "fields" instead of "energy fields," as using the word "energy" in two differant ways will be confusing. I classify fields as entities, not actions; they can cause changes and be changed, but they are not themselves a process of change.

Then the rest energy of a particle would also not fit.
Good point. That would definitely go in the same file as potential energy. I'm thinking more and more that my concept of energy does not match the definition of modern science.

"1. The laws governing the changes of the state of any physical system do not depend on which one of the two coordinate systems in uniform translational motion relative to each other these changes of the state are referred to.

"2. Each ray of light moves in a coordinate system 'at rest' with the definite velocity V independent of whether this ray of light is emitted by a body at rest or a body in motion. Here, velocity = light path/time interval..."

Yes, that is differant from what I thought. And it removes the objection I was going to give to your claim that you can't use a photon as a point of origin. Not that I'm conceding the point just yet (I'm still thinking it through), but my first counter-arguement doesn't hold.

p.s. What is the title of the course you are taking and what is the title of the text?

It's called "Quantum Topics" here (Loyola University of New Orleans), though I'm told that most other universities just call it "Modern Physics." It's a second-year course. As for the text...

Title: Modern Physics (for scientists and engineers), second edition

Authors: Stephen T. Thornton & Andrew Rex

ISBN: 0-03-006049-4

On a tangent, I was thinking about what you said earlier about how we can't measure length contraction with modern instrumentation. But there's another way; if you can get a rocket going fast enough for length contraction to become pronounced, you can just launch that sucker past some measuring instruments.

I realize we can't do that on Earth, but with the success of SpaceShipOne and all we may soon have the infrastructure to build rockets in space that don't have to worry about escaping atmosphere or overcoming air drag. Give one a big enough fuel tank, fire it towards the sun for bonus acceleration from gravity and you're there. Of course I'm sure the price tag would make even Bill Gates blink twice, but for something as big as experimental verification of length contraction I'm sure you could get enough people to contribute.

What do you think? Could we actually see this happen in a couple of decades?

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I have a question regarding the 1916 paper (revised 1924) by Albert Einstein on Special and General Relativity. He says in Section 7

w = c-v

The velocity of propagation of a ray of light relative to the carriage thus comes cut smaller than c.

But this result comes in conflict with the principle of relativity set forth in Section V

For, like every other general law of nature, the law of transmission of light in vacuo [in vacuum]must, be according to the principle of relativity...

Is the velocity of light in vacuum actually regarded as a law of physics?

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Argh.Â  I caught that mistake shortly after I posted and changed it to say "gravitational fields" instead, but you must have grabbed a copy to work with offline too quickly.

No, not too quickly. My board settings give me email updates of threads I participate in, and sometimes I just compose a response later from that email. Unfortunately I only get the first of a batch, so sometimes I miss a follow up and/or other postings.

To answer your questions, no.Â  Entities are independent substances, energy is a quantitative measure of change in entities and as such by definition can't exist independently of them.Â  Not in my book, anyway.

Examples are gravitational fields, magnetic fields, etc.Â  I'll just call them "fields" instead of "energy fields," as using the word "energy" in two differant ways will be confusing.Â  I classify fields as entities, not actions; they can cause changes and be changed, but they are not themselves a process of change.

Then of what are these entities, say, the gravitational field, composed?

Then the rest energy of a particle would also not fit.

Good point.Â  That would definitely go in the same file as potential energy.Â  I'm thinking more and more that my concept of energy does not match the definition of modern science.
That in itself is not necessarily bad. Definitions range from "the ability to do work," to "the generator of time-translation symmetry." In some aspects of quantum mechanics your view of energy makes sense as tracking the rate of change of the wavefunction. In special relativity when you project the time component of the 4-momentum onto a set of inertial coordinates, then you have energy. In general relativity the stress-energy-momentum tensor can specify the energy properties of matter, and local conservation of energy can be well-defined. But there is not, in general, anyway in GR to have global energy conservation. And in quantum chromodynamics, as well as in general relativity, your concern about potential energy is satisified because there really is no potential energy in these theories.

Yes, that is differant from what I thought.Â  And it removes the objection I was going to give to your claim that you can't use a photon as a point of origin.Â  Not that I'm conceding the point just yet (I'm still thinking it through), but my first counter-arguement doesn't hold.

It is a reasonable question to ask, but once you understand relativity then it becomes clear that it is meaningless to think about transforming into the rest frame of a photon. Long before relativity Einstein himself asked a similar question:

"How, then, could such a universal principle be found? After ten years of reflection such a principle resulted from a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as a spatially oscillatory electromagnetic field at rest. However, there seems to be no such thing, whether on the basis of experience or according to Maxwell's equations."

-- Albert Einstein, "Autobiographical Notes" in "Albert Einstein: Philosopher-Scientist," Ed. Paul Arthur Schilpp, p. 53, Harper Torchbook, 1959.

On a tangent, I was thinking about what you said earlier about how we can't measure length contraction with modern instrumentation.Â  But there's another way; if you can get a rocket going fast enough for length contraction to become pronounced, you can just launch that sucker past some measuring instruments.

I realize we can't do that on Earth, but with the success of SpaceShipOne and all we may soon have the infrastructure to build rockets in space that don't have to worry about escaping atmosphere or overcoming air drag.Â  Give one a big enough fuel tank, fire it towards the sun for bonus acceleration from gravity and you're there.Â  Of course I'm sure the price tag would make even Bill Gates blink twice, but for something as big as experimental verification of length contraction I'm sure you could get enough people to contribute.

What do you think?Â  Could we actually see this happen in a couple of decades?

It would be a good exercise to first calculate the length contraction for various fractions of the speed of light, and then, after determining a value that could be measurable, determine the energy and thrust required to accelerate a spacecraft towards the Sun so as to reach the necessary speed before burning up in the Sun. As a bonus also calculate the size of the fuel tank to hold such a quantity, and the strength of the material to withstand the necessary acceleration.

The only proposal for measuring length contraction that I have ever seen, but is itself rather dubious, utilizes the Space Interferometry Mission (SIM), due to be lauched by NASA in 2009. SIM is supposed to provide a +/- 1 micro-arcsecond resolution in a field of view of 1 degree. The proposal is to discern a length contraction of 18 micro-arcseconds per degree of separation of two stars located out of the plane of the ecliptic.

The reference is "A direct test of the Lorentz length contraction," C. Renshaw, IEEE Aerospace and Electronic Systems Magazine, 13: (9), pp. 3-7, September 1998. But, as I said, this is rather dubious, as is the author himself.

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I have a question regarding the 1916 paper (revised 1924) by Albert Einstein on Special and General Relativity. He says in Section 7

That is actually a popular book that Einstein wrote, not a paper.

Is the velocity of light in vacuum actually regarded as a law of physics?

Not a law of physics, but rather, for several centuries, a physical constant to be measured. That too has changed in the past two decades. Measurement of the speed of light has become so precise that since 1983 the meter is defined in terms of the distance traveled by light during the time interval 1/299,792,458 of a second. Nowadays, rather than thinking of light speed as a physical constant, many try to characterize it as a conversion factor between units of measurement.

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Then of what are these entities, say, the gravitational field, composed?

Heh. This is where I'm supposed to say "energy," right? Maybe that's where my problem is coming from. Too many uses for the same word.

That said, though, I don't see the point of the question. I don't need to say that the Earth is composed of "matter" to classify it as an entity, I just need to know that it is something that acts and is acted upon, as opposed to being a process of action (or a relation). The same goes for the gravitational field the Earth generates. We can give it a name if you'd like, but where are you going with this?

That in itself is not necessarily bad. Definitions range from "the ability to do work," to "the generator of time-translation symmetry." In some aspects of quantum mechanics your view of energy makes sense as tracking the rate of change of the wavefunction. In special relativity when you project the time component of the 4-momentum onto a set of inertial coordinates, then you have energy. In general relativity the stress-energy-momentum tensor can specify the energy properties of matter, and local conservation of energy can be well-defined. But there is not, in general, anyway in GR to have global energy conservation. And in quantum chromodynamics, as well as in general relativity, your concern about potential energy is satisified because there really is no potential energy in these theories.
Oh yes, *definitely* too many meanings for the same word. Special relativity (SR) deals with frames moving at uniform velocity at not rotating with respect to one anthor, while general relativity (GR) deals with frames that can be accelerating and rotating relative to one another, correct?

Question. If the energy conservation law breaks down in GR, why is it still held to be a law? If GR and the conservation law contradict one another, why are both still around? My textbook jumped through some hoops to keep conservation of linear momentum and energy intact in SR...

It is a reasonable question to ask, but once you understand relativity then it becomes clear that it is meaningless to think about transforming into the rest frame of a photon.

Well, I'm not there yet. I still find the question very meaningful. Right now it makes more sense to me to say that something must be wrong with Maxwell's equations if they break down like that.

Long before relativity Einstein himself asked a similar question:

"How, then, could such a universal principle be found?Â  After ten years of reflection such a principle resulted from a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as a spatially oscillatory electromagnetic field at rest. However, there seems to be no such thing, whether on the basis of experience or according to Maxwell's equations."

Interesting. I haven't studied electrodynamics yet, so I can't really comment on Maxwell's equations. But what does he mean by "on the basis of experience?" There's no way Einstein was running around at relativistic speeds at 16, so what experimental data is he talking about?

It would be a good exercise to first calculate the length contraction for various fractions of the speed of light,

That part is easy enough. (L' = L/y), where L is the proper length (rocket's frame), L' is Earth's frame and y is gamma, correct?

and then, after determining a value that could be measurable,
Here's where I start having trouble. I don't know how precise the best of modern instrumentation can get, and I'd need that information before I could select values of L and v that would do the job.

determine the energy and thrust required to accelerate a spacecraft towards the Sun so as to reach the necessary speed before burning up in the Sun. As a bonus also calculate the size of the fuel tank to hold such a quantity, and the strength of the material to withstand the necessary acceleration.

I don't know how to calculate for fuel requirements and stress. Ask me again in two or three years when I have some engineering courses under my belt.

That said, keep in mind that to deal with stress you can always start from further out or just not bother using the sun (to give yourself more time to accelerate gradually).

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That said, though, I don't see the point of the question.Â  I don't need to say that the Earth is composed of "matter" to classify it as an entity, I just need to know that it is something that acts and is acted upon, as opposed to being a process of action (or a relation).Â  The same goes for the gravitational field the Earth generates.Â  We can give it a name if you'd like, but where are you going with this?

It was a bit of a Socratic process, attempting to have you get to the root. I'll cut to the chase. The field concept is, at best, ill-defined, and, at worst, often a floating abstraction. The location in a field cannot, in and of itself, give rise to a particle emission process. Particle emission requires available states, but available states of nothing cannot give rise to particles. Either the field is something distinct from the particles or it is the particles themselves. In other words, either the field exists and is something in its own right, or it does not exist. But standard theory takes it both ways; the field is something, and nothing. You might as well have used "gravitational energy" for the gravitational field because either form is ill-defined. In general relativity, what is the gravitational field. Is it the metric tensor field, as some say? Or is it one of the curvature tensor fields? Or, the connection? In either case, are the metric or curvature tensor fields, or the connection, actual physical existents? What is typically known as the gravitational field is a spin 2 field, but matter sources are spin 1/2 or 1. No matter is described by a symmetric rank-2 tensor, but nevertheless that is the description of the gravitational field.

Special relativity (SR) deals with frames moving at uniform velocity at not rotating with respect to one anthor, while general relativity (GR) deals with frames that can be accelerating and rotating relative to one another, correct?
No. That is a quite common misconception, even among some physicists. Special relativity can deal with accelerating and rotating frames just fine. They are handled differently than inertial frames, and at times can become somewhat complex, but nevertheless the framework of SR is sufficient. Many advanced texts on relativity have a section on this.

In 1907, as early as two years after introducing SR, Einstein began to work with an "accelerated reference system" in the context of SR, in his first review paper on relativity ( "On The Relativity Principle and the Conclusions Drawn From It," Jahrbuch der Radioaktivitat und Elektronik 4, pp. 411-462, 1907). He has a whole section in that paper dedicated to just that. And, if you study the history of relativity, the rotating disk problem has been identified as the "missing link" between SR and Einstein's formulation of general relativity.

Question.Â  If the energy conservation law breaks down in GR, why is it still held to be a law?Â  If GR and the conservation law contradict one another, why are both still around?Â  My textbook jumped through some hoops to keep conservation of linear momentum and energy intact in SR...
It is not that the conservation law itself breaks down, but rather that the concept of total energy on a global scale is ill-defined. The local energy density of matter is well-defined -- energy is conserved locally -- but it cannot lead to an unambiguous global conservation law.

Well, I'm not there yet.Â  I still find the question very meaningful.Â  Right now it makes more sense to me to say that something must be wrong with Maxwell's equations if they break down like that.
That is a bit of a strange way of putting it. We do not deduce how the world should be; we induce our understanding by looking at reality. Maxwell's equations, and relativity as well, is not an out-of-context absolute that must handle any situation that we can just conceive of in our minds. All of the experimental evidence demonstrates that we cannot accelerate any massive object to reach a speed of c. That fact is perfectly consistent with Maxwell's equations and relativity, and it does not indicate that anything is "wrong." That we cannot Lorentz transform into the frame of a photon simply reflects the experimental and theoretical facts.

Interesting.Â  I haven't studied electrodynamics yet, so I can't really comment on Maxwell's equations.Â  But what does he mean by "on the basis of experience?"Â  There's no way Einstein was running around at relativistic speeds at 16, so what experimental data is he talking about?
He is referring to the constancy of the speed of light, which was demonstrated in the Michelson-Morley experiment in 1887. If light traveled at a speed with respect to something else, then one would expect results in the MM experiment that the speed with respect to the Earth would have been c - v in one direction, and c + v in the other. But the result was c. Note that Einstein once identified this as the "first path which led me to the special theory of relativity." (Albert Einstein, "How I Created The Theory of Relativity", Speech at Kyoto University, Dec. 1922.)

I don't know how to calculate for fuel requirements and stress.Â  Ask me again in two or three years when I have some engineering courses under my belt.Â
That's okay. I did not really expect you to carry out the calculations. I was trying to imply that if you did you would find enormous technical problems with such a scenario. Is engineering your field of study, or is it physics? Or, something else? It is nice to see a young student interested in thinking about these issues.

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No. That is a quite common misconception, even among some physicists. Special relativity can deal with accelerating and rotating frames just fine. They are handled differently than inertial frames, and at times can become somewhat complex, but nevertheless the framework of SR is sufficient. Many advanced texts on relativity have a section on this.
So what exactly is it that GR does that SR can't?

It is not that the conservation law itself breaks down, but rather that the concept of total energy on a global scale is ill-defined. The local energy density of matter is well-defined -- energy is conserved locally -- but it cannot lead to an unambiguous global conservation law.

So fields and energy conservation are both ill-defined... You're making it sound as though not just me but physics as a whole is in need of a linguistic overhaul. I'm not sure whether to be relieved or even more worried.

That is a bit of a strange way of putting it. ...Â  That we cannot Lorentz transform into the frame of a photon simply reflects the experimental and theoretical facts.
Okay, forget about frame transformations for a moment and let me try this another way. I'm going to describe a thought experiment, and maybe you can explain what happens and why.

Take two observers (A and B ), both using the same coordinate system (no transformations). A is standing at the point of origin (0, 0) and B is standing 10 meters away along the negative direction of the x axis (-10, 0). The experiment begins when (t = 0 seconds), with synchronicity ensured by means of a flashbulb halfway between them being set off (they each start when the light reaches them).

At t = 0, A generates a flash of light (which we'll designate as L) from his position in the positive direction of the x axis. A remains still. B begins moving backwards at a rate of 1 m/s.

Now, I have two conceptual problems here. First, according to Einstein L must be moving at velocity c with respect to both A and B, even though B is moving away from L in addition to L's own speed. Second, if A and B both try to compute L's position based on the amount of time that has elapsed using the same velocity of c, they should get differant positions for L (indicating that L is in two differant places at once). Both of these strike me as contradictions.

What gives?

He is referring to the constancy of the speed of light, which was demonstrated in the Michelson-Morley experiment in 1887. If light traveled at a speed with respect to something else, then one would expect results in the MM experiment that the speed with respect to the Earth would have been c - v in one direction, and c + v in the other. But the result was c.

Hang on. I'm somewhat familiar with that experiment, and my understanding was that the +/- v was supposed to come from the relative motion of Earth and the theoretical ether. If the measuring devices were not moving relative to the light source and mirrors, then once you discard the ether idea it makes perfect sense - even from a Galilean perspective - that you would measure the same speed for light in each direction. I see how that experiment discredits the ether theory, but not how it supports relativity.

Is engineering your field of study, or is it physics? Or, something else? It is nice to see a young student interested in thinking about these issues.

I'm older than you think, I just got a late start (for various unpleasant reasons I won't go into). I'm actually 27. I've been studying physics and computer science, and am just beginning to get into engineering-related courses.

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So what exactly is it that GR does that SR can't?

Gravitation.

Unlike in SR, where the spacetime metric is flat, in GR this is not necessarily so.

Okay, forget about frame transformations for a moment and let me try this another way.Â  I'm going to describe a thought experiment, and maybe you can explain what happens and why.

Take two observers (A and , both using the same coordinate system (no transformations).Â  A is standing at the point of origin (0, 0) and B is standing 10 meters away along the negative direction of the x axis (-10, 0).Â  The experiment begins when (t = 0 seconds), with synchronicity ensured by means of a flashbulb halfway between them being set off (they each start when the light reaches them).

And by what means did you determine this halfway point? (Rhetorical question.) Such determination itself is dependent upon the particular method of synchronization that was assumed in the first place. But, let's move on ...

At t = 0, A generates a flash of light (which we'll designate as L) from his position in the positive direction of the x axis.Â  A remains still.Â  B begins moving backwards at a rate of 1 m/s.

Once there is relative motion between A and B their clocks are no longer synchronous.

Now, I have two conceptual problems here.Â  First, according to Einstein L must be moving at velocity c with respect to both A and B, even though B is moving away from L in addition to L's own speed.
According to Einstein, and according to experimental fact, L will be measured to be traveling at c by all inertial observers, including A and B. For of an object traveling at a speed other than c, measurements of that speed made by different inertial observers will, in general, vary. But light speed is an invariant, not dependent on the motion of the source, nor dependent on the motion of the observer. If you think otherwise then you are contradicting experimental fact.

Second, if A and B both try to compute L's position based on the amount of time that has elapsed using the same velocity of c, they should get differant positions for L (indicating that L is in two differant places at once).

As I indicated above, once B is in motion relative to A, their clocks are no longer synchronous (even if they were synchronous to begin with), so both their spatial and time measurements will not coincide.

Both of these strike me as contradictions. What gives?
There are no contradictions. Relativity is a completely consistent theory and if you think you have found a contradiction then you are either mis-using or misunderstanding relativity.

Hang on.Â  I'm somewhat familiar with that experiment, and my understanding was that the +/- v was supposed to come from the relative motion of Earth and the theoretical ether.Â  If the measuring devices were not moving relative to the light source and mirrors, then once you discard the ether idea it makes perfect sense - even from a Galilean perspective - that you would measure the same speed for light in each direction.Â  I see how that experiment discredits the ether theory, but not how it supports relativity.

Though it is often stated as such, the Michelson-Morley experiment did not disprove the ether. The experiment was not consistent with the fixed ether, but it remained consistent with George Stokes' partially-entrained ether, where the ether is at rest at the surface of the Earth, but it has a potential which tapers off to zero at some distance away. And, of course, later, the ether implied by Lorentz' contraction hypothesis was also consistent with the MM experiment.

Anyway, to briefly sketch the Einstein connection from the null result of the MM experiment to the constancy of light ... By 1903 Einstein had read "Attempt at a Theory of Electrical and Optical Phenomena in Moving Bodies," an 1895 book by Lorentz. Einstein's writings at that time make clear that he then considered Lorentz' theory to be the best explanation yet of electromagnetic and optical phenomena, though he could not accept it all. The theory was consistent with the MM experiment and in it the velocity of light was constant and independent of source motion, but only in the ether frame. Einstein was not able to construct a plausible emission theory of light, but his investigations into electromagnetic induction led him to accept the principle of relativity, which was consistent with an emission theory. But while working on his revolutionary light quanta paper (for which he eventually was awarded the Nobel Prize) Einstein further called into question the very notion of the ether. Unable to find any differential equations that described the emission theory, and having put aside the ether, Einstein's principle of relativity motivated him further to extend the Lorentz concept such that the constancy of light held true in all inertial frames, not just the ether frame. This is the connection between the MM experiment and the constancy of light, and which eventually led to Einstein's own independent formulation of the Lorentz transformation.

I'm older than you think, I just got a late start (for various unpleasant reasons I won't go into).Â  I'm actually 27.Â  I've been studying physics and computer science, and am just beginning to get into engineering-related courses.

Well, I hope you enjoy your studies. These survey courses usually cover a lot a ground, but they do so at the expense of any depth. Do you intend to take a course in at least special relativity?

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What book do you use? I've used Modern Physics for Scientists and Engineers I found it to be one of the worst modern physics text books out there. I'd say if you're having serious problems with the book just have a chat with the professor, or another professor, they get excited chatting about this stuff. I would also recommend "A Brief History of Time" Hawking explains things much better than any of my professors have.

-Nate

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Once there is relative motion between A and B their clocks are no longer synchronous.

Okay, I missed that point. Thanks.

But light speed is an invariant, not dependent on the motion of the source, nor dependent on the motion of the observer.
Question - does that include the oscillations due to wave-like motion? In other words, if a photon's overall motion is along the x axis but it's oscillating up and down in the direction of the y axis, is it only the motion in the x direction that equals c, or is it (x^2 + y^2)^1/2 that equals c?

There are no contradictions. Relativity is a completely consistent theory and if you think you have found a contradiction then you are either mis-using or misunderstanding relativity.

Probably a little of both, though neither intentionally.

Well, I hope you enjoy your studies. These survey courses usually cover a lot a ground, but they do so at the expense of any depth.Â  Do you intend to take a course in at least special relativity?

You mean this *isn't* such a course?

If I stay on this path, there's Quantum Mechanics in my future. Does that count?

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Question - does that include the oscillations due to wave-like motion?

In special relativity we generally talk of rays of light, or a light beam. Relativity, per se, does not address the issue of what that light is composed of, nor does it ask what is the fundamental nature and structure of light. So when you start to speak of the wave nature of light, or the particle nature of light, or whatever, you are then in the province of particle physics and quantum field theory, and then the answers are vey theory-dependent. Now, there is a relativistic quantum theory of electromagnetic interactions, known as quantum electrodynamics (QED), but one should first master relativity before knocking on the door of QED. Relativity is more interested in an operational view of light, rather than a structural one. Courses in electromagnetism deal with aspects of this, but at the beginning there is much hand-waving. The study of light is a specialty unto itself.

You mean this *isn't* such a course?

As I understood you previously, I thought you were taking an introductory survey course in modern physics. If that is the case, these sort of courses just touch upon a variety of subjects and cannot give a grounding in any given area. Courses given in relativity, both the special and the general theories, have at least a half or full year of study devoted to each as an introduction, with follow-on courses to explore these areas in more depth.

If I stay on this path, there's Quantum Mechanics in my future.Â  Does that count?

Well, quantum mechanics certainly counts, but that is not relativity.

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In special relativity we generally talk of rays of light, or a light beam. Relativity, per se, does not address the issue of what that light is composed of, nor does it ask what is the fundamental nature and structure of light.Â  So when you start to speak of the wave nature of light, or the particle nature of light, or whatever, you are then in the province of particle physics and quantum field theory, and then the answers are vey theory-dependent.

Hmm. I was trying to integrate some things from my modern physics textbook (the invarience of c and the claim that all of a photon's energy comes from momentum) with some things from my chemistry textbook (color being based on a photon's wavelength), but I'm starting to wonder which theories I'm supposed to integrate and which I'm supposed to treat as mutually exclusive.

As I understood you previously, I thought you were taking an introductory survey course in modern physics. If that is the case, these sort of courses just touch upon a variety of subjects and cannot give a grounding in any given area. Courses given in relativity, both the special and the general theories, have at least a half or full year of study devoted to each as an introduction, with follow-on courses to explore these areas in more depth.

Hmm... Off the top of my head I still need to take Thermodynamics, Electromag Theory, Classical Mechanics, Quantum Mechanics and Intro to Electronics.

On another note... Some questions about book recommendations.

1) In another thread you recommended a book called Spacetime Physics, and it turns out that I can get my hands on a copy from the library from one of my universities' libraries. The problem: they only have the 60's version, which you say doesn't define the concepts involved quite as precisely as the 90's version.

Is this a problem? Are there any errors I should be aware of before using the 60's version, or should I order and wait for the 90's version? Or can I just use the 60's version as is without worrying about it?

2) Elsewhere you've mentioned having issues with set theory, which I hear is currently used as the basis of all mathematics. Set theory is something I've been wanting to look into for a while. Can you recommend any book(s)? Something with a gentle learning curve is prefered, though not strictly necessary.

What are your problems with it?

3) This one is for anyone who cares to answer... I see that Peikoff has put out a taped lecture on his DIM Hypothesis and is working on the book. Does anyone know about when the book will be out? If it will be a while I may want to see if I can get one of the university libraries here to pick up the tape series, but I'm not sure how eagar they'll be to take requests that cost hundreds of dollars a pop...

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Hmm.Â  I was trying to integrate some things from my modern physics textbook (the invarience of c and the claim that all of a photon's energy comes from momentum) with some things from my chemistry textbook (color being based on a photon's wavelength), but I'm starting to wonder which theories I'm supposed to integrate and which I'm supposed to treat as mutually exclusive.

There is a much longer history of applying quantum mechanics to chemistry than there is with relativity and chemistry. It is only really in the past few decades, since the 1970's, that the role of relativity in chemistry became appreciated, so I would not worry too much at this early stage in integrating the theories as much as first learning them independently. There are fascinating questions in chemistry that only become sensible when relativity is taken into account; everything from the now well known answer as to why gold has a yellow glitter, to the more esoteric question as to why heavier molecules have certain strong and intense spectroscopic transitions as compared to their lighter analogs in the periodic table.

1)Â  In another thread you recommended a book called Spacetime Physics, and it turns out that I can get my hands on a copy from the library from one of my universities' libraries.Â  The problem: they only have the 60's version, which you say doesn't define the concepts involved quite as precisely as the 90's version.

Is this a problem?Â  Are there any errors I should be aware of before using the 60's version, or should I order and wait for the 90's version?Â  Or can I just use the 60's version as is without worrying about it?

Yes, the newer version has sharpened the terminology but I am sure the earlier work will suit you just fine. I once had an errata sheet for that edition; I'll look for it and pass it on if I locate it. One advantage to the 60's edition is that it uses hyperbolic functions which I think gives a nice mathematical intuition into some aspects of relativity.

2) Elsewhere you've mentioned having issues with set theory, which I hear is currently used as the basis of all mathematics.Â  Set theory is something I've been wanting to look into for a while.Â  Can you recommend any book(s)?Â  Something with a gentle learning curve is prefered, though not strictly necessary.

I have not used it myself by Robert Stoll's Set Theory and Logic has been mentioned several times as a real gentle introduction to set theory.

What are your problems with it?

I think that set theory has some useful applications, but it lacks a strong enough grounding in reality to be a real foundation for mathematics.

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There is a much longer history of applying quantum mechanics to chemistry than there is with relativity and chemistry. It is only really in the past few decades, since the 1970's, that the role of relativity in chemistry became appreciated, so I would not worry too much at this early stage in integrating the theories as much as first learning them independently.

Unless I'm getting more of those "little white lies" you mentioned, I'm thinking that the two are incompatible. The formula I'm getting from my chemistry textbook is (wavelength * frequency = c), and since wavelength is a straight-line measurement that means that oscillation is not taken into account. And it sounds like the same can be said of relativity's "light rays."

So unless the claim that observers will measure the same velocity for c refers only to a photon's motion along a single axis (which is not what I've been hearing), these two theories don't add up. If I measure a photon's motion along the x axis to be 1 lightsecond per second, but I also measure oscilation along a different axis, then I'm measuring the total path travelled per second to be greater than a lightsecond (and thus, a velocity greater than c).

Yes, the newer version has sharpened the terminology but I am sure the earlier work will suit you just fine. I once had an errata sheet for that edition; I'll look for it and pass it on if I locate it.
Have I mentioned how much I appreciate your help and patience with all of this? Because I really do.

I have not used it myself by Robert Stoll's Set Theory and Logic has been mentioned several times as a real gentle introduction to set theory.

I checked out both books yesterday. I've been through the first two parts of the first chapter of Stoll's book, and so far it seems good. There were a couple of parts where I had to go over the same paragraph or two several times to "get it," but I can already tell that it could have been much worse.

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Unless I'm getting more ...

Maybe I have not made myself clear, so let me try another way. In relativity we are not really concerned much with light as photons, but rather with the geometrical optics approximation to light. Initially light is thought of as a wave emitted from a source, propagating in a homogenous and isotropic space in all directions at a constant velocity. But then this is reduced to the more simple concept of a light ray, singling out a specific trajectory of a ray of light propagated in straight-line motion. Relativity is then concerned with events, the event in which light is emitted and the event in which light is detected. When the distance and time between these events is measured, the velocity of light is always c. The issue of what light really is, is the province of other fields in physics, such as quantum field theory, and there exist many different views of its nature. Your view of this "oscillation" of photons (whatever that means and wherever you are getting that from) requires an integration of relativity with whatever theory you have in mind.

Have I mentioned how much I appreciate your help and patience with all of this?Â  Because I really do.

Thanks, and I enjoy discussions like this.

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Maybe I have not made myself clear, so let me try another way. In relativity we are not really concerned much with light as photons, but rather with the geometrical optics approximation to light.

That helps a little, thanks.

Your view of this "oscillation" of photons (whatever that means and wherever you are getting that from) requires an integration of relativity with whatever theory you have in mind.Â

Thanks, and I enjoy discussions like this.

I suppose I should spell out what I'm thinking. The image I have in my mind is a particle which moves back and forth (oscillates) along an axis perpindicular to its forward motion (tracing out a wave-like path).

I'm sure you can poke some holes in that.

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I suppose I should spell out what I'm thinking.Â  The image I have in my mind is a particle which moves back and forth (oscillates) along an axis perpindicular to its forward motion (tracing out a wave-like path).

I'm sure you can poke some holes in that.Â

Rather than me poking holes, your own question should be: what facts of reality give rise to such a notion? Proper physics, just as with all proper thinking, requires some grounding for our hypotheses as opposed to arbitrary assertions.

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Rather than me poking holes, your own question should be: what facts of reality give rise to such a notion?

Just to amplify a bit on my rather terse comment, some other questions to answer are ... What physical facts are explained by the hypothesis? Are those facts explained better by existing theories? How does the hypothesis integrate with what we already know? Is it possible to design an experiment to test the hypothesis? But, above all, it is most often an inductive process which gives rise to new explanations that are tied to reality.

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