Relative velocities of particles and photons

From the neutrino's perspective, you are Time Dilated and you have gained mass. From your perspective, the neutrino is Time Dilated and it has gained mass.
  • #1
DiracPool
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According to my understanding of SR, a light photon traveling at c, of course, relative to me "experiences" no time. In other words, it is not traveling through, at least, the time dimension I am traveling through. A neutrino, say, moving close to c does, but it is traveling very slowly through time compared to me. Now we can say that the neutrino, in it's own frame, is experiencing it's own proper time as "normal," and experiences me as traveling very slowly through it's time dimension. So far so good.

But what about the "experience" of the photon. If I experience the photon as traveling at c relative to me, doesn't the photon necessarily have to experience me traveling at c relative to it? Doesn't this, then, necessarily mean that I have to be massless in order for the symmetry to hold? Last time I checked I weighed over 200 pounds. How do we reconcile this? Also, am I frozen in time from the perspective of the photon? What form does that take?

From the neutrinos perspective, traveling at say .99+ the speed of light, I must seem enormous, a huge, heavy structure of mass-energy. However, if I just travel a tiny bit faster and reach the speed of c, all of that mass vanishes, and I become massless. I'm a bit confused on what the nature of that bridge is, or means. Now I know that the objection is that I can't reach the speed of light compared to the neutrino so it's a null argument, and I'd agree, but that is why I brought up the relative speed compared to the photon in the beginning. What do I look like from the perspective of the photon?
 
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  • #2
DiracPool said:
According to my understanding of SR, a light photon traveling at c, of course, relative to me "experiences" no time.

Then your understanding is not quite correct. We have a FAQ on this:

https://www.physicsforums.com/showthread.php?t=511170

Briefly, it would be correct to say that the Minkowski length of a photon's worldline is zero; but interpreting that length as "experienced time" for the photon is the problem, since the assumptions that ground that interpretation for timelike objects like you and me do not hold for photons.

DiracPool said:
In other words, it is not traveling through, at least, the time dimension I am traveling through.

This is incorrect too, even leaving aside the points made in the FAQ. If you insist on thinking of a photon as "traveling through the dimensions", then you would have to say it travels through space and time "at the same speed", whereas you and I, for example, travel through space much more "slowly" than we travel through time. But this is a very limited interpretation and I don't recommend it.

DiracPool said:
A neutrino, say, moving close to c does, but it is traveling very slowly through time compared to me. Now we can say that the neutrino, in it's own frame, is experiencing it's own proper time as "normal," and experiences me as traveling very slowly through it's time dimension.

If you insist on this kind of interpretation, yes, the "rate of travel through time" is frame-dependent; it is not an invariant. (Which is why I don't recommend spending too much effort on this interpretation.)

DiracPool said:
But what about the "experience" of the photon. If I experience the photon as traveling at c relative to me, doesn't the photon necessarily have to experience me traveling at c relative to it?

No. The concept of "speed relative to a photon" makes no sense, because a photon does not have a "rest frame" the way you and I do. The FAQ entry goes into this.

DiracPool said:
What do I look like from the perspective of the photon?

The question has no answer because "the perspective of the photon" is not a well-defined notion.
 
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  • #3
DiracPool said:
According to my understanding of SR, a light photon traveling at c, of course, relative to me "experiences" no time.
I wouldn't say it that way because it implies that a photon "experiences" something, just not time. A better way is to say it is that "experience" does not apply to a photon just as time does not apply to a photon. Then the rest of your post doesn't make any sense.

DiracPool said:
In other words, it is not traveling through, at least, the time dimension I am traveling through.
I wouldn't say that either. You're not traveling through time. In your rest frame, you're not traveling at all but a photon is traveling at c, by definition.

DiracPool said:
A neutrino, say, moving close to c does, but it is traveling very slowly through time compared to me.
A neutrino traveling at close to c in your rest frame is Time Dilated. It's a very simple concept. If you know its speed, you can calculate its Time Dilation according to your rest frame. You can transform to any other rest frame and it may have a new speed and a new Time Dilation. Why are you trying to complicate such as simple concept?

DiracPool said:
Now we can say that the neutrino, in it's own frame, is experiencing it's own proper time as "normal," and experiences me as traveling very slowly through it's time dimension.
You can transform from your rest frame to the neutrino's rest frame and it will not be Time Dilated but you will be. What's with this "traveling through a time dimension"?

DiracPool said:
So far so good.
So far not so good.

DiracPool said:
But what about the "experience" of the photon.
A meaningless concept.

DiracPool said:
If I experience the photon as traveling at c relative to me, doesn't the photon necessarily have to experience me traveling at c relative to it?
No, you can't transform from your rest frame to that of a photon and the rest of your questions are meaningless.

DiracPool said:
Doesn't this, then, necessarily mean that I have to be massless in order for the symmetry to hold? Last time I checked I weighed over 200 pounds. How do we reconcile this? Also, am I frozen in time from the perspective of the photon? What form does that take?

From the neutrinos perspective, traveling at say .99+ the speed of light, I must seem enormous, a huge, heavy structure of mass-energy. However, if I just travel a tiny bit faster and reach the speed of c, all of that mass vanishes, and I become massless. I'm a bit confused on what the nature of that bridge is, or means. Now I know that the objection is that I can't reach the speed of light compared to the neutrino so it's a null argument, and I'd agree, but that is why I brought up the relative speed compared to the photon in the beginning. What do I look like from the perspective of the photon?
 
  • #5
DiracPool said:
Doesn't this, then, necessarily mean that I have to be massless in order for the symmetry to hold?
Your wordline is timelike. Light's wordline isn't. Thus, there no symmetry to be enforced.

PeterDonis said:
Then your understanding is not quite correct. We have a FAQ on this:

https://www.physicsforums.com/showthread.php?t=511170
Yet the FAQ is mistaken (bracketed addition mine):
"One of the key axioms of special relativity is that light moves at c in all [inertial?] reference frames."​
Without the additional qualifier of "inertial", the statement is false, and the thrust of the "no rest frame" unravels with it. In fact, neither lightcone coordinates nor null tetrads (frame fields) are problematic, so there's no problem with a frame in which a light ray is at rest. It's just not an inertial frame.

If the FAQ was up-front about interpreting "rest frame" as "rest inertial frame" and then followed-up with an explanation that light isn't at rest in any inertial frame, it would be right.

PeterDonis said:
Briefly, it would be correct to say that the Minkowski length of a photon's worldline is zero; but interpreting that length as "experienced time" for the photon is the problem, since the assumptions that ground that interpretation for timelike objects like you and me do not hold for photons.
An electromagnetic wave behaves just like a stopped clock moving at c. One can of course define proper time as specifically applicable to timelike wordlines only, but... why? I'm not sure what utility there is in excluding light.
 
  • #6
Vorpal said:
An electromagnetic wave behaves just like a stopped clock moving at c.

I'm not sure I understand what you mean by this. Can you elaborate?

Vorpal said:
One can of course define proper time as specifically applicable to timelike wordlines only, but... why? I'm not sure what utility there is in excluding light.

I can think of a couple of reasons:

First, proper time for timelike worldlines is an affine parameter, and this gives an obvious mathematical grounding to the physical statement that different clocks can have different natural rates and that the "zero point" of time is arbitrary. But the Minkowski length of a null worldline obviously can't be used as an affine parameter. A somewhat more intuitive way of saying this is that, on a timelike worldline, different proper times label distinct events; but you obviously can't use the Minkowski length to label distinct events on a null worldline. Equating that zero Minkowski length with "zero time" invites the erroneous inference that light rays are somehow "everywhere at once", or something like that. (This has happened many times here on PF...)

Second, important physical quantities of interest on timelike worldlines are standardly expressed as derivatives with respect to proper time: the two obvious ones are 4-velocity and 4-acceleration. This doesn't work the same for null worldlines, since, as above, the Minkowski length can't be used as an affine parameter. You can still define a tangent vector for a null worldline (though it can't be a unit vector, as it can with a timelike worldline--this, btw, is IMO the key physical difference between timelike and null worldlines, which underlies all the other things I'm saying), and take its derivative in order to find the path curvature of the null worldline; but to do so, you have to pick a valid affine parameter, which breaks the relationship with the Minkowski length.
 
  • #7
PeterDonis said:
I'm not sure I understand what you mean by this. Can you elaborate?
If you have a clock traveling in the x-direction with speed v with not acceleration, then its internal state changes and can be parametrized by λ = x-vt (incidentally also an affine parameter that is definitely not the proper time). Whatever it's really doing is not particularly relevant, just that its state is changing. On the other hand, if you have an electromagnetic wave traveling in the x-direction in vacuum, then its profile is going to be a function of the u = x-ct light-cone coordinate, but this profile does not evolve. Rather, it's simply the same pattern moving along instead. Thus, it is like a stopped clock.

PeterDonis said:
First, proper time for timelike worldlines is an affine parameter, and this gives an obvious mathematical grounding to the physical statement that different clocks can have different natural rates and that the "zero point" of time is arbitrary. But the Minkowski length of a null worldline obviously can't be used as an affine parameter.
A key property of being an affine parameter is that not just the "zero point", but also the scale, is completely irrelevant. This conceptual identification between affine parameters and proper time invites trouble--yes, in the situation given, one can serve as the other, but that doesn't mean we should collapse the distinction. I don't understand in what way this gives "grounding to the physical statement that different clocks can have different natural rates". The "natural rate" of the clock is completely independent of the scale of the affine parameter, because we are always free to rescale by it by arbitrary factor regardless of any physical properties of the clock.

While agree that the possibility of having proper time be the affine parameter is important, I don't see why that should exclude light from having zero proper time. Rather, this connection is due to the possibility of having an instantaneously comoving inertial frame, which lightlike worldlines lack. Meanwhile, insufficient emphasis of the key qualifier "inertial" leads to wrong explanations, such as the linked FAQ entry.

PeterDonis said:
Equating that zero Minkowski length with "zero time" invites the erroneous inference that light rays are somehow "everywhere at once", or something like that. (This has happened many times here on PF...)
An electromagnetic wave profile behaves exactly like a stopped clock, so the "zero time" is actually completely sensible. Furthermore, in light-cone coordinates it is both stationary and at every point along its trajectory at once (wrt one light-cone coordinate). What you're describing sounds like a confusion regarding the conceptual role of inertial frames, and so can be addressed directly by emphasizing that light has no inertial (rest) frame.

PeterDonis said:
Second, important physical quantities of interest on timelike worldlines are standardly expressed as derivatives with respect to proper time: the two obvious ones are 4-velocity and 4-acceleration. This doesn't work the same for null worldlines, since, as above, the Minkowski length can't be used as an affine parameter. You can still define a tangent vector for a null worldline (though it can't be a unit vector, as it can with a timelike worldline--this, btw, is IMO the key physical difference between timelike and null worldlines, which underlies all the other things I'm saying), and take its derivative in order to find the path curvature of the null worldline; but to do so, you have to pick a valid affine parameter, which breaks the relationship with the Minkowski length.
A tangent vector makes sense in any parametrization. For timelike worldlines, using proper time makes it normalized, but if that's the key property you're after, then there was no need to bring up affine parameters at all, because they don't generally do that either. In any case, of course one shouldn't expect a null worldline to have a normalizable four-velocity--one should expect a null four-velocity instead. This is completely orthogonal to the issue of interpreting worldline length as proper time. As four four-acceleration, this is also sensible generally: ##a = \nabla_uu##.
 
  • #8
Vorpal said:
If you have a clock traveling in the x-direction with speed v with not acceleration, then its internal state changes and can be parametrized by λ = x-vt (incidentally also an affine parameter that is definitely not the proper time).

No, it's just a constant factor (namely, ##\sqrt{1 - v^2}##) times the proper time. In other words, it's just the proper time with the "rate" adjusted.

Vorpal said:
Whatever it's really doing is not particularly relevant, just that its state is changing. On the other hand, if you have an electromagnetic wave traveling in the x-direction in vacuum, then its profile is going to be a function of the u = x-ct light-cone coordinate, but this profile does not evolve. Rather, it's simply the same pattern moving along instead. Thus, it is like a stopped clock.

By "profile" you must mean "phase"; yes, the phase of an electromagnetic wave doesn't change along a given null worldline that is parallel to the wave's motion. But if you're going to view the light as a wave at all, its motion can't be restricted to a single null worldline; it must occupy a region bounded by distinct parallel null worldlines, and the phase of the wave *does* change from worldline to worldline within that region.

Vorpal said:
A key property of being an affine parameter is that not just the "zero point", but also the scale, is completely irrelevant.

True.

Vorpal said:
This conceptual identification between affine parameters and proper time invites trouble--yes, in the situation given, one can serve as the other, but that doesn't mean we should collapse the distinction.

I agree the distinction can be useful in some circumstances, yes.

Vorpal said:
The "natural rate" of the clock is completely independent of the scale of the affine parameter, because we are always free to rescale by it by arbitrary factor regardless of any physical properties of the clock.

Yes, but that's just saying that we are always free to pick a mathematical model that is consistent in the abstract but bears no relation to the actual physical system we are supposed to be modeling. You can do that, but why would you want to? My point is that being able to rescale and reset the zero point of an affine parameter *can* be used, mathematically, to reflect the physical fact that clocks can have different rates and zero points.

Vorpal said:
While agree that the possibility of having proper time be the affine parameter is important, I don't see why that should exclude light from having zero proper time. Rather, this connection is due to the possibility of having an instantaneously comoving inertial frame, which lightlike worldlines lack.

I'm not sure I understand. Are you saying we should allow the concept of "proper time" to apply to light, by breaking the connection between "proper time" and inertial frames? I suppose this would be just as valid a use of terminology, in the abstract, as the standard usage, but I'm still not sure I see why it's an improvement.

Vorpal said:
What you're describing sounds like a confusion regarding the conceptual role of inertial frames, and so can be addressed directly by emphasizing that light has no inertial (rest) frame.

Which is why the FAQ entry is entitled "rest frame of a photon". Proper time comes into it because of the association, in standard usage, between proper time and inertial rest frames (and I agree that the FAQ entry should be explicit about the fact that it uses the term "frame" exclusively to mean "inertial frame").

Vorpal said:
In any case, of course one shouldn't expect a null worldline to have a normalizable four-velocity--one should expect a null four-velocity instead.

And you will find plenty of people who object to the term "four-velocity" being used in the null case, because to them, "four-velocity" implies a unit vector (as opposed to the term "tangent vector", which doesn't). (This came up in a PF thread quite a while back.) Again, this is a matter of terminology and standard usage, but standard usage does have a purpose, even if it's only standardization.

Vorpal said:
This is completely orthogonal to the issue of interpreting worldline length as proper time.

To you, perhaps it is. But I don't think it is to everybody. Basically, you are viewing the differences between null vectors/worldlines and timelike vectors/worldlines as minor compared to the similarities; to you, the two kinds of vectors/worldlines are basically the same thing, just with some different quirks, so to speak. But to me, and I think to people who favor the "standard" usages I've been arguing for, the differences between null and timelike vectors/worldlines are fundamental, pointing to a fundamental physical difference between the two types of objects; and because of this, we want the terminology to emphasize that difference. I'll agree that this is a matter of preference and terminology, not physics; we'll make the same physical predictions either way, and that's what really matters.
 

1. What is the difference between the speed of particles and photons?

The speed of particles refers to the velocity at which matter moves through space, while the speed of photons refers to the velocity at which light travels through space. In a vacuum, photons travel at the speed of light, which is approximately 299,792,458 meters per second. Particles, on the other hand, can have varying speeds depending on their mass and energy.

2. How do particles and photons interact with each other?

Particles and photons can interact with each other through various mechanisms such as absorption, emission, and scattering. When a particle absorbs a photon, it gains energy and its velocity may change. When a particle emits a photon, it loses energy and its velocity may also change. Scattering occurs when a photon bounces off a particle, changing its direction and potentially its energy as well.

3. Can particles and photons have the same velocity?

No, particles and photons cannot have the same velocity. This is because photons always travel at the speed of light in a vacuum, while particles have varying speeds depending on their mass and energy. However, particles can reach speeds close to the speed of light, known as relativistic speeds, but they can never exceed or match the speed of light.

4. How does the relative velocity of particles and photons affect the Doppler effect?

The Doppler effect is the change in frequency of a wave due to the relative motion between the source of the wave and the observer. For particles, the Doppler effect is observed in sound waves, while for photons, it is observed in electromagnetic waves (such as light). The relative velocity between particles and photons can affect the frequency of the waves, resulting in a shift in the observed wavelength.

5. Can particles and photons have different relative velocities in different reference frames?

Yes, particles and photons can have different relative velocities in different reference frames. This is due to the principles of relativity, which state that the laws of physics should be the same in all inertial reference frames. Therefore, the relative velocity between particles and photons may appear different depending on the reference frame in which it is observed.

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