I A question about the speed of light and electromagnetism

[Dale]

It's worth noting that dividing the distance I measure you to travel by the time I measure you to take is a quantity called velocity. Dividing the distance I measure you to travel by the time you measure you to take is a quantity called celerity. The two values are always different, and celerity is indeed infinite for light (if one is careful in interpreting "time you measure" in terms of "interval along worldline").

So the OP is talking about something that exists in physics, but it's just a choice between two different quantities and not any kind of duality. Nobody uses celerity for anything that I'm aware of because everything it does velocity also does, and with less potential for mathematical problems.

@johnfrancismurray you should really pay attention to this post above by @Ibix

Physicists use technical words with precise meanings. Speed is one of those words. The speed of light is a very specific quantity and it is finite, not infinite. Saying that it is infinite is simply wrong no matter how many ways you try to say it. In fact, the fact that the invariant speed is finite is the single key difference between relativistic and Newtonian mechanics.

There is a different quantity called celerity which has units of speed, and which goes to infinity as an object's speed goes to $c$ in an inertial frame. There are also related quantities called rapidity which is the hyperbolic angle between two four-velocities and which is infinite if one of those four-velocities is light like.

 

[Herman Trivilino]

why can you not accelerate anything to the speed of light Dave? please elaborate.

It's assumed that light travels at speed $c$ for all observers, regardless of their speed relative to the source of the light beam. Therefore, if you were to chase after a light beam in an attempt to catch it, it would recede from you at speed $c$ regardless of your speed. Thus you can never catch up with it, or in other words, you can never travel at speed $c$.

The only question is whether or not that assumption is valid. Many if not most physicists wouldn't accept it when Einstein proposed it almost 120 years ago. But since that time it has been shown to be valid and is an accepted fact of life for thousands of scientists, engineers, and technicians working in hundreds of places all across the globe.

but because time stops at the speed of light

The passage of time is not defined at light speed. That is very different from saying the passage of time is zero at light speed. In the latter case it is being given a definite value, which can't be done for something that's undefined.

 

[A.T.]

Popular science sources, however, are often not satisfied with things that cannot be defined (like $\frac 1 0$) and so they like to make a big deal of it. Instead of saying simply: proper time cannot be defined along a light-like trajectory, ...

Unlike $\frac 1 0$, the proper time interval approaches the finite value of $0$ in the limit of $v \rightarrow c$.

 

[ohwilleke]

The passage of time is not defined at light speed. That is very different from saying the passage of time is zero at light speed. In the latter case it is being given a definite value, which can't be done for something that's undefined.

I'm not convinced that the oversimplification that time is not passing in the reference frame of a particle with no rest mass has no use.

This oversimplification could be useful in understanding why individual photons, gluons, and gravitons do not decay, no matter how much energy they carry.

It could also be useful in a heuristic understanding of why forces carried by bosons with zero rest mass don't experience CP violation, which is equivalent to time symmetry violation. If there is no experience of the passage of time in the reference frame of the massless particle, then it can't have time symmetry violation, ergo the forces it carries can experience CP violation. And, indeed, none of the forces carried by zero rest mass bosons do experience CP violation.

 

[phinds]

Unlike $\frac 1 0$, the proper time interval approaches the finite value of $0$ in the limit of $v \rightarrow c$.

But I assume that you are NOT implying that a photon does experience (zero) time.

 

[PeroK]

I'm not convinced that the oversimplification that time is not passing in the reference frame of a particle with no rest mass has no use.

The reference to particle decay is interesting, but we were trying to establish the kinematics of light in relativity. Light is studied using an affine parameterisation (so we don't need proper time along a light-like trajectory). Ironically, many of the tests of GR are experiments involving light: the Pound-Rebka experiment; Eddington's original experiment using a solar eclipse; the Shapiro delay. So, far from being problematic, the kinematics of light are well understood and modelled within relativity, and provide many of the key tests of the theory.

 

[PeterDonis]

the reference frame of a particle with no rest mass

There is no such thing. It is impossible to have a reference frame in which a zero rest mass object is at rest.

You can have a coordinate chart in which the worldline of a zero rest mass object is one of the coordinate axes. But that chart will not meet the requirements for a reference frame, because it is impossible to construct an orthonormal frame field using that coordinate chart's basis vectors.

 

[PeterDonis]

This oversimplification could be useful in understanding why individual photons, gluons, and gravitons do not decay, no matter how much energy they carry.

No, it isn't, because even though the spacetime arc length along the worldlines of such particles is zero, those worldlines still consist of distinct events, and a decay could still happen at any of those events, if all we are looking at is the spacetime geometry. To explain why decays do not happen at any of those events, you have to show that the amplitude for such decays is zero at all of those events; and just showing that the arc length along the worldline is zero is not sufficient to do that.

none of the forces carried by zero rest mass bosons do experience CP violation.

I don't think this is true. Above the electroweak symmetry breaking threshold, the electroweak gauge bosons are massless, but AFAIK they can still induce CP violating interactions.

 

[Herman Trivilino]

I'm not convinced that the oversimplification that time is not passing in the reference frame of a particle with no rest mass has no use.

It may have some use, but it's still an oversimplification and is the source of a lot of misunderstanding.

 

[johnfrancismurray]

We should be cautious about this line of argument. The standard formulas of SR are derived using assumptions that imply that $v\lt c$ so cannot be expected to apply when it is not. Thus the infinities that appear in these standard formulas when we plug in $v=c$ (and likewise the negative numbers that appear under a square root sign when we plug in $v\gt c$) aren't telling us anything about how the world works, they're the math telling us that we're misusing it.

I'm happier with the argument that no matter how much energy we add to an object initially at rest relative to us, the resulting speed of the object relative to us will be less than $c$. This result follows from the velocity addition rule without introducing any infinities or trying to make sense out of a division by zero.

Thank you Nugatory, it's a very good point that you have made here and if other contributors from this thread are reading I want to pass on a thankyou to all of them also. Although I feel like my original statement and idea still stands up and is important I have learnt a lot from reading all the responses that overwhelmingly state that it should not be, is not, or is not relevant to an overall picture.
When I have time I can make my point again from a better position with the appropriate language. But if I may leave you with a thought for consideration as you have with me, it is that infinity has a very important function and is vital to the possibility of a universe and is not a place where the maths breaks down and speculation is out of bounds.
many thanks and hope 2025 is a great year for all
john

 

[phinds]

Although I feel like my original statement and idea still stands up

It would appear that you have not taken in what you have been told. Your original idea "an observation that light has both a 'true' and 'apparent' speed." most emphatically does NOT stand up and changing the language isn't going to change that.

Also, in physics, usually infinity IS the place where our models break down. To claim otherwise, in those cases, is pointless.

 

[Nugatory]

Thread is open again after a bit of minor cosmetic surgery to clean up confusing quoting

 

[Dale]

But if I may leave you with a thought for consideration as you have with me, it is that infinity has a very important function and is vital to the possibility of a universe and is not a place where the maths breaks down and speculation is out of bounds.

The concept of infinity is pretty well understood. It is not part of the real numbers, but there are infinite hyperreal numbers.

However, be aware that even though the hyperreals have infinite numbers, division by 0 is still undefined.

 

[Hornbein]

But I assume that you are NOT implying that a photon does experience (zero) time.

It depends on what you mean by experiencing zero time. I'd say that time depends on change. We able to perceive time because things change. A photon hits some rhodopsin in the the retina which causes it to change. If our body were completely unchanged then we could not perceive anything, could not think, and would have no concept whatsoever of time or anything else for that matter. Neither could a static observer use us to measure time. Something that isn't moving and never changes -- seems timeless to me. Similarly, if there is a completely empty Universe then there is no such thing as time. It never changes at all so how could anyone say that time is passing there.

AE said "time is what a clock measures." If clocks of any sort cannot exist (stopped clocks don't count) is there such a thing as time?

As far as we know a photon doesn't change at all until it is absorbed and ceases to exist. This is why we can see clearly galaxies billions of years old. So I think it is fair to say the photon doesn't experience time. An observer may be able to measure the movement of pulses of light, but the photon doesn't know anything about that so it is the observer experiencing time, not the photon.

How about a Universe with nothing but photons that don't interact? If there were an observer there they might see change. But there is no observer there. So is time passing or isn't it? I dunno.

 

[renormalize]

How about a Universe with nothing but photons that don't interact? If there were an observer there they might see change. But there is no observer there. So is time passing or isn't it? I dunno.

Consider an expanding universe like ours, but filled with nothing but the photons of the cosmic background radiation. According to physics, that radiation continuously reddens, which corresponds to the passage of time, even with no observers.
Or are you pondering philosophy, like whether a falling tree makes a sound when there's no observer around to hear it?

 

[phinds]

It depends on what you mean by experiencing zero time. I'd say that time depends on change. We able to perceive time because things change. A photon hits some rhodopsin in the the retina which causes it to change. If our body were completely unchanged then we could not perceive anything, could not think, and would have no concept whatsoever of time or anything else for that matter. Neither could a static observer use us to measure time. Something that isn't moving and never changes -- seems timeless to me. Similarly, if there is a completely empty Universe then there is no such thing as time. It never changes at all so how could anyone say that time is passing there.

AE said "time is what a clock measures." If clocks of any sort cannot exist (stopped clocks don't count) is there such a thing as time?

As far as we know a photon doesn't change at all until it is absorbed and ceases to exist. This is why we can see clearly galaxies billions of years old. So I think it is fair to say the photon doesn't experience time. An observer may be able to measure the movement of pulses of light, but the photon doesn't know anything about that so it is the observer experiencing time, not the photon.

How about a Universe with nothing but photons that don't interact? If there were an observer there they might see change. But there is no observer there. So is time passing or isn't it? I dunno.

As far as I can tell, none of that has anything at all to do with whether or not a photon experiences time.

 

[weirdoguy]

When I have time I can make my point again from a better position with the appropriate language.

Please don't. Your point has been refuted over and over again. It's not a matter of opinion, it's a matter of facts. Facts are against your point. Period.

Similarly, if there is a completely empty Universe then there is no such thing as time.

Nonsense. And I don't even see why someone with so many posts would even say such things. You should know better.

 

[jbriggs444]

I'm not convinced that the oversimplification that time is not passing in the reference frame of a particle with no rest mass has no use.

Any sentence involving "the reference frame of a particle with no rest mass" is sure to be nonsense. There is no such reference frame.

It is a classic blunder. Like "Never go up against a Sicilian when death is on the line".

 

[PeroK]

It is a classic blunder. Like "Never go up against a Sicilian when death is on the line".

Are you talking about chess?

 

[jbriggs444]

Are you talking about chess?

Popular movie reference.

 

[PeroK]

Popular movie reference.

Ah, okay. Personally, I'd be more worried by the King's Indian Defence.

 

[DaveC426913]

Are you talking about chess?

PeroK inadvertently reveals he is not actually an Earthling...