A oarticle traveling at c is length contracted to what?

[CosmicVoyager]

A particle traveling at c is length contracted to what?

Greetings,

A particle traveling at c (which would have to be massless) would be length contracted to what? Zero? Would it be two-dimensional? Or would it be whatever the smallest possible length is, Plank length?

And the same question about how much it is time dilated.

Thanks

 

[Fredrik]

The length of a classical particle is 0 by definition (regardless of speed). A quantum particle doesn't have a well-defined size. Concepts like size and position are especially problematic for massless particles.

Regarding time dilation, since a particle doesn't carry a clock, the only kind of time dilation we can meaningfully discuss is an unstable particle's decay rate. For massive particles, times like the half-life are changed by a factor of gamma. I don't know if massless particles can decay.

 

[Dale]

A particle traveling at c (which would have to be massless) would be length contracted to what? Zero?

The length contraction and time dilation formulas don't apply to massless particles. They each require that two measurements be made in a frame where the object is at rest and no such frame exists for massless particles.

 

[tiny-tim]

Greetings, CosmicVoyager!

A particle traveling at c (which would have to be massless) would be length contracted to …

Contraction is relative …

contracted from what? ​

 

[Naty1]

"The length of a classical particle is 0 by definition (regardless of speed)."

yes, this is the best we can do...so far...within the standard model of particle physics...

In laymen's (simplistic) terms you could say initially size is zero and no time passes, but in reality we don't have the mathematics yet to describe those conditions.

Planck length might be the theoretical minimum size in quantum theory, but size becomes indeterminate as posted above, via Heisenberg uncertainty for example, and "Planck size" plays no part in relativty...

These inconsistent factors are among those that cause physicsts to want to "unify" quantum theory and [general] relativity.

 

[Huttate]

OK, I just registered to add my bit here. Have been a lurker and shirker for a while. Had a dig and this thread appears most relevant to my question.

I have been reviewing relativity so that I might explain it clearly [and simply?] to someone. Whilst doing so I had a WOW! moment when the implications of it hit me.

If we think of a photon as a point particle gauge boson for the electromagnetic force, i.e a real particle moving through space.

And we accept that it is traveling at c.

The implication is that, for the photon's frame of reference, it moves from any point to any other point in zero time [ root (1-v^2/c^2) = 0 ].

I think this has mostly been said in this thread already.

But explicitly this would mean that a photon traveling to us from a billion light years away does so in zero time in its reference frame.

Is this the correct interpretation?

I would assume this is a subject for some discussion and, if so, could someone point me at a source for further reading on this specific implication of relativity please?

 

[Fredrik]

The implication is that, for the photon's frame of reference, it moves from any point to any other point in zero time [ root (1-v^2/c^2) = 0 ].
...
I would assume this is a subject for some discussion and, if so, could someone point me at a source for further reading on this specific implication of relativity please?

Welcome to Physics Forums. It's not a bad question, but it's one we've answered many times before. There are probably hundreds of threads about it. A photon doesn't have a frame of reference. D H wrote a short FAQ entry about it here. You can also check out my posts in this thread if you want to know a little more.

 

[Huttate]

Thanks for the interest and the references. Obviously a question that is raised again and again.

The answer seems to be "we don't know" presented as "the question is meaningless".

To my mind the question is pretty fundamental to our understanding of the universe and the fact that it cannot even be tackled by our current understanding of physics says that our understanding is limited.

The photon (whatever it is) is there and we think it travels at c.

We should therefore be able to describe its motion in a more intuitive way.

I suppose we only move forward when an intellectual genius arises whom is able to think anew, rather than teach what he has learned from others.

 

[Fredrik]

The answer seems to be "we don't know" presented as "the question is meaningless".

No, that's not the case at all.

We should therefore be able to describe its motion in a more intuitive way.

You didn't ask about how to describe its motion. That's actually very easy. The motion of a massless particle is described by a line that makes a 45 degree angle with the time axis in a spacetime diagram. Physics doesn't get much more intuitive than that. You asked about inertial frames in which a photon is stationary, and since nothing like that exists in the theory, the answer is definitely not "we don't know".

I suppose we only move forward when an intellectual genius arises whom is able to think anew, rather than teach what he has learned from others.

Right, but we don't need to move forward to talk about things that have been well understood for a hundred years.

 

[DrGreg]

The answer seems to be "we don't know" presented as "the question is meaningless".

If I asked you "what is the colour of three?" would you say "we don't know" or "the question is meaningless"?

 

[bobc2]

If I asked you "what is the colour of three?" would you say "we don't know" or "the question is meaningless"?

Good job, DrGreg.

 

[Huttate]

Thanks for taking the time to reply - I have learned something.

For me the colour of three is usually a blue that I would describe as azure. Four is very definitely mauve and two a sadly dull green. I will not bore you with the rest - though some of the fractions are quite bizarre! And the colours do alter dependent on context.

I must remind myself to be very precise with the questions I pose here. I realize that semantics are everything but I felt that I was simply posing a question that someone called Albert posed a few years back. If I recall his starting point was "Was would I see in a mirror if I was traveling at the speed of light?" - or thereabouts. So I would argue as to how meaningless it is.

I have seen people in other threads being rebuked for posing philosophical questions. I find that odd unless this forum is simply to spread the received wisdom rather than broaden the mind.

I know how we plot light on a spacetime diagram but that does not answer my original question.

I am unhappy with the idea that we ignore the photon frame of reference or accept that photons are ageless particles [no half life] and simply move on.

I have a picture developing in my mind that I need to develop a bit before I return to be mauled once more and will hopefully pose an acceptable question then.

 

[DrGreg]

Huttate, to be fair, the question you asked is a perfectly reasonable question to ask, it just turns out that within the theory of relativity it turns out to be meaningless. You weren't to know that. It's down to the way that we humans choose to define what an "inertial frame of reference" is, and the definition we choose rules out the possibility of light being stationary within one.

It is possible to define a coordinate system in which light is at rest, but in that coordinate system we do not have one time coordinate and three space coordinates, i.e. there is no sensible definition of "distance" and "time" relative to such a coordinate system.

 

[Fredrik]

I must remind myself to be very precise with the questions I pose here. I realize that semantics are everything but I felt that I was simply posing a question that someone called Albert posed a few years back. If I recall his starting point was "Was would I see in a mirror if I was traveling at the speed of light?" - or thereabouts. So I would argue as to how meaningless it is.

I agree with DrGreg that it's a reasonable question. The problem is just that the theory that defines the terms says that the question is meaningless. It's impossible to know that until you've studied the theory, and given it some thought.

I have seen people in other threads being rebuked for posing philosophical questions. I find that odd unless this forum is simply to spread the received wisdom rather than broaden the mind.

I find it odd that you think there's a dichotomy there. It's not like you have to choose to either study the established theories or to broaden your mind. You broaden your mind by studying the established theories.

I have participated in a lot of those "philosophical" threads, and I think they're almost always a waste of everyone's time. They are usually started by people who aren't interested in what some theory says, and wants to speculate about what things are "really" like, without studying the appropriate theory. We like to help people who are trying to learn physics, not people who are trying to avoid doing that.

I am unhappy with the idea that we ignore the photon frame of reference or accept that photons are ageless particles [no half life] and simply move on.

But that's not what we did. We examined the procedure that's used to associate a coordinate system with the motion of a massive particle and found that it doesn't work for massless particles. We looked at the inertial frames and found that none of them has a time axis that coincides with a null geodesic (the type of curve that can represent the motion of a massless particle). We looked at the coordinate systems that have a time axis that coincides with a null geodesic and found that there are lots of them, but there's no reason to prefer one of them over any of the others. Etc.

We couldn't have ignored massless particles' frames of reference even if we wanted to. There just isn't anything in the theory that can be associated with those words in a meaningful way, so there's nothing there to ignore.

 

[Huttate]

Thanks for the considered response.

I suppose that I was looking for a response here beyond what I have received.

I am content that I understand the current theory. I am not content that the theory satisfactorily explains the phenomena that we now experimentally see. Well we all know that.

So another theory is required that satisfies all we know and explains the anomalies. We all know that.

I shall not waste anyone's time further until I have something to nail my question to that develops directly upon the accepted wisdom.

 

[harrylin]

Greetings,

A particle traveling at c (which would have to be massless) would be length contracted to what? Zero? Would it be two-dimensional? Or would it be whatever the smallest possible length is, Plank length?

And the same question about how much it is time dilated.

Thanks

Hello CosmicVoyager,

I'm not sure if you got the answer you were looking for; thus here my 2cts. No massless particle exists IMHO (this may be a matter of semantics).

A massive particle (as a small object, not a mathematical point) would contract to almost zero when nearly reaching the speed of light. As Einstein put it:

"For v=c all moving objects --viewed from the ``stationary'' system-- shrivel up into plane figures." *

Similarly if it's a radioactive particle, it will (nearly) stop decaying.
You could google for "muon time dilation" for more on this.

And for the length of a wave packet ("light complex") as seen from different perspectives, see section 8 of that same paper.

Cheers,
Harald

*http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

[Dale]

I am content that I understand the current theory. I am not content that the theory satisfactorily explains the phenomena that we now experimentally see.

such as what? What experimentally observed phenomena (within the domain of SR) are not explained by SR?