Skip to main content

Bell’s Spaceships: The Views from Bow and Stern

  • Geraint F. Lewis (a1), Luke A. Barnes (a1) and Martin J. Sticka (a1)

Unravelling apparent paradoxes has proven to be a powerful tool for understanding the complexities of special relativity. In this paper, we focus upon one such paradox, namely Bell’s spaceship paradox, examining the relative motion of two uniformly accelerating spaceships. We consider the view from either spaceship, with the exchange of photons between the two. This recovers the well-known result that the leading spaceship loses sight of the trailing spaceship as it is redshifted and disappears behind what is known as the ‘Rindler horizon’. An immediate impact of this is that if either spaceship tries to measure the separation through ‘radar ranging’, bouncing photons off one another, they would both eventually fail to receive any of the photon ‘pings’ that they emit. We find that the view from this trailing spaceship is, however, starkly different, initially, seeing the leading spaceship with an increasing blueshift, followed by a decreasing blueshift. We conclude that, while the leading spaceship loses sight of the trailing spaceship, for the trailing spaceship the view of the separation between the two spaceships, and the apparent angular size of the leading spaceship, approach asymptotic values. Intriguingly, for particular parameterisation of the journey of the two spaceships, these asymptotic values are identical to those properties seen before the spaceships began accelerating, and the view from the trailing spaceship becomes identical to when the two spaceships were initially at rest.

Corresponding author
Hide All
Bell, J. S. 2004, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy (2nd rev. edn.; Cambridge: Cambridge University Press)
Boughn, S. P. 1989, AmJPh, 57, 791 10.1119/1.15894 1989AmJPh. .57. .791B
Cornwell, D. T. 2005, EL, 71, 699
Dewan, E., & Beran, M. 1959, AmJPh, 27, 517
Evett, A. A. 1972, AmJPh, 40, 1170
Fernflores, F. 2011, Int. Stud. Phil. Sci., 25, 351
Franklin, J. 2010, EJPh, 31, 291
Franklin, J. 2013, FoPh, 43, 1489 10.1007/s10701-013-9757-x
Hartle, J. B. 2003, Gravity: An Introduction to Einstein’s General Relativity (San Francisco: Addison Wesley)
Lewis, G. F., Francis, M. J., Barnes, L. A., Kwan, J., & James, J. B. 2008, MNRAS, 388, 960 10.1111/j.1365-2966.2008.13477.x 2008MNRAS.388. .960L
Marzlin, K.-P., & Lee, T. 2014, PhRvA, 89, 062103 10.1103/PhysRevA.89.062103 2014PhRvA. .89f2103M
Maudlin, T. 2012, Philosophy of Physics: Space and Time (Princeton: Princeton University Press)
Narlikar, J. V. 1994, AmJPh, 62, 903 10.1119/1.17679
Nikolić, H. 1999, AmJPh, 67, 1007 10.1119/1.19161
Nikolic, H. 2000, Phys. Let.,13, 5952000physics. . .4024N
Perlick, V. 2008, in Lasers, Clocks and Drag-Free Control: Exploration of Relativistic Gravity in Space, eds. Dittus, H., Lämmerzahl, C., & Turyshev, S. G. (Berlin: Springer), 131
Redzić, D. V. 2008, EJPh, 29, N11
Redzic, D. V. 2014, SerAJ, 188, 55 10.2298/SAJ1488055R 2014SerAJ.188. . .55R
Rindler, W. 1960, PhRv, 119, 2082 10.1103/PhysRev.119.2082 1960PhRv. .119.2082R
Rindler, W. 1966, AmJPh, 34, 1174 10.1119/1.1972547
Styer, D. F. 2007, AmJPh, 75, 805 10.1119/1.2733691
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Publications of the Astronomical Society of Australia
  • ISSN: 1323-3580
  • EISSN: 1448-6083
  • URL: /core/journals/publications-of-the-astronomical-society-of-australia
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Altmetric attention score

Full text views

Total number of HTML views: 4
Total number of PDF views: 27 *
Loading metrics...

Abstract views

Total abstract views: 129 *
Loading metrics...

* Views captured on Cambridge Core between 14th January 2018 - 15th August 2018. This data will be updated every 24 hours.