# I Mass and constrained massless particles

1. Nov 14, 2017

### kiwizimbo

Poorly phrased but here goes - I'm trying to understand some of the SpaceTime videos on youtube, specifically the massless mirrored box and how the mass (ie resistance to acceleration) is a function of the change in momentum of the contained (constrained) photons.

It makes sense but raises a few questions. If the box contained a single photon, would it still have mass? and if so, does that mass require that the photon be reflected twice? . The photon takes a finite time to cross the box and be reflected again, so is there any logic in deducing that mass is transitory, existing only at the time of reflection (constraint) of the photon?

Obviously in any realistic physical measurement, the number of photons/quarks etc is huge so mass would appear to be static.

(Mentor note: Removed text bordering on personal theory ie seeing a link to...)

Last edited by a moderator: Nov 14, 2017
2. Nov 14, 2017

### Staff: Mentor

Also please be aware that we don’t discuss personal theories. You can ask questions to clarify your understanding but keep your personal theory thoughts private.

3. Nov 15, 2017

### Staff: Mentor

A massless box is fundamentally problematic for several reasons. Would you be willing to discuss a massive mirrored box instead? The system of the massive box plus the light has more mass than the box alone.

4. Nov 15, 2017

### PAllen

Ah yes, amusing to consistently treat a massless box in SR! Imagine a massless box moving at c in the +x direction (movement at c required by massless condition), and a light pulse inside moving at c in the -x direction. Assume their momenta are of equal magnitude, p. Then when the light pulse hits the side of the box, the only consistent result is a merged object of mass 2p.

[edit: actually, there is another obvious possible result - the box rebounds to moving at c in the -x direction, while the light reflects to the +x direction. Mass of system is 2p at all times for both reflection case and absorption case.]

Last edited: Nov 15, 2017
5. Nov 15, 2017

### Mister T

Are they the PBS videos? I just did a YouTube search for "massless mirrored box" and the one hit I got was When Time Breaks Down. I started watching and saw a fundamental error made in the first five seconds. The narrator mentions that in the previous video "we saw how matter fills mass". That's absurd. Mass is a property of matter, saying matter can "fill" one of it's properties is nonsense. Like saying that the sky fills blue.

A bit later on he claims that time freezes at the speed of light, but that is also nonsense. To the observer on top of that light clock, the clock is not moving. If that light clock were able to move at the speed of light relative to that other observer it would mean that the observer at rest on the clock would see the clock not moving. But a fundamental assumption is that if something moves at the speed of light relative to one observer, it moves at the speed of light relative to all observers. The only way that fundamental assumption can be valid is if no clock can ever move at the speed of light. Moreover, many many other consequences that follow from that assumption have been confirmed by experiment and observation, so it's kinda hard to believe a YouTube video that claims otherwise. PBS should be embarrased.

Last edited: Nov 15, 2017
6. Nov 15, 2017

### kiwizimbo

A massive box would be acceptable - the important part is the single photon and the finite time between collisions/reflections

7. Nov 15, 2017

### kiwizimbo

Just to confirm the parameters of the question - a perfectly mirrored box (massless or massive), stationary with respect to the viewer, containing a single photon. Does the resistance to acceleration (mass) vary as the photon is a) being reflected by the side and b) travelling between the sides

8. Nov 15, 2017

### Staff: Mentor

A massless box cannot be stationary with respect to the viewer. It would have to be moving at c. That's at least one reason why @Dale recommended a massive box instead.

9. Nov 15, 2017

### PAllen

Mass of the system is constant. However, the center of energy shifts, and this would lead to uneven motion in response to an applied force. It is equivalent to a Newtonian situation where you apply force to box with a ball bouncing inside.

Last edited: Nov 15, 2017
10. Nov 15, 2017

### Ibix

As others have noted, the box can't be massless. Furthermore, the box cannot be stationary with respect to the observer. Naively, you would expect it to shift left and right as the photon travels right and left, in order to conserve momentum. However, the box can't behave as a rigid entity on this timescale, so in fact parts of the box will be travelling to the left and parts to the right. The net momentum will still be in the opposite sense to the photon's current direction of motion, but the distribution of momentum will be dynamical.

So I think the box's resistance to acceleration would depend very much on how you applied the force. It would certainly be time varying, as the photon could only be affected when it interacted with the walls.

Perhaps imagine a slinky with sealed ends and a ball bouncing back and forth inside it to get a simple idea.

11. Nov 15, 2017

### Staff: Mentor

There are at least two ways to work this problem. One is a simple classical approach and the other is fully quantum mechanical.

The simple classical approach would be to treat the light as a classical massless point particle which collides elastically with each wall in turn. As a point particle it has a definite position, and thus the center of mass of the box+light system is slightly displaced from the center of mass of the box. As a force is applied to the box, the center of mass of the box+light accelerates uniformly at the rate given by the mass of the box+light. The box accelerates at a slightly higher rate, but the acceleration is not uniform but is punctuated with brief impulses at each collision. The rearward ones being larger than the forward ones.

The other way to work the problem would be fully quantum mechanically. In this case you would treat the photon similar to the well known “particle in a box” or “infinite square well”. This wavefunction does not have a well defined position within the box nor does it have a discrete position or collision with the wall. That simply isn’t the way that QM photons work, they are not classical point particles.

12. Nov 16, 2017

### kiwizimbo

Thanks Dale, PAllen, Ibix. The QM is beyond me at the moment