Relativistic photonic rocket

  • I
  • Thread starter bob012345
  • Start date
  • #26
pervect
Staff Emeritus
Science Advisor
Insights Author
9,737
960
I think that should read ##w=\tanh^{-1}\beta=\tanh^{-1} v/c##
Ooops - fixed.
 
  • #27
pervect
Staff Emeritus
Science Advisor
Insights Author
9,737
960
MTW's "Gravitation" has a good section on the accelerated observer, but it's couched in terms of tensors, unfortunately.
 
  • #28
bob012345
Gold Member
411
64
MTW's "Gravitation" has a good section on the accelerated observer, but it's couched in terms of tensors, unfortunately.
Thanks, I own that. It's hard to misplace because it's so large it distorts the spacetime around it.....
 
  • Like
Likes PeterDonis
  • #30
PAllen
Science Advisor
2019 Award
8,071
1,359
I heard that MTW disproves the principle of equivalence - it falls faster than everything else.
 
  • Like
Likes PeterDonis
  • #31
bob012345
Gold Member
411
64
This brings up a related question. I tried applying the work energy theorem in the relativistic regime. I have no problems with the relativistic kinetic energy difference but the integration force over distance got unwieldy. Then I realized than no books I have seen have relativistic kinematics covered. I don't mean Lorentz transformations, I mean in one frame where the acceleration changes for a fixed force because the mass increases. I couldn't match the integrated work with the change in relativistic energy.
Newton's Second Law is relativistically modified as F= gamma^3 ma where m is rest mass. This can be derived from the relativistic form of momentum. A few proper substitutions and integrate over x equals mc^2( gamma2- gamma1). All is well.
 
  • #32
PAllen
Science Advisor
2019 Award
8,071
1,359
Newton's Second Law is relativistically modified as F= gamma^3 ma where m is rest mass. This can be derived from the relativistic form of momentum. A few proper substitutions and integrate over x equals mc^2( gamma2- gamma1). All is well.
That form is only if force is colinear with velocity. I assume you know this, but it is a crucial caveat to this formula - which is NOT a general form of relativistic force law.
 
  • #33
654
148
Thanks all. I'm digging into these issues. I've picked up Rindler's book and other sources. Started working through some problems. Thanks again!
Sounds like you probably don't need this, but for those that do not have the book there is a concise but well paced derivation of the relativistic rocket equations in this link.
 
  • Like
Likes vanhees71
  • #34
bob012345
Gold Member
411
64
That form is only if force is colinear with velocity. I assume you know this, but it is a crucial caveat to this formula - which is NOT a general form of relativistic force law.
Thanks, yes. I know the vector form but was primarily interested in co linear motion. Interesting that there is parallel inertia and perpendicular inertia.
 
  • #35
bob012345
Gold Member
411
64
Sounds like you probably don't need this, but for those that do not have the book there is a concise but well paced derivation of the relativistic rocket equations in this link.
It's all useful. Thanks.
 
  • #36
bob012345
Gold Member
411
64
Here’s a question I’ve always wondered. Is it possible to slow light within some gaseous medium and thus increase its momentum? Imagine creating a region around a ship where c=1 m/s and then using a beam where P=E.
 
  • #37
130
47
Here’s a question I’ve always wondered. Is it possible to slow light within some gaseous medium and thus increase its momentum? Imagine creating a region around a ship where c=1 m/s and then using a beam where P=E.
Try applying conservation of momentum to your question, if the light is increasing its momentum then something else would have to increase its momentum in the opposite direction to keep the total constant. What would that be and how?
 
  • #38
bob012345
Gold Member
411
64
Try applying conservation of momentum to your question, if the light is increasing its momentum then something else would have to increase its momentum in the opposite direction to keep the total constant. What would that be and how?
I know, that would be both the ship and the medium the light is slowed in if light could actually be slowed. The gaseous medium would carry the momentum away that the ship gains as the light passes out of the medium and returns to normal. The question is if light can actually be slowed in a way that increases it's momentum greatly? I've read where light can be slowed to meters per second in certain vapors but don't know about the momentum of such light. I've heard that light actually does have a bigger kick inside glass but don't have a good reference.
 
Last edited:
  • #39
1,420
112
Here’s a question I’ve always wondered. Is it possible to slow light within some gaseous medium and thus increase its momentum? Imagine creating a region around a ship where c=1 m/s and then using a beam where P=E.

Imagine creating a region around a ship where c=0.00000001 m/s, or slower if needed, so that we will say that light becomes trapped in the region.

How do light traps behave? For example a mirror lined box with a door which is closed after some light has entered.
 
  • #40
bob012345
Gold Member
411
64
Imagine creating a region around a ship where c=0.00000001 m/s, or slower if needed, so that we will say that light becomes trapped in the region.

How do light traps behave? For example a mirror lined box with a door which is closed after some light has entered.
I don't know about 'light traps'. Please enlighten me. Thanks.
 
  • #41
1,420
112
I don't know about 'light traps'. Please enlighten me. Thanks.
Two examples of "light traps":

Trap 1: Vertical light beam enters a box, then the light beam bounces inside the box horizontally. First the light had vertical momentum, then it has no vertical momentum, vertical momentum must be conserved, so the box must now have the vertical momentum that the light had.

Trap 2: An atom absorbs a photon, momentum of the photon becomes momentum of the atom.

Some mathematics:

Energy-momentum relation:
E2=p2c2+m2c4

So massless energy E has momentum: E/c

And energy that has some mass has momentum: Less than E/c

So E/c is the maximum momentum of energy E.

So massless constant energy can not gain more momentum by changing its propagation speed. It can lose momentum by gaining mass and slowing down its propagation speed.

For example: A system consisting of two parallel light beams collides with a lens, which collision causes the beams to become less parallel. After the collision the system has a rest mass that is moving at some speed lower than c, and the system has less momentum than originally, and the lens has absorbed some momentum.
 
Last edited:
  • #42
bob012345
Gold Member
411
64
Two examples of "light traps":

Trap 1: Vertical light beam enters a box, then the light beam bounces inside the box horizontally. First the light had vertical momentum, then it has no vertical momentum, vertical momentum must be conserved, so the box must now have the vertical momentum that the light had.

Trap 2: An atom absorbs a photon, momentum of the photon becomes momentum of the atom.

Some mathematics:

Energy-momentum relation:
E2=p2c2+m2c4

So massless energy E has momentum: E/c

And energy that has some mass has momentum: Less than E/c

So E/c is the maximum momentum of energy E.

So massless constant energy can not gain more momentum by changing its propagation speed. It can lose momentum by gaining mass and slowing down its propagation speed.

For example: A system consisting of two parallel light beams collides with a lens, which collision causes the beams to become less parallel. After the collision the system has a rest mass that is moving at some speed lower than c, and the system has less momentum than originally, and the lens has absorbed some momentum.
Thanks. The question was what happens when c is smaller, like 1 m/s like in a BEC that envelops the ship. Experimental results are hard to come by and theoretical results are contradictory. There has been a over a century of controversy concerning the momentum of a photon in a medium. I just read a paper that claimed to prove the momentum is the same no matter what the speed of light in any medium. Any thoughts here?

P.S. Photon recycling allows one to use the momentum of a photon over and over as long as there is something close to bounce it back. It's been done in the lab with thousands of bounces, moving kg scale objects with typical lab lasers.
 
Last edited:

Related Threads on Relativistic photonic rocket

  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
11
Views
13K
  • Last Post
3
Replies
70
Views
6K
Replies
11
Views
865
Replies
3
Views
2K
Replies
14
Views
805
Replies
4
Views
2K
  • Last Post
Replies
17
Views
4K
  • Last Post
Replies
4
Views
2K
Replies
8
Views
905
Top