Value of c and strange things that don't happen when at c

[ZirkMan]

Hi there,

I became really serious studying the basic principles of physics few months ago. There is a plenty of good study material out there, so there was no need to ask anybody anything. Until now.

The problem is with the speed of light c and why it has properties and value it has.
Few questions which I would like to elaborate:

1. Is there really no theory or framework from which I can derive the value of speed of light without knowing in advance what its value should be nor by measuring it directly? Basically I'm looking for an equation where c is the only unknown and when I add all values right into it I get the correct value of c (no tautologies please :)

2. The basic principle of the Special relativity is that all observers perceive a light wave move at c regardless of their relative speeds to each other and to the light source. So it must be true that if you reverse it, relative to a light wave all (matter) objects move with one speed the c. For a light wave this would be as real as it gets. If matter moves at c, it's mass becomes infinite and time in the matter world stops for the observer (it essentially becomes a singularity. I quess that's why there is the fear that LHC will create miniscule black holes by accelerating some particles too close to the speed of light).
If this reversal of perspective is true, why the path of light rays we see doesn't act as if any mass object it encounters was a singularity?

 

[HallsofIvy]

Hi there,

I became really serious studying the basic principles of physics few months ago. There is a plenty of good study material out there, so there was no need to ask anybody anything. Until now.

The problem is with the speed of light c and why it has properties and value it has.
Few questions which I would like to elaborate:

1. Is there really no theory or framework from which I can derive the value of speed of light without knowing in advance what its value should be nor by measuring it directly? Basically I'm looking for an equation where c is the only unknown and when I add all values right into it I get the correct value of c (no tautologies please :)

I'm not sure what you mean by this. "c" is a physical property and can only be derived by physical measurement. Here, http://galileoandeinstein.physics.virginia.edu/lectures/spedlite.html, is a nice description of how Ole Römer did it in 1676. And, of course, that measurement has to be made in a particular system of units- meters and seconds, or miles and hours. You can't just "solve" a purely mathematical equation for it, if that's what you mean.

2. The basic principle of the Special relativity is that all observers perceive a light wave move at c regardless of their relative speeds to each other and to the light source. So it must be true that if you reverse it, relative to a light wave all (matter) objects move with one speed the c. For a light wave this would be as real as it gets. If matter moves at c, it's mass becomes infinite and time in the matter world stops for the observer (it essentially becomes a singularity. I quess that's why there is the fear that LHC will create miniscule black holes by accelerating some particles too close to the speed of light).
If this reversal of perspective is true, why the path of light rays we see doesn't act as if any mass object it encounters was a singularity?

As you say, mass (of matter with nonzero rest mass) becomes infinite (more correctly it is the momentum that becomes infinite) which is why that can't[/t] happen. And "time stops" for an observer moving at the speed of light which is why light cannot have a "frame of reference" and it is meaningless to talk about motion "relative to a light wave".

 

[ZirkMan]

I'm not sure what you mean by this. "c" is a physical property and can only be derived by physical measurement. Here, http://galileoandeinstein.physics.virginia.edu/lectures/spedlite.html, is a nice description of how Ole Römer did it in 1676. And, of course, that measurement has to be made in a particular system of units- meters and seconds, or miles and hours. You can't just "solve" a purely mathematical equation for it, if that's what you mean.

Well, I was hoping for an explanation that will tell me why the value of c has the value it has and not some other value. Perhaps derived from some properties of spacetime that limit it to c.
I understand there must be a finite value of c. Otherwise traveling backwards in time would be possible in some frames of reference. (Is this really true?) But as far as I know, it would be perfectly OK, if it was a little bit higher or lower.

But if the current view is that it is an inherent property of our spacetime, then fine, I can live with that. I just wanted to know how far is the cause-consequence knowledge in in this particular case.

As you say, mass (of matter with nonzero rest mass) becomes infinite (more correctly it is the momentum that becomes infinite) which is why that can't[/t] happen. And "time stops" for an observer moving at the speed of light which is why light cannot have a "frame of reference" and it is meaningless to talk about motion "relative to a light wave".

OK, so even when I would give up observer's frame of reference of a light wave and switch to a reference frame of an observer with a nonzero rest mass and relative speed of 0.999c (which has a meaning now) all other mass objects I would encounter with this relativistic speed would have a pretty high momentum but their gravitational fields' effects (bending of spacetime) would not change compared to when I was in rest in relation to them?

So gravitational field is not relative to speed because mass is not relative, only momentum is.
Then why is weight relative to speed of an observer?

 

[pervect]

I'm not sure what you're looking for either, but if you measure the electric permittivity of free space, and the magnetic permeability, you can calculate c.

But the more modern view is that c is the natural "limiting speed" of the universe. And that meters and seconds are human units.

You can ask why the value of the meter and the second have the values they do, but the answer will have more to do with physics than history.

But this doesn't seem to be what you're after - hopefully the fact that the speed of light can be computed from Maxwell's equations, which depend on the permittivity and permeability of free space will be what you're after?

 

[Jonathan Scott]

Although historically it was an experimental result, since Special Relativity the value of c is now primarily a conversion constant between units used to measure space and units used to measure time, and of course it is now defined in that way too.

 

[Naty1]

For perspective, there is a LOT we don't know: not only why the speed of light is a certain value, we also do not know things like the why the mass of the electron, proton and neutron are what we measure, and we don't know what constitutes about 96% of the universe, dark matter and dark energy. In fact, we don't know if we live in the only universe or whether there are an infinite number of universes.

So lot's of good stuff remains to be discovered!

 

[ZirkMan]

I'm not sure what you're looking for either, but if you measure the electric permittivity of free space, and the magnetic permeability, you can calculate c.

This is a derivation of a constant from another constants which is a tautology for me. But that is actually OK. This is what I wanted to know. It tells me that this is the most fundamental layer of reality which we can measure and that we have not discovered another deeper level from which mechanics the value of c is a natural consequence (in any units system).

So now, only the problem of why gravity is not relative to speed is opened. Can please anybody explain that?

 

[Dale]

The value of c is due to the choice of units. It can have any value depending on the units you choose to use.

 

[S.Vasojevic]

Light is EM radiation. It propagates at C, and it is fundamental property of our universe. You can ask why we perceive time at the rate we do, and that would be much more interesting question.

Now basic carrier of EM radiation is photon. It has no mass, and its energy depends solely on its frequency. You can even have photon with no energy, assuming that it has zero frequency, and it would be still propagating at the speed of light, although we could never detect it because it has no energy.
Your question comes to accelerated frames. I suggest that you search for "tween paradox" in older threads.

 

[ZirkMan]

Your question comes to accelerated frames. I suggest that you search for "tween paradox" in older threads.

I'm quite familiar with the twin paradox, thank you. I know that observers in non-stationary frames of reference observe time dilation, length contraction and increase of mass. What I would like to know is if that relativistic increase in mass (momentum) has any effect on intensity of gravitation field of the object in relative motion? In other words, if gravitation is relative to speed or not? And why.

 

[S.Vasojevic]

Yes, if you accelerate object with mass, you are adding to its energy-mass content, and thus increasing its gravitational potential.

 

[Dale]

Yes, if you accelerate object with mass, you are adding to its energy-mass content, and thus increasing its gravitational potential.

No, you don't. http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html

 

[ZirkMan]

Yes, if you accelerate object with mass, you are adding to its energy-mass content, and thus increasing its gravitational potential.

OK, if this is true and gravity is indeed relative to observer and varies with the observer's relative speed (this comes from what you've said) then there must be a HUGE difference in a trajectory of high energy cosmic rays around Earth in comparison to particles traveling with conventional relative speeds. I can imagine that for such particles really heavy objects like neutron stars would literally become black holes when they would fly with relativistic speeds close enough.
It would also open a possibility to create a black hole for an observer just by increasing his relative speed relative to the object. Even when before the acceleration the object wasn't one. Sorry, if it sound crazy but this is what it implies.

Maybe according to transformation equations these effects won't occur. Is there a way I can find out how big this effect will be for various relative speeds and masses?

 

[ZirkMan]

No, you don't. http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html

Ok, so does this mean: No and at the same time, we are not quite sure and why? Because that's how I understood it.

 

[S.Vasojevic]

OP is struggling with notion that from photons frame mass is traveling at C. You are about to confuse him even more.
To OP:
Consider astronaut piching baseball in a empty space. They separate at 30 m/s. Astronaut has 1000 times more mass then ball. Can we calculate when their frames separate, how much is each frame accelerated, or we can just tell that they are separating at 30 m/s?

 

[ZirkMan]

To OP:
Consider astronaut piching baseball in a empty space. They separate at 30 m/s. Astronaut has 1000 times more mass then ball. Can we calculate when their frames separate, how much is each frame accelerated, or we can just tell that they are separating at 30 m/s?

You assume you can look at the situation from some 3rd absolute frame of view from which you can look at both frames at once. But you can't. That's what SR is about. I'm not sure if this has something to do with my question though or maybe I just didn't understand your point.

 

[S.Vasojevic]

No, you can look from their initial frame, and calculate that astronaut has been accelerated 1000 times less then a ball.
Now consider light bulb emmiting a photon. Photon has no mass, but it has momentum. It ventures to space and slightly recoils light bulb in a opposite direction.
Using the same principle as above you can see that photon is the one traveling at C, not the object with mass.

 

[ZirkMan]

No, you can look from their initial frame, and calculate that astronaut has been accelerated 1000 times less then a ball.
Now consider light bulb emmiting a photon. Photon has no mass, but it has momentum. It ventures to space and slightly recoils light bulb in a opposite direction.
Using the same principle as above you can see that photon is the one traveling at C, not the object with mass.

I know what you are trying to say. But this is only from perspective from the initial frame of reference. If you were an observer standing in the initial frame you would observe what you describe. If you were in the frame of reference of the bulb you would see the photon running away by speed c and you (the observer in the initial frame) would recoil slightly in the same direction as the escaping photon. From the photon's perspective (if there was any possible) the bulb and you would suddenly accelerate away with c. There is no way you can tell that any of those frames is truer than other. This is the beauty of the Special Relativity. There is no other lesson in that.

We still do not know what would happen with gravity of the bulb and observer in relation to the photon (or better a 0.999c accelerated particle).

 

[Integral]

If you are interested in learning the basics of physics you would not start with relativity and the speed of light. If you want to learn the basics, start with classical mechanics and electromagnetism.

With learning electromagnetism you would find that Clerk Maxwell derived the speed of light from electromagnetic theory in 1867. As mentioned earlier in this thread the value depends upon the permittivity and permeability of free space.

$$c = \frac 1 {\sqrt {\mu_0 \epsilon_0}}$$

This is not a result that is included in "basic" physics, you need sophicated math, (partial differential equations} and a good understanding of electromagnetism. You will not see this derivation until upper division undergrad work in most universities.

 

[ZirkMan]

Thanks Integral. I will certainly look into it. However. for now I find this problem of derivation of the value of c a closed case.

Maybe I should open a new thread on the question of the relativity of gravity alone so that those 2 topics don't mix anymore. Is that question that's more interesting for me right now.

 

[S.Vasojevic]

I told you few posts earlier to try to really understand twin paradox. If you insist on your opinion, then tell me how can you say which twin is aging slower towards his brother?
Your questions are perfectly logical, but answered many times over. So as Integral suggested, just keep reading.

 

[ZirkMan]

I told you few posts earlier to try to really understand twin paradox. If you insist on your opinion, then tell me how can you say which twin is aging slower towards his brother?
Your questions are perfectly logical, but answered many times over. So as Integral suggested, just keep reading.

I guess that the difference must come from the fact that one of the twins jumps frames (accelerates/deaccelerates). Also some difference in frames will come from the General theory of relativity (the twin that stays on Earth will be in a differently curved spacetime that the other). So it is quite understandable there is not a symetry in their frames of reference therefore their age will differ. I still do not get what this has to to with my question?

 

[S.Vasojevic]

There you go, so at what point mass you are claiming is moving at C was accelerated?

 

[ZirkMan]

There you go, so at what point mass you are claiming is moving at C was accelerated?

If I was in an inertial frame of reference and moving in relation to you in constant uniform motion with a relative speed of 0.999c (I'm material so not c) there would be no way you can tell if I am at rest and you are moving or you are at rest and I am moving with 0.999c. Perfect symetry here. Do you agree?

In this situation I would see identical clocks in your hands ticking much slower than mine, length of an identical meter stick would be contracted and if I could measure your mass you would appear much heavier than me (although we are twins :). The same would apply to you in respect to me. Basic special relativity so far.

Now the question is if the higher mass of you at 0.999c will cause the gravitation field around you to increase and influence my trajectory in a different way than if I was moving in realation to you in constant uniform motion with relative speed of 0.001c?

If this has been answered many times over then I just want to know the answer. You have said that yes, it will be different. Then I have showed you that this could lead to paradoxes with creation of black holes out of objects that weren't black holes before. If the answer is no, I just want an explanation why when everything else changes the gravity isn't?

 

[S.Vasojevic]

That would be truth if you and I were alone in the universe. In reality it is easy to distinguish who is moving at 0.999 C, and his time would tick slower, and the others one faster. You should familiarize yourself with notion of comoving observers.

How the gravity potential increases with speed is not straight forward, but no black holes would emerge.

 

[matheinste]

If I was in an inertial frame of reference and moving in relation to you in constant uniform motion with a relative speed of 0.999c (I'm material so not c) there would be no way you can tell if I am at rest and you are moving or you are at rest and I am moving with 0.999c. Perfect symetry here. Do you agree?

That would be truth if you and I were alone in the universe. In reality it is easy to distinguish who is moving at 0.999 C, and his time would tick slower, and the others one faster. You should familiarize yourself with notion of comoving observers.

QUOTE]

Is the second quote in answer to the first?

Matheinste.

 

[pervect]

If I was in an inertial frame of reference and moving in relation to you in constant uniform motion with a relative speed of 0.999c (I'm material so not c) there would be no way you can tell if I am at rest and you are moving or you are at rest and I am moving with 0.999c. Perfect symetry here. Do you agree?

In this situation I would see identical clocks in your hands ticking much slower than mine, length of an identical meter stick would be contracted and if I could measure your mass you would appear much heavier than me (although we are twins :). The same would apply to you in respect to me. Basic special relativity so far.

Now the question is if the higher mass of you at 0.999c will cause the gravitation field around you to increase and influence my trajectory in a different way than if I was moving in realation to you in constant uniform motion with relative speed of 0.001c?

If this has been answered many times over then I just want to know the answer. You have said that yes, it will be different. Then I have showed you that this could lead to paradoxes with creation of black holes out of objects that weren't black holes before. If the answer is no, I just want an explanation why when everything else changes the gravity isn't?

Is *that* what you were asking? Your question was worded in a very strange manner and was almost incomprehensible up to now.

The theoretical prediction of the gravitational field from rapidly moving bodies is well understood from the standpoint of GR. See for instance http://arxiv.org/abs/gr-qc/0110032. Basically, the gravity from a relativistically moving source will appear as an impulsive shock wave in the extreme relativistic limit.

What isn't clear is how to explain the predictions of GR in this case to people who view gravity as some sort of "force".

Probably the easiest thing to do is not to disabuse them of this notion, and to use the analogies drawn between the gravitational field of a rapidly moving body and the electric field of a rapidly moving body. They won't get quite the full correct understanding, but it will probably be close enough. Unfortunately, I strongly suspect that most people who ask this question aren't already familiar with the electric field of a rapidly moving body, either.

I don't think I can add much , unless you're interested in a lecture on the electric field of a rapidly moving body? If I had to guess, I would guess you are one of the vast majority who aren't familiar with this, though I think it's an interesting topic.

 

[S.Vasojevic]

yes it is

 

[ZirkMan]

That would be truth if you and I were alone in the universe. In reality it is easy to distinguish who is moving at 0.999 C, and his time would tick slower, and the others one faster. You should familiarize yourself with notion of comoving observers.

I think we can safely presume that for the purpose of the thought experiment we are both comoving observers and our peculiar velocity is 0. I do not see how you can now break the symetry of our views and easily distinguish who is moving and who is not? All will be relative.

 

[ZirkMan]

The theoretical prediction of the gravitational field from rapidly moving bodies is well understood from the standpoint of GR. See for instance http://arxiv.org/abs/gr-qc/0110032. Basically, the gravity from a relativistically moving source will appear as an impulsive shock wave in the extreme relativistic limit.

Great, so basically both the Special theory and General theory effects will combine as one would expect from their transformation laws which will result in this length contracted shockwave of the curved spacetime according to general theory. The local gravitational intensity of the shockwave at its peak will be much stronger than the strenght of the field for a non relativistic speed observer in the same relative distance. Right?

What isn't clear is how to explain the predictions of GR in this case to people who view gravity as some sort of "force".

Not one of them, so don't worry. Gravity is the result of curved spacetime for me.

 

[S.Vasojevic]

I think we can safely presume that for the purpose of the thought experiment we are both comoving observers and our peculiar velocity is 0. I do not see how you can now break the symetry of our views and easily distinguish who is moving and who is not? All will be relative.

Ok, I didn't put it to well. Try reading this: https://www.physicsforums.com/showthread.php?t=349396"

Also some usefull links are:
http://www.einstein-online.info/en/"
http://www.astro.ucla.edu/~wright/cosmolog.htm"

If we are comoving, and our peculiar velocity, is 0, but we are separating at 0.999 C, then you are sitting on the very edge of my observable universe, and vice versa, and we are moving due to the expansion.

 

[ZirkMan]

If we are comoving, and our peculiar velocity, is 0, but we are separating at 0.999 C, then you are sitting on the very edge of my observable universe, and vice versa, and we are moving due to the expansion.

Ok, I see your point now. You are right, I cannot be comoving and at the same time "accelerated" to 0.999c by something else but the expansion of space.

So, Ok, in my experiment we are not comoving observers. But even then the measurement of your and my relative velocity in relation to the comoving frame of reference doesn't give you any base to judge who is moving and who is not in absolute terms (only relative to the comoving frame). And it certainly doesn't give rise to the difference in age of the traveling twins. The existence of the comoving frame is totally irelevant to the effect because the geometry of the universe in the comoving frame is considered to be flat (so we do not presume any global diferences in the background spacetime curvature of the frames in comparison). The difference in age after the journey is solely based on the broken symetry resulting from the cumulation of differences of the frames both twins went through during the duration of the journey (as I have explained above). But this would apply only for the twins experiment.

For our experiment if we were twins and we would be born into our inertial frames of reference moving in relation to each other with 0.999c and then I would suddenly stop and meet you (so no slow acceleration/deacceleration would occur) we would be the same age after we met. Even though before I was moving with 0.999c in relation to you. I know this is not realistic but as an illustration should be enough.

 

[S.Vasojevic]

For our experiment if we were twins and we would be born into our inertial frames of reference moving in relation to each other with 0.999c and then I would suddenly stop and meet you (so no slow acceleration/deacceleration would occur) we would be the same age after we met. Even though before I was moving with 0.999c in relation to you. I know this is not realistic but as an illustration should be enough.

If we are twins we must be born in the same frame, by definition. If something suddenly stops, it is infinite deacceleration. Speck of dust falling on the floor of your room would exert infinite force if instantly stopped, thus can not be instantly stopped.

It is not like when SR, GR and new age stuff came along that we dropped classic physics.
It is absolutely essential to have good knowledge of classical mechanics and electromagnetism in order to trully comprehend paths of modern physics.
I suggest that you start with Newtonian mechanics.

EDIT: When you are coming up with thought experiment, in order to make any sense, you should obey every known law of physics. If you ask what would happen if something instantly stops, the only result you will get is answer why it can not be so. You can not put it in any broader contest.

 

[ZirkMan]

All right. I think we came as long as we could. I wanted to demonstrate the basic principles not to model an exact experiment in the real universe (not yet). Thank you for your time.

 

[ZirkMan]

I suggest that you start with Newtonian mechanics.

My personal opinion on that this is really wrong. We should start teaching physics even small children from the beginning from the relativity's point of view (of course not matematically but as a principle) and introduce classical mechanics as a special limited case later as a historic note.

This is because the relativistic model of the world is so much real model of reality than any other model and when you study for years physics in the classical framework of absolute time and space and only a after many years you are introduced to the relativity as if it was some special case of the previous model (most people won't even reach this stage and physics will remain for them classical forever), no wonder people have problem to understand even basic principles of relativity and struggle with a twin paradox or other thought experiments for such a long time (and even then their explanation must not be based on correct principles)

So this is my personal view, and I am going to watch the Mechanical Universe series now so that nobody can point to me that I should study that first (which I have but not full time). :)