Speed of Light question

OK, I voted for you. Your theory is as good as anyone else's on here. No way anyone will prove is disprove any of this anyhow. It is all theory based on observation and measurements which may or may not be factual given that we don't really understand quantum physics, gravity, time or any of the other stuff. If you think you know, that's good enough for me. I'm movin' on...

AHA! That's the divide I was trying to remember. Baryons are things like photons, etc., that can not travel faster than c. Tachyons are theoretical companions that can not travel slower than c. We could be in a universe filled with tachyons, but not be able to measure them.

I believe you have your terms confused. Baryons are particles such as the proton and neutron. As they have mass they always travel at speeds less than c. Photons are bosons which are particles with integral spin, which being massless have to always travel at exactly c.

Here I must respectfully disagree. Since a photon has energy, it also has mass in accordance with E=MC² even if that mass is vanishingly small. Furthermore, within that definition, there can be no such thing as a mass-less particle. Even a neutrino has mass, infinitesimal though it may be. Bottom line, a photon at any given frequency has a definable energy level, which means it has a calculable mass, no matter how small, and this applies for any member of the sub-atomic zoo as well.

Since I'm being pedantic on this post, I might as well go for broke. A lot of people avoid this whole confusion by using mass to only mean rest mass.

Then you get a straightforward representation in

E² = p²c² + m_o²c⁴

where m_o is rest mass. Since a photon is never at rest, it has no rest mass and E = pc which gives a self-consistent result.

Um... Would you mind terribly defining "p" for me?

Momentum. Sorry.

Having looked up the definitions and worked through the math, I see your point. But I admit I get a nagging feeling...

DrMoose, the fact is that in modern physics parlance, the term "mass" is only used for the rest mass. There is a fundamental difference between particles with a very small mass and particles with no mass. The neutrino is a very interesting example, as it was originally completely unknown whether it had mass or not. As I understand it, experiments observing neutrino oscillation (at different distances from nuclear power plants, if I recall correctly) have shown that the mu and tau neutrinos have mass, and I believe it is widely accepted that the electron neutrino almost certainly has a small mass as well.

So really it is semantics. But if you say everything has mass, the term mass becomes virtually redundant, as it means the same as energy. Which is why the modern restricted usage of the term has arisen, I suppose.

It would seem that my understanding of Relativity is incomplete. I guess I am really a simple experimentalist, a mechanic.

So, if mass must be redefined as rest mass, or mass which is at rest or stationary, I think it begs the question, stationary relative to what? A thing can only be at rest relative to a particular inertial frame of reference, and we have already established that there is no truly stationary or at rest frame of reference, so how then do we establish this rest mass? It almost sounds like a contradiction in terms.

I concede that this may be nothing more than a paradox of semantics. Am I trying to make too much soup from this bone?

One other thing, didn't I read somewhere just recently that someone had succeeded in bringing a photon to a halt?

So, if mass must be redefined as rest mass, or mass which is at rest or stationary, I think it begs the question, stationary relative to what?"

Relative to you, or the scientist who is measuring the rest mass. Relative to something else, it has a different mass.

"didn't I read somewhere just recently that someone had succeeded in bringing a photon to a halt?"

NIST has brought atoms to a halt using lasers, I'm not sure about photons.

Yes, I recall an experiment where electromagnetic radiation was (I think literally) brought to a walking pace in some sort of exotic material. Of course the speed of light in a normal material is slowed down according to the refractive index. This does not contradict the fact that the speed of light is constant, as what you are observing in a material is a complicated interaction of electromagnetic waves and electrons which overall has a speed less than c.

[A search for "stopped light" found the news we remembered - eg http://news.bbc.co.uk/1/hi/sci/tech/1124540.stm]

Think about it. The only way for the speed of light to be a constant is if it is infinitely fast or has no speed at all. Any other measured speed is the product of a time frame difference created by spacial difference. Can anyone actually prove otherwise? How can we say time is not a constant but light is? If you travel away from the earth at near the speed of light isn't the earth travelling away from you at near the speed of light from your perspective? Who is to say which object is the referrence? All previous measurements must be faulty due to time differences created by spacial differences. If you could create a worm hole and travel through you would not only end up in a different place in the universe but also a different time frame. Wouldn't it be a hoot if black holes are doors back to the beginning of it all and time/space is constantly being recycled?

The true and final answer to what happens when the train reaches the speed of light is that Scotty says to Kirk "I cannae hold her captain. She's gonna blow, I tell ye."

Check me on this. The last time I studied Relativity, both General and Special, the contention, verified as much as possible by experiment, was that for any frame of reference, the speed light is constant. Dr. Einstein himself contended that for any observer in a state of constant motion, it is impossible to determine if the observer is in motion or those objects he is passing. So, free-falling through flat space, say a few million lightyears from any other frame of reference, it would be impossible to determine if you were traveling at 2m/s or 30%c.

I guess the point is that speed and velocity are only measurable in terms of an external, or privileged frame of reference. But, Relativity specifies that there is no privileged frame of reference, and that the constancy of "c" guarantees this. Almost makes it seem like motion is meaningless.

Relative motion is the only type of motion. More precisely you can never determine your speed relative to space (that was the topic of the crucial experiments that tried to determine the speed of the Earth relative to the aether and discovered instead that the speed of light seemed to be a constant), but only relative to other objects. Of course such relative velocities are meaningful and well-defined (from a specific frame of reference, such as yours).

All velocities are relative velocities, so to say a spaceship is moving is (pedantically) meaningless, but to say it is moving with a certain velocity relative to the Earth makes perfectly good sense. So it is only the concept of absolute motion that is meaningless. The reason this is a little unintuitive is that we have a single reference frame (the frame of the surface of the Earth) which we use to define most of the velocities we deal with in our lives, but this is not always the case in more general situations.

I think that because photons behave as waves there may be a Doppler effect. If so then a signpost in front of our "train" travelling at 0.999c would appear to be twice as close when the headlights shone on them, because the reflected light travels back to the driver at c. whilst the light from the tailights shining on the back of the signpost we just passed, pointing the way to Alpha Centauri perhaps, would take a long time to catch up to the driver/observer. This would make it appear to be even further away than it is. Once the train reaches c my universe will implode and my brain will fry.

Yes sir, there is a Doppler effect with visible light, as well as any other electromagnetic radiation. As the light emitting object moves, the waves in the direction of motion tend to pile up on each other, thus increasing the frequency and shortening the wavelength, and in the other direction the oposite. Of course, since light is of such a high frequency and short wavelength that you have to be moving pretty fast to make any significant difference. But, this is where we get red and blue shifts from when we look at objects in deep space. Objects moving away from us display a red-shifted spectrum, objects moving towards us a blue shift.

I wouldn't be worried about anything exceeding "c", though, as the mathematics of Special Relativity show that it would require infinite force to accelerate an object that last tiny fraction of a percent to actually attain lightspeed, much less exceed it. So I think the universe and your brain are both safe.

Let's do an experiment

RIGHT! You drive, I'll observe, we compare notes when you get back. Deal?

Assuming the validity of "special relativity" as a model, this can of course never actually happen, as only objects with zero mass can travel at the speed of light.

However, we can still give a mathematically-based (but meaningless) answer to this hypothetical question.
This is one of those questions about limiting conditions. The proper way to handle it would be using abstract mathematical tools. The assumption must be that you measure time and distance using your local measures. Thus, if we formulate the special relativistic equations in terms of your measures of position and time we create an equation for your perceived speed of light in any direction in terms of your velocity. And the equation gives the value c for all velocities, including those above and below the speed of light. At exactly the speed of light, the equation as I formulated it includes " 0÷0 ", so it is only deterministic if we use the limiting value (defined in the usual way).
And the answer is: the calculated value for the speed of light remains 'c' regardless of your velocity, and that would include when you are travelling exactly at the speed of light, were that possible.

But there is another (pseudo-philosophical) way to approach this:
Newtonian physics is also relativistic - at least in terms of the conservation of momentum and of energy being maintained for all inertial observers. What was initially special about Einstein's "Special Theory of Relativity" was that the equations were specifically set up to add conservation of the speed of light to these constraints. Therefore, a failure of the speed of light at any velocity would represent a failure to achieve its theoretical objectives - and the theory has been well tested and examined, and no such failure reported.

"only objects with zero mass can travel at the speed of light."

If they have zero mass, do they really exist?

The speed of light relative to what?

Apologies for the missing word: it should have read zero rest-mass. At the moment the only entity known to travel at the speed of light is electromagnetic radiation (though "General Relativity" posits that gravitational waves also travel at the speed of light, there are some competing theories, and astronomical observations are thus far unable to distinguish between these).

Speed ... relative to what? to any inertial frame of reference (being the whole point of the question and indeed at the heart of Einstein's special theory of relativity - which of all physical theories is probably the one whose accuracy is the most precisely validated)

Light exists. Light is made of photons which have no mass. Anything that moves at the speed of light appears to move at the speed of light relative to all things that are not moving at the speed of light (this sounds paradoxical but is the basis of special relativity, a self-consistent and well-tested theory).

I know we've discussed this in the past and I don't wish to belabor the point, but, as I see it, there is nothing in SR that prohibits an object from traveling at, or above, the speed of light or even being accelerated to the speed of light provided the energy source is not in the observer's frame. It is, of course, fairly meaningless to hold that point of view since we would not be in communication with such an object and quite likely would not even know of its existence.

I know also there is some wide disagreement about the significance (or even existence) of a relativistic mass, with folks like me clinging to a use of energy instead. Am I wrong or only different?

Yes, TVP45. SR permits sth to already has speed equal or greater than c. Photons and gravitons (if gravitons really exist) already have speed c. Hypothetical particles, called tachyons, are supposed to already have a speed greater than c. (In another forum I had presented the weird behaviour of tachyons.) But "c" is supossed to be sth like a barrier for the speed: if sth is moving below c (a usual particle) it cannot obtain a speed above (or even equal to) c. And if sth is moving above c (a tachyon) it cannot obtain a speed below (or even equal to) c.

Hi Ejay,

Your question of speed is meaningless without a reference frame. According to special relativity light travels at c from any reference frame. If you are on the train it travels at c from you. If you are watching the train, it still travels at c from your perspective.

S

p.s. Trains do not travel at light speed, they travel at heavy speed.

Hey diddle diddle the grinch and the fiddle

The cow jumped over the moon at night

Would the little dog laugh to see such a sight

If the cow was moving at the speed of light?

And then there are Quasars, some of which we think we "see" as receeding faster than the speed of light. As Ricky would say, "Somebody's got a lotta 'splaining to do."

My quasar set died many years ago. When the garbage truck took it, I saw it recede at the speed of the garbage truck.

The thing about relativity is that from the point of view of the train crew, the speed of light from the head light, and the dashboard lights and the light in the loo, is c. All is normal to them, even though they may be nearly two dimensional from your point of view.

Relativity can have serious engineering applications, believe it or not. About thirty years ago, back when computers had stacks of punch cards for input, as keyboards had not been invented yet, I was involved in a effort to model the electron optics of Traveling Wave Amplifier Tubes, pronounced.... No, spelled TWT. TWTs are like linear accelerators run backwards. Instead of using microwaves to accelerate a beam of electrons, it slows down a beam of electrons to generate microwaves. They are delightful devices, much more efficient and reliable than transitors. The trick is to properly focus the electron beam, using electrostatic forces and magnetic lenses. We modeled, using Newtonian mechanics, the trajectories of about 100 "packets" of charge and compared them to what we observed. The electrons were accelerated through about 20,000 volts, and our model did not work well, until we applied a relativistic mass correction to the electrons. Using relativistic mechanics, the electron trajectories were spot on, within the 1 per cent sampling error implied in having only 100 packets of electrons. We were able to design tubes which accelerated the electrons, converted some of their kinetic energy into microwaves, and then decelerated the electrons to catch them (in a "collector") at very low velocity, thus dissipating very little energy as heat. The microwave output was about 20 times the heat output. (You will never get a 95% efficient transistor)

Typical of government projects, our super-efficient TWTs impressed no one. They (the NASA managers) wanted solid state amplifiers, which routinely failed in space (not radiation hard like a vacuum tube) and weighed much more than the TWT amplifers, because they needed bigger power supplies and huge heat sinks. The fact that there were "old-fashioned vacuum tubes" in the space shuttle (and in the B-1 bomber) was a politically sensitive secret.

#$$%^! I really should learn to read English. Ejay said "you are on a train going..." Of course the headlight projects. You have no idea how fast you're going. In your local inertial frame you're sitting still.

My apologies to those I badgered.

Yes, but since you are already at the speed of light it would appear that no

light was leaving the headlight. This is disregarding that time would be stopped and mass infinite.