Speed of Light and Energy...?

[Loki_999]

Damn it... i'm an idiot and posted in haste then rushed off from work. Of course I meant to say why doesn't mass stay constant and c change....

What i'm trying to get at (i think) is perception. We perceive c to be constant, but maybe its not. Kind of like looking at one of those black and white images where one minute its an image of a white vase and the next two black faces facing each other.

Sure, this is just insane ramblings, and I know flies in the face of common wisdom, but on the other hand, some great ideas have come from insane ideas.

[hackenslash]

Damn it... i'm an idiot and posted in haste then rushed off from work. Of course I meant to say why doesn't mass stay constant and c change....

What i'm trying to get at (i think) is perception. We perceive c to be constant, but maybe its not. Kind of like looking at one of those black and white images where one minute its an image of a white vase and the next two black faces facing each other.

Sure, this is just insane ramblings, and I know flies in the face of common wisdom, but on the other hand, some great ideas have come from insane ideas.

When you get the answer to the question 'why is the speed of light the same regardless of inertial frame', you will have answered your own question. It isn't about perception. That's actually what happens, as has been verified.

[dj357]

i'm still lost as to a definite explanation to that question. i'm guessing it's something to do with the total velocity through all dimensions? (since that was the last exchange you mentioned)

[oddmanout]

That's why we have nuclear fusion fission reactors and (regrettably) atom bombs, but conversely why we will (hopefully) have nuclear fission fusion reactors (like the sun) in the future.

Had a 50-50 chance of getting it right.

[hackenslash]

i'm still lost as to a definite explanation to that question. i'm guessing it's something to do with the total velocity through all dimensions? (since that was the last exchange you mentioned)

Exactly right. Now go and think about that for a second. It should lead you to why the speed of light is always the same, no matter what frame of reference you're in.

[Twiglet]

In the simplest terms, as far as you are concerned, you can always go 1mph faster, and your mass is the same (unless you insist on eating a sandwich or taking a piss).

The difference is accounted for in other frames of reference by time dilation.

The full expression of E=mc^2 is actually

Energy= Rest mass x c^2/(1-v^2/c^2)^1/2

Many people fall for the linguistic trap of equating mass with rest mass....

Sorry if this has all been said before, I'm just responding to the last few posts and couldn't be bothered to trawl back to see if it's already been explained.

[hackenslash]

Not a problem. We were trying to gently lead dj537 to the answer on his own, but it's not a problem that you've directly provided it.

So, dj, does this answer makes sense to you?

[dj357]

pretty much yeah. what twiglet said was a tacit/inherent point within the understanding I gained throughout the discussion which is why I couldn't directly formulate it

[Farsight]

Our mass does change when we travel fast. E=mc2, remember. Kinetic energy is still energy. That's another reason for the lightspeed barrier, because the increase in mass means that more energy is required for further acceleration. By the time you get to just shy of the speed of light, mass gets close to infinity, meaning that an infinite amount of energy is required to get the rest of the way. This is why light speed is impossible for any body with rest mass.

You're talking about "relativistic mass" there. When people talk about mass, they're usually talking about rest mass aka invariant mass. See http://en.wikipedia.org/wiki/Mass_in_special_relativity.

[Farsight]

dj357: The local speed of light in vacuo is always measured to be the same because we use the motion of light to define the second and the metre. See http://tf.nist.gov/cesium/fountain.htm to read about the NIST caesium fountain clock and http://en.wikipedia.org/wiki/Second for the definition of the second:

"Since 1967, the second has been defined to be the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. This definition refers to a caesium atom at rest at a temperature of 0 K (absolute zero), and with appropriate corrections for gravitational time dilation."

In the NIST fountain clock, lasers and a microwave cavity are employed to cause hyperfine transitions, which are electron spin flips within caesium atoms. These emit microwaves of a given "frequency", which is measured by a detector:



Microwaves are of course electromagnetic radiation - light in the wider sense. I put the word frequency in quotes above because frequency is measured in Hertz, which is defined as cycles per second. What the detector essentially does, is count incoming microwave peaks. When it gets to 9,192,631,770, we say that's a second. Hence the frequency is 9,192,631,770 Hz by definition.

Note the mention of gravitational time dilation in the wiki article. If you were to take this clock and place it in a region of low gravitational potential, it would be like pressing a slow-motion button. All electromagnetic and other processes would then occur at a reduced rate, including the spin-flip and the motion of the microwaves towards the detector. However regardless of this, when the detectors get to 9,192,631,770, we'd still say that's a second. In this situation, the light is moving slower, and this is why the second is bigger. We then use this second... to measure the speed of light. That's why we always measure the local speed of light in vacuo to be 299,792,458 m/s.

PS: provided you avoid the radial length contraction of general relativity, the metre is not affected. It's defined as the distance travelled by light in free space in 1⁄299,792,458th of a second, so the slower light and the bigger second cancel each other out. Do trust your initial instincts on all of this, because all measures of time involve some kind of motion. Thus time is a dimension in the sense of measure, but it isn't a dimension that offers freedom of movement. You cannot "move" through a cumulative measure of motion. Hence time machines are science fiction.

[Twiglet]

Microwaves are of course electromagnetic radiation - light in the wider sense. I put the word frequency in quotes above because frequency is measured in Hertz, which is defined as cycles per second. What the detector essentially does, is count incoming microwave peaks. When it gets to 9,192,631,770, we say that's a second. Hence the frequency is 9,192,631,770 Hz by definition.

Note the mention of gravitational time dilation in the wiki article. If you were to take this clock and place it in a region of low gravitational potential, it would be like pressing a slow-motion button. All electromagnetic and other processes would then occur at a reduced rate, including the spin-flip and the motion of the microwaves towards the detector. However regardless of this, when the detectors get to 9,192,631,770, we'd still say that's a second. In this situation, the light is moving slower, and this is why the second is bigger. We then use this second... to measure the speed of light. That's why we always measure the local speed of light in vacuo to be 299,792,458 m/s.

PS: provided you avoid the radial length contraction of general relativity, the metre is not affected. It's defined as the distance travelled by light in free space in 1⁄299,792,458th of a second, so the slower light and the bigger second cancel each other out. Do trust your initial instincts on all of this, because all measures of time involve some kind of motion. Thus time is a dimension in the sense of measure, but it isn't a dimension that offers freedom of movement. You cannot "move" through a cumulative measure of motion. Hence time machines are science fiction.

Farsight, I think it's important to stress that the speed of light is an absolute limit for more reasons that the kind oi "by definition the speed of light is x many caesium decays" which you are offering.

The speed of light is the speed at which a body containing any mass whatsoever would require infinite energy to attain. The same finding can be used to proved mathematically that any body which has no mass must, by definition, be travelling at the speed of light.

The point is illustrated easily with this thought experiment. If someone moving away from you at close to the speed of light shone a torch at you, both you and they would measure the speed of light coming from that torch to be exactly the same, regardless of the time dilation and lorentz contraction you both experience. What would be different is that the light you measure would be red-shifted.

Despite the fact you both experience time and distance differently, you measure the speed of the beam of light to be exactly the same.

Talking about x many Caesium decays implies that we somehow fudge the calculation to fit what we see, and that there is some overall frame of reference in which everything is the same. In fact both the observer and observeds frame of reference are equally valid, and despite the fact he is moving away from you, the light arrives at the same speed as it would if he were stationary.

That's a really weird concept. If he were throwing a ball to you, and walking away, the ball would arrive at you much slower than if he threw it at the same speed (as far as he is concerned) while standing still.

[Farsight]

Farsight, I think it's important to stress that the speed of light is an absolute limit for more reasons that the kind of "by definition the speed of light is x many caesium decays" which you are offering.

Fair enough.

The speed of light is the speed at which a body containing any mass whatsoever would require infinite energy to attain. The same finding can be used to proved mathematically that any body which has no mass must, by definition, be travelling at the speed of light.

Again, fair enough. But do you know the underlying reason for this? It's fairly obvious when you look at pair production. We can make bodies such as an electron and a positron out of light. Or should I say a +1022keV gamma photon, but it's light in the widest sense. The electron and the positron have angular momentum and magnetic dipole moment, so there's something "going round and round" in there. When we annihilate the electron and the positron the result is light. So it's reasonable to assume that it's light going round and round in there. To move an electron you have to deform this circulating light into a helical path, by adding extra energy, eg by Compton scattering. No matter how much extra energy you add, you can't make this circulating light move linearly faster than light. It's rather like stretching a helical spring. It gets harder and harder to stretch it striaghter and straighter. But no matter how hard you pull, you can't stretch it straighter than straight.

The point is illustrated easily with this thought experiment. If someone moving away from you at close to the speed of light shone a torch at you, both you and they would measure the speed of light coming from that torch to be exactly the same, regardless of the time dilation and lorentz contraction you both experience. What would be different is that the light you measure would be red-shifted.

No problem. Light is a wave in space. The speed of the emitter doesn't change the speed of the light.

Despite the fact you both experience time and distance differently, you measure the speed of the beam of light to be exactly the same.

Yes, and it is the same in an SR situation. The difference only arises in a GR situation where there isn't the time-dilation symmetry. Instead, it's absolute. Then you still measure the speed of light to be 299,792.458 m/s, but if your seconds are bigger the speed isn't really the same.

Talking about x many Caesium decays implies that we somehow fudge the calculation to fit what we see, and that there is some overall frame of reference in which everything is the same. In fact both the observer and observeds frame of reference are equally valid, and despite the fact he is moving away from you, the light arrives at the same speed as it would if he were stationary.

It's no fudge, this is how it is. Look at the NIST fountain clock and check out what I said about frequency. We really do count 9,192,631,770 microwave peaks and call it a second, hence the frequency is 9,192,631,770 hertz by definition. By the way It's microwave radiation from Caesium hyperfine transitions rather than Caesium decays per se.

That's a really weird concept. If he were throwing a ball to you, and walking away, the ball would arrive at you much slower than if he threw it at the same speed (as far as he is concerned) while standing still.

It isn't like throwing a ball. It's like he's moving away from you whilst splashing a pond that you're both standing in. The speed of the resultant waves is not related to his speed. Hence you see that redshift.

[Twiglet]

Again, fair enough. But do you know the underlying reason for this? It's fairly obvious when you look at pair production. We can make bodies such as an electron and a positron out of light. Or should I say a +1022keV gamma photon, but it's light in the widest sense. The electron and the positron have angular momentum and magnetic dipole moment, so there's something "going round and round" in there. When we annihilate the electron and the positron the result is light. So it's reasonable to assume that it's light going round and round in there.

What does the conservation of momentum and AM have to do with the price of fish in relation to why c is a limit?

Yes, and it is the same in an SR situation. The difference only arises in a GR situation where there isn't the time-dilation symmetry. Instead, it's absolute. Then you still measure the speed of light to be 299,792.458 m/s, but if your seconds are bigger the speed isn't really the same.

Please explain, preferably with a link.

It's no fudge, this is how it is. Look at the NIST fountain clock and check out what I said about frequency. We really do count 9,192,631,770 microwave peaks and call it a second, hence the frequency is 9,192,631,770 hertz by definition. By the way It's microwave radiation from Caesium hyperfine transitions rather than Caesium decays per se.

You are putting the cart before the horse. A body which moves faster and faster away from me (relative to itself) approaches the speed of light asymptotically as far as I'm concerned. the fact this coincides with a frequency count is irrelevant.

[Farsight]

What does the conservation of momentum and AM have to do with the price of fish in relation to why c is a limit?

The conservation of angular momentum doesn't. It's the existence of angular momentum that's important. It means there's something going round and round. It's doing so at c, and the electron really is made from a photon via pair production. The electron really is made from light. That's why it can't go faster than light. And neither can you. See beta decay re how a neturon decays into a proton, an electron, and an antineutrino in about 15 minutes. Also see low-energy proton/antiproton annihilation which tends to produce two neutral pions that decay in a nanosecond into gamma photons. Neutrinos are a bit special, but other than that, the common factor is light.

Please explain, preferably with a link.

I thought I did that with the NIST fountain clock link. We count 9,192,631,770 incoming microwave peaks to define the second and thence the frequency is 9,192,631,770 Hertz by definition. In a place where there's gravitational time dilation, the second is bigger because the coordinate speed of light is less. Locally you always measure the same old 299,792,458 m/s in vacuo because when the light moves slower the second is bigger, and they cancel each other out. It's called an immersive scale change. Einstein started with a constant-speed-of-light postulate in 1905, but in 1911 he wrote On the Influence of Gravitation on the Propagation of Light, where we can see his ideas evolving. He gives the expression c = c0 (1 + Φ/c²), which is c varying with gravitational potential. Then in 1912 he said it again when he wrote "On the other hand I am of the view that the principle of the constancy of the velocity of light can be maintained only insofar as one restricts oneself to spatio-temporal regions of constant gravitational potential". He repeated this in 1913 when he said: "I arrived at the result that the velocity of light is not to be regarded as independent of the gravitational potential. Thus the principle of the constancy of the velocity of light is incompatible with the equivalence hypothesis". I'm not sure of the original source of those two, but it's there again in 1915 when he says "the writer of these lines is of the opinion that the theory of relativity is still in need of generalization, in the sense that the principle of the constancy of the velocity of light is to be abandoned." That’s on page 259 of Doc 21, see this link re the collected papers. He says it again in late 1915, on page 150 of Doc 30, within The Foundation of the General Theory of Relativity, 3.6 Mbytes. Einstein says "the principle of the constancy of the velocity of light in vacuo must be modified.". He spells it out in section 22 of the 1916 book Relativity: The Special and General Theory where he says this:

"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. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. But in reality this is not the case. We can only conclude that the special theory of relativity cannot claim an unlimited domain of validity; its results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light)".

People tend to see the word velocity in the translations without seeing the context and without noticing that he’s repeatedly referring to “the principle”. They don’t see that he's talking about the SR postulate, which was the constant speed of light. They don't realise that what he actually said was die Ausbreitungsgeschwindigkeit des Lichtes mit dem Orte variiert which translates into the speed of light varies with the locality. He was saying the speed varies with position, and hence it causes curvilinear motion. It causes the light to follow a curved path. like a car veers when the near-side wheels encounter mud at the side of the road.

You are putting the cart before the horse. A body which moves faster and faster away from me (relative to itself) approaches the speed of light asymptotically as far as I'm concerned. The fact this coincides with a frequency count is irrelevant.

I'm just telling you how it is. No problem re that body. A body accelerating away from you does so at an ever-reducing rate as it approaches the speed of light. And it can never get there. Pair production is real. The simplest body is an electron, think of it as light moving in a circular path at c. If it's going past you, that path looks helical. It can't be going round at c and moving forward at c. It just can't happen.

[Twiglet]

Im responding to farsights post above, which is massive, so I'm not going to quote the whole lot.

Electrons can't reach c because they contain mass and therefore would require infinite energy to attain c. The manner of their creation is utterly irrelevant. As is the issue of spin.

The GR time dilation effect of gravity is also superflous to why c constitutes an absolute limit, and is explicable because of the curvature in space-time caused by gravity fields. SR time dilation stacks with Gravitational time dilation, it doesn't replace it.