Exploring the Mysteries of Theoretical Physics

[SpazAttack]

Lately I have been studieng up on my Theoretical Physics. I feel I have a pretty good understanding of SR, but there are still some holes that nobody, not even my science teacher can help me out with (Im only in 8th grade, so Its not a big surprise that my teacher has no idea... no offense teachers out there). Oddly, SR is the only theory that has given me trouble... GR, QM, ST etc make perfect sense to me...

Its pretty basic knowlage that the speed of light is the same no matter who is measuring it, no matter how fast they are going. Any book I have read on the subject of Relativity (mostly non mathamatical books... e= what now?) has flat out avoided answering WHY this happens. A quick google search gives me the common answer of that, of course, time slows down, thereby magically making the speed of light the same no matter who is measuring it. This makes NO sense to me. Sure all time process are slowed down, but his movement through space isnt. If his movment through space was slowed down, it would have to be down to a complete stand still, no matter what speed he was going. Even if he didnt have to be slowed completely down, him moving through space due to time dilation would just cancel out the time dilation that caused it, because it was originally caused by him moving through space. But that same resuming of normal time would cause him to resume going through space at his normal speed! Which would slow down time again! Gah!
So what's going on? Please god keep it un mathimatical. Spare me the headache.

#2
Same line of thinking as before, but now let's just accept that the speed of light is the same for everyone, who cares why.
So let's say we have a single photon, Nick, who is at a complete standstill, shoots it out into empty space at the speed of light. Now Jimmy run beside the photons at the speed of light. Sinse we know that they both should see it shooting away from themselves at the speed of light, no more, no less, wouldn't that mean that when they get back together and compare where they saw the photon at any given time, wouldn't they report two completely separate places for the photon?
From Nicks standpoint it would look like:
nick ---------------------------@
jimmy -> Because he's running at speed of light
But from Jimmys standpoint it would look like:
Nick--------------------------------------------------------@
Jimmy -> because the photon is running away from him at the speed of light.
So where is the photon? At the time of when special relativity was published, quantum mechanics wasnt around to say that a particle could be in two places at once (so please don't use that answer).
Thanks alot.

 

[pmb_phy]

Its pretty basic knowlage that the speed of light is the same no matter who is measuring it, no matter how fast they are going. Any book I have read on the subject of Relativity (mostly non mathamatical books... e= what now?) has flat out avoided answering WHY this happens.

The answer is pretty simple - Nobody knows. This means that Einstein took the invariance of the speed of light to be a postulate (aka axiom). All theories start with certain things that are assumed to be true and then the theory is formulated. This allows predictions to be made and therefore verified (at least in principle). This is the case with special relativity. One could start with other postulates for which the invariance of the speed of light could be predicted. For example: If we start with postulating that Maxwell's equations are correct then we can derive a wave equation for which (1) the the wave propagates at the speed of light and (2) the speed of light is independant of the motion of anything in the frame and has the same value in all frames of reference. This is because Maxwell's equations and the first postulate of relativity (all laws of physics are the same in all inertial frames) combined mean that the constants used in the equations are frame independant.

For a derivation of the wave equations from Maxwell's equations is on my website at

http://www.geocities.com/physics_world/em/maxwells_equations.htm

Pete

 

[matheinste]

Hello SpazAttack.

It is hard to believe that your teachers cannot clear this point up for you.

Time dilation ( and length contraction ) is a consequence of the postulate that the speed of light is the same for all observers not the reason for it being so.

Ignoring a certain lack of rigour the general idea is that both observers will see ( observe, measure, compute etc. ) the photon follow the same spatial path but will asign different times to its being at any particular point because of their relative motion.

Ther is really nothing more to it than that but this is absolutely fundamental and must be understood before going any farther.

Mateinste.

 

[SpazAttack]

The answer is pretty simple - Nobody knows. This means that Einstein took the invariance of the speed of light to be a postulate (aka axiom). All theories start with certain things that are assumed to be true and then the theory is formulated. This allows predictions to be made and therefore verified (at least in principle). This is the case with special relativity. One could start with other postulates for which the invariance of the speed of light could be predicted. For example: If we start with postulating that Maxwell's equations are correct then we can derive a wave equation for which (1) the the wave propagates at the speed of light and (2) the speed of light is independant of the motion of anything in the frame and has the same value in all frames of reference. This is because Maxwell's equations and the first postulate of relativity (all laws of physics are the same in all inertial frames) combined mean that the constants used in the equations are frame independant.

For a derivation of the wave equations from Maxwell's equations is on my website at

http://www.geocities.com/physics_world/em/maxwells_equations.htm

Pete

Well that's dissapointing, thanks for an answer.

Hello SpazAttack.

It is hard to believe that your teachers cannot clear this point up for you.

Time dilation ( and length contraction ) is a consequence of the postulate that the speed of light is the same for all observers not the reason for it being so.

Ignoring a certain lack of rigour the general idea is that both observers will see ( observe, measure, compute etc. ) the photon follow the same spatial path but will asign different times to its being at any particular point because of their relative motion.

Ther is really nothing more to it than that but this is absolutely fundamental and must be understood before going any farther.

Mateinste.

Yea, it is kind of sad. But he/she doesn't teach anything higher than 8th grade, so I don't think he/she really needs to know that kind of thing.
So what if I ask them both where the photon was at one particular time, they would both give different locations. If I were to take a freeze frame of that one moment, wouldn't the photon be in 2 places at once?

 

[turbo]

The answer is pretty simple - Nobody knows. This means that Einstein took the invariance of the speed of light to be a postulate (aka axiom).

Einstein did not believe that the speed of light through a vacuum was invariant. This is a misunderstanding interpretation that is perverting physics to this day and it needs to be killed!

In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position.

You can read the whole book here.

http://www.bartleby.com/173/

 

[matheinste]

Hello again SpazAttack.

In answer to your original post and accepting Einstein's postulates :-
One person will record one photon at one place at one time. The second observer moving relative to him will also record the one photon at one place at one time but will not record it as being at the same place at the same time as the first observer.

Matheinste.

Matheinste.

 

[JesseM]

#2
Same line of thinking as before, but now let's just accept that the speed of light is the same for everyone, who cares why.
So let's say we have a single photon, Nick, who is at a complete standstill, shoots it out into empty space at the speed of light. Now Jimmy run beside the photons at the speed of light. Sinse we know that they both should see it shooting away from themselves at the speed of light, no more, no less, wouldn't that mean that when they get back together and compare where they saw the photon at any given time, wouldn't they report two completely separate places for the photon?
From Nicks standpoint it would look like:
nick ---------------------------@
jimmy -> Because he's running at speed of light
But from Jimmys standpoint it would look like:
Nick--------------------------------------------------------@
Jimmy -> because the photon is running away from him at the speed of light.
So where is the photon? At the time of when special relativity was published, quantum mechanics wasnt around to say that a particle could be in two places at once (so please don't use that answer).

Photons don't have their own "standpoint" in SR--the only inertial frames are the rest frames of sublight objects. The Lorentz transformation gives nonsensical answers if you try to use it to find the "frame" of an object moving at c.

 

[pervect]

Lately I have been studieng up on my Theoretical Physics. I feel I have a pretty good understanding of SR, but there are still some holes that nobody, not even my science teacher can help me out with (Im only in 8th grade, so Its not a big surprise that my teacher has no idea... no offense teachers out there). Oddly, SR is the only theory that has given me trouble... GR, QM, ST etc make perfect sense to me...

Probably, the element that you are missing is the relativity of simultaneity. I note that you do not mention it at all, and it is the most commonly missed and/or not understood aspect of the theory.

Time dilation and Lorentz contraction are only PART of what makes relativity work. The third element is the fact that simultaneity is relative.

Relativity just won't make sense until you grasp and accept this fact.

Note that understanding the relativity of simultaneity will not explain "why relativity is true". It will help you to understand how relativity is self consistent, however. Experimental data is what will (or at least should) convince you that relativity is the correct description of our universe, once you get that far.

As far as explanations of the relativity of simultaneity go,
http://en.wikipedia.org/w/index.php?title=Relativity_of_simultaneity&oldid=134021936

is a reasonable place to start. Check the references, for instance Einstein's explanation of it online is available at http://www.bartleby.com/173/8.html and is mentioned in the Wikipedia article.

I rather like Bondi's "K-calculus" approach for a high school level explanation of relativity. See for instance "relativity and Common Sense" by Bondi for this sort of explanation. (But I'm not aware of any good interent sources for this sort of explanation. It does involve a rather small amount of mathematics - if you are completely math-phobic, it might not help.)

As far as "running along a light beam", that's a question we get a lot, and there's a simple answer - within the context of the theory, you can't do it.

One of the consequences of having the speed of light be equal to 'c' is that you can never travel as fast as a light beam, no matter how hard you accelerate.

 

[pmb_phy]

Einstein did not believe that the speed of light through a vacuum was invariant. This is a misunderstanding interpretation that is perverting physics to this day and it needs to be killed!

I disagree. Its very clearly stated in his original paper.

Pete

 

[turbo]

I disagree. Its very clearly stated in his original paper.

Pete

He postulated an invariant speed of light for SR, but that is a special limited case, in which gravitational effects on light can be disregarded. It is not accurate to generalize and assume that light propagates through vacuum at a constant velocity in the presence of gravitational fields. He was quite clear on this and you can read his reasoning in Chapter 22.

http://www.bartleby.com/173/22.html

He treated space as if it had physical properties that were modified by its interaction with embedded matter, and these properties include the ability to refract light, which implies a variable speed of light propagation through the vacuum.

 

[SpazAttack]

Probably, the element that you are missing is the relativity of simultaneity. I note that you do not mention it at all, and it is the most commonly missed and/or not understood aspect of the theory.

Time dilation and Lorentz contraction are only PART of what makes relativity work. The third element is the fact that simultaneity is relative.

Relativity just won't make sense until you grasp and accept this fact.

Note that understanding the relativity of simultaneity will not explain "why relativity is true". It will help you to understand how relativity is self consistent, however. Experimental data is what will (or at least should) convince you that relativity is the correct description of our universe, once you get that far.

As far as explanations of the relativity of simultaneity go,
http://en.wikipedia.org/w/index.php?title=Relativity_of_simultaneity&oldid=134021936

is a reasonable place to start. Check the references, for instance Einstein's explanation of it online is available at http://www.bartleby.com/173/8.html and is mentioned in the Wikipedia article.

I rather like Bondi's "K-calculus" approach for a high school level explanation of relativity. See for instance "relativity and Common Sense" by Bondi for this sort of explanation. (But I'm not aware of any good interent sources for this sort of explanation. It does involve a rather small amount of mathematics - if you are completely math-phobic, it might not help.)

As far as "running along a light beam", that's a question we get a lot, and there's a simple answer - within the context of the theory, you can't do it.

One of the consequences of having the speed of light be equal to 'c' is that you can never travel as fast as a light beam, no matter how hard you accelerate.

Im all well and good with the relativity of simultaneity, I just didnt mention it because I didnt think it was relavent to my problem. Thanks though.
Yes, it was my flaw to say running next to it, because that is impossible. Let's just say he was running 99.99%. Either way, they will both record different possitions at any given time for the photon.

Photons don't have their own "standpoint" in SR--the only inertial frames are the rest frames of sublight objects.

I apologize, but I have no idea what this means, Can you dumb it down for me? I just in middle school!
------------------------
A new problem! My first post was talking about weather or not time slows down your movment through space. I then talked about why I think that this can not be the case. So what exactly does it mean to slow down time by time dilation? Arent all time process just movment of particles through space?
Here is my reasoning from my first post:

"If his movment through space was slowed down, it would have to be down to a complete stand still, no matter what speed he was going. Even if he didnt have to be slowed completely down, him moving through space due to time dilation would just cancel out the time dilation that caused it, because it was originally caused by him moving through space. But that same resuming of normal time would cause him to resume going through space at his normal (faster) speed! Which would slow down time again! Gah!"

Can someone please point out the flaw(s) in my reasoning?

 

[pmb_phy]

He postulated an invariant speed of light for SR, but that is a special limited case, in which gravitational effects on light can be disregarded.

Sorry. I was unaware of the fact that you were speaking in terms of SR. And I perhaps mistatked the postulate since the invariance of the speed of light pertains only to inertial frames, the only frames that Einstein spoke of in 1905.

In GR the meaning of invariance is that if at point P in the spacetime manifold you were to measure the speed of light then you'd be doing a local experiment and you'd always get the value of c.

However when it comes to non-local measurements, i.e. the observer is not located at the spatial position as the light, then you'll get a different value of c.

No need to post links to books. I've already read them. About 10 years ago as I recall. And I'm very intimately familiar with the dependence of the speed of light on the gravitational pointial, but thank you anyway.

I wrote up a few examples calculations for the varying speed of light which are located under my website here
http://www.geocities.com/physics_world/gr/gr.htm

Some of the speed of light calculations web pages have gotten mixed up and its on my list of "thing to do." This one seems to work but fo some reason the picture is gone. Yet another thing to add to my things to do list.

Best regards

Pete

 

[turbo]

Thanks for the link, Pete. That's an impressive page.

 

[pervect]

This makes NO sense to me. Sure all time process are slowed down, but his movement through space isnt. If his movment through space was slowed down, it would have to be down to a complete stand still, no matter what speed he was going

I'm afraid, after reading this a couple of times, I can't even figure out what you meant, much less figure out why you think that "movement through space" would have to be a complete stand still (?).

Try drawing a space-time diagram, like the one below. Yes, there is a certain amount of "math" involved in doing it, but maybe if you do that we can follow what the heck you're talking about.

Here's the explanation of the diagram below, and how it illustrates that GR implies time dilation.

If you've ever listened to a horn on a moving vehicle, you are probably familiar with the "doppler shift" effect. The sound emitted from a moving vehicle is higher in pitch when it approaches, and lower when it leaves.

In relativity, doppler shift is replaced with redshift and blueshift. If a transmitter transmits signals at a regular 1 second interval, they will be received at higher frequencies, and hence intervals shorter than 1 second by an approaching observer. Similarly, a receeding observer will receive the signals at intervals of longer than 1 second. This is not yet "time dilation", this is what is directly observed, including propagation delays.

Because the speed of light is constant for all observers, in relativity the doppler shift factor depends only on the relative velocity. This fact alone is sufficient to derive all the equations of SR. This is done in, for instance, "Relativity and common sense" by Bondi, the approach of using doppler shifts in this manner is usually called K-calculus.

In the diagram below, time points upwards, and space is horizontal. The stationary observer S (stationary only in the sense that the diagram is drawn from his perspective) is represented by a vertical black line - it's vertical because his space position never changes. The moving observer is represented by a slanting black line. Red lines are light signals.

The transmitter emits a light signal (red line) at 1 second after the origin - the origin is the point where the two observers are at the same point at the same time. Because of the constancy of the doppler shift, this will be recived at some time multiple of the transmitting time. In this diagram, this multiplying factor, bondi's "k" factor, is 2. So the signal is transmitted at t=1, and received at t'=2, where the prime mark indicates that that's the time assigned to the event by the moving observer M.

It's a bit confusing to have a couple of different "times" on the diagram, but any point on the diagram will have one set of coordinates (t,x) in the stationary frame S, and another ,possibly different set of corrdinates (t', x') in the moving frame M.

In this example, we have only one value in the moving frame, this is the value of T' for the moving observer which is equal to 2 at the event marked '2' on the diagram. All other times on the diagram occur in the non-moving frame.

Now, suppose the moving observer sends a signal back (or the original signal reflects) at his time T'=2. Because the doppler shift factor depends only on velocity, and because all motion is relative, we can apply the same formula to conclude that the signal will arive back at the first observer at T=4.

These points are labelled 1,2, and 4 on the diagram.

By the constancy of the speed of light, the stationary observer can conclude that the event that occurred at T'=2, the reflection of the signal, had a time T (a T-coordinate) of (1+4)/2 = 2.5. This is true because the light, emitted at 1 second, must have a travel time of 1.5 seconds, arriving at the moving obserevr M at 1+1.5 = 2.5 seconds, and returning at 2.5 + 1.5 = 4 seconds.

This illustrates that T is not equal to T' for the event labelled '2', the reception of the signal emitted at the event labelled '1'.

Further, it illustrates that T' < T, showing 'time dilation'.

 

[pmb_phy]

Thanks for the link, Pete. That's an impressive page.

You're most welcome!

This page seems to work except for a diagram
http://www.geocities.com/physics_world/gr/uniform_light.htm

Pete