Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Wonderful, Wonderful Copenhagen

Bruce Rosenblum, Fred Kuttner

Published Jun 29, 2006• 0 citations
Publisher

Abstract

Abstract The meaning of Newton’s mechanics was clear. It described a reasonable world, a “clockwork universe.” It needed no interpretation. Einstein’s relativity is surely counterintuitive, but no one interprets relativity. We come to accept the idea that moving clocks run slow. It’s harder to accept that observation creates the reality observed. That needs interpretation.

DOI
10.1093/oso/9780195175592.003.0011

Related papers

The nature of Einstein's objections to the Copenhagen interpretation of quantum mechanics

Michel Paty

Foundations of Physics•Jan 1, 1995•37 citations

The Quantum Measurement Problem-collapse of the wave function explained.pdf

Rochelle Forrester

Quantum physicists have made many attempts to solve the quantum measurement problem, but no solution seems to have received widespread acceptance. The time has come for a new approach. In Sense Perception and Reality: A Theory of Perceptual Relativity, Quantum Mechanics and the Observer Dependent Universe and in a new paper The End of Realism I suggest the quantum measurement problem is caused by a failure to understand that each species has its own sensory world and that when we say the wave function collapses and brings a particle into existence we mean the particle is bought into existence in the human sensory world by the combined operation of the human sensory apparatus, particle detectors and the experimental set up. This is similar to the Copenhagen Interpretation suggested by Niels Bohr and others, but the understanding that the collapse of the wave function brings a particle into existence in the human sensory world removes the need for a dividing line between the quantum world and the macro world. The same rules can apply to both worlds and the ideas stated in this paper considerably strengthen the Copenhagen Interpretation of quantum mechanics.

•Jan 1, 2017•0 citations

Wave with Self-Spacetime Creating Notion of Average Particle in Wave-Particle Duality?

Francesco R. Ruggeri

A quantum particle is often described as exhibiting dual particle-wave nature. A particle seems to be an object which obeys Newton’s laws/special relativity with a wave also being a phenomenon existing in Newtonian mechanics (special relativity). In other words the particle and wave are governed by x-t external variables which have infinite resolution. It was originally thought that x and t in addition to being external were absolute, but special relativity changed this idea. We have suggested in previous notes that a free quantum particle with energy E and momentum p creates its own space time i.e time intervals are proportional to 1/E and space to 1/p. This means no external clock is needed and different internal rulers and clocks exist for different E,p. It also suggests finite time and space intervals. In fact, an absolute is introduced namely A=0 = -Et+px with t and x being independent. This suggests that t→b/E and x→b/p. A is the free particle Lagrangian (both relativistic and nonrelativistic) with x and t being considered independent. Thus we suggest that the external x ruler and t clock of Newtonian mechanics represent an average of the internal picture and are also described by A, but with x/t=v and not x and t being treated as independent. In (1) we showed that having discrete x spacing with a running time (i.e. Netwon’s time variable) and insisting on spatial invariance leads to dA/dx partial = p. Thus instead of considering particle wave duality we suggest an underlying wave structure which creates its own spacetime intervals (1/E, 1/p), but may be mapped in certain situations to the external running x and t of Newton’s theory. For example, consider an electron (a quantum particle) with a fixed p moving over a distance much greater than its wavelength. It may be mapped to Newton’s external running x,t values with x=vt, but this is an average mapping into continuous x and t. In reality the situation is more complicated because there may be a Bohm-Aharonov effect occurring. Thus the underlying wave picture is in fact physically important and linked to interactions. Thus a self-ruler is not simply a measuring device - interactions may occur unlike in the case of the external ruler. Given that p defines a kind of spatial invariance approximated by a periodic function exp(ipx) (eigenfunction of -id/dx) and that Newton’s running time is not needed in a quantum bound state equilibrium, one may wonder what one should do in the case of a particle bound in a V(x) potential. In Newtonian mechanics V(x) suggests non-spatial invariance and v(x) velocity changes with x as well in contrast with exp(ipx) which is periodically invariant. In fact Newtonian mechanics (and Lagrangian/Hamiltonian as well) focus on d/dt i.e x(t). We have argued above that time intervals 1/E are independent of 1/p spatial ones. It may be noticed, however, that different p values lead to different wavelengths and so even though there is a kind of spatial invariance for each, when compared to each other this invariance is broken and superpositions of exp(ipx) may create local x probability densities. At the same they create spatial momentum densities because -d/dx (d/dx) 1/2m yields a kind of average kinetic energy when normalized. This seems to describe the x-p uncertainty relationship. In order to create spatial resolution (other than the built-in one in the wavelength) one needs to superpose different momenta, each of which are spatially invariant according to their periodic scheme exp(ipx). Thus one may create an average 1/2m <pp> and obtain a vrms. This may be described in terms of Newtonian external running x and t variables which have infinite resolution, but this vrms does not map to a physical state i.e to exp(i (mvrms) x) localized at x. Rather the various exp(ipx)’s which create vrms are the physical entities as may be seen by knocking a particle out of a bound state. The physical exp(ipx) momenta states have spatial invariance and so cannot be associated with a specific position in space. Only their superposition creates the notion of specific position in space, but then there is a distribution of p. This seems to be the basis for the x-p uncertainty principle. Thus we suggest that the particle of particle-wave duality is created through a mapping of a physical wave scenario to a continuous (infinite resolution) x-t scheme which in reality is an abstraction because each p,E free particle state has it sown internal clock-ruler i.e. 1/E and 1/p time and space units. Given that 1/E and 1/p have finite values the idea of dt and dx tending to 0 only makes sense as an abstraction which only holds in certain situations.

•Nov 2, 2022•0 citations

The Many Worlds Interpretation

Jonathan Allday

It’s di cult to gauge where popular opinion stands among physicists on the question of interpretation. My personal view is that the majority of professional working physicists (engaged in academic or industrial research of one form or another) probably think in terms of the Copenhagen interpretation they were taught at university, if they worry about interpretations at all. e chances are that they spend their time calculating amplitudes and probabilities and rarely li their heads from the computer monitor to ask what all of it means.

CRC Press eBooks•Mar 3, 2009•4 citations

Wonderful Copenhagen?

Alastair I. M. Rae

The 1935 paper by Einstein, Podolski and Rosen represented the culmination of a long debate that had begun soon after quantum theory was developed in the 1920s. One of the main protagonists in this discussion was Niels Bohr, a Danish physicist who worked in Copenhagen until, like so many other European scientists of his time, he became a refugee in the face of the German invasion during the Second World War. As we shall see, Bohr's views differed strongly from those of Einstein and his co-workers on a number of fundamental issues, but it was his approach to the fundamental problems of quantum physics that eventually gained general, though not universal, acceptance. Because much of Bohr's work was done in that city, his ideas and those developed from them have become known as the ‘Copenhagen interpretation’. In this chapter we shall discuss the main ideas of this approach. We shall try to appreciate its strengths as well as attempting to understand why some believe that there are important questions left unanswered. When Einstein said that ‘God does not play dice’, Bohr is said to have replied ‘Don't tell God what to do!’ The historical accuracy of this exchange may be in doubt, but it encapsulates the differences in approach of the two men. Whereas Einstein approached quantum physics with doubts, and sought to reveal its incompleteness by demonstrating its lack of consistency with our everyday ways of thinking about the physical universe, Bohr's approach was to accept the quantum ideas and to explore their consequences for our everyday ways of thinking.

Cambridge University Press eBooks•Oct 7, 2004•0 citations

Resolving a paradox

P. J. Bussey

There are few topics in physics that have excited so many different contrary opinions as Einstein’s so-called ‘Twin Paradox’, otherwise known as the ‘Clock Paradox’. It arises as an apparent conseq...

Contemporary Physics•Oct 2, 2021•0 citations
Abstract The meaning of Newton’s mechanics was clear. It described a reasonable world, a “clockwork universe.” It needed no interpretation. Einstein’s relativity is surely counterintuitive, but no one interprets relativity. We come to accept the idea that moving clocks run slow. It’s harder to accept that observation creates the reality observed. That needs interpretation.
Quantum physicists have made many attempts to solve the quantum measurement problem, but no solution seems to have received widespread acceptance. The time has come for a new approach. In Sense Perception and Reality: A Theory of Perceptual Relativity, Quantum Mechanics and the Observer Dependent Universe and in a new paper The End of Realism I suggest the quantum measurement problem is caused by a failure to understand that each species has its own sensory world and that when we say the wave function collapses and brings a particle into existence we mean the particle is bought into existence in the human sensory world by the combined operation of the human sensory apparatus, particle detectors and the experimental set up. This is similar to the Copenhagen Interpretation suggested by Niels Bohr and others, but the understanding that the collapse of the wave function brings a particle into existence in the human sensory world removes the need for a dividing line between the quantum world and the macro world. The same rules can apply to both worlds and the ideas stated in this paper considerably strengthen the Copenhagen Interpretation of quantum mechanics.
A quantum particle is often described as exhibiting dual particle-wave nature. A particle seems to be an object which obeys Newton’s laws/special relativity with a wave also being a phenomenon existing in Newtonian mechanics (special relativity). In other words the particle and wave are governed by x-t external variables which have infinite resolution. It was originally thought that x and t in addition to being external were absolute, but special relativity changed this idea. We have suggested in previous notes that a free quantum particle with energy E and momentum p creates its own space time i.e time intervals are proportional to 1/E and space to 1/p. This means no external clock is needed and different internal rulers and clocks exist for different E,p. It also suggests finite time and space intervals. In fact, an absolute is introduced namely A=0 = -Et+px with t and x being independent. This suggests that t→b/E and x→b/p. A is the free particle Lagrangian (both relativistic and nonrelativistic) with x and t being considered independent. Thus we suggest that the external x ruler and t clock of Newtonian mechanics represent an average of the internal picture and are also described by A, but with x/t=v and not x and t being treated as independent. In (1) we showed that having discrete x spacing with a running time (i.e. Netwon’s time variable) and insisting on spatial invariance leads to dA/dx partial = p. Thus instead of considering particle wave duality we suggest an underlying wave structure which creates its own spacetime intervals (1/E, 1/p), but may be mapped in certain situations to the external running x and t of Newton’s theory. For example, consider an electron (a quantum particle) with a fixed p moving over a distance much greater than its wavelength. It may be mapped to Newton’s external running x,t values with x=vt, but this is an average mapping into continuous x and t. In reality the situation is more complicated because there may be a Bohm-Aharonov effect occurring. Thus the underlying wave picture is in fact physically important and linked to interactions. Thus a self-ruler is not simply a measuring device - interactions may occur unlike in the case of the external ruler. Given that p defines a kind of spatial invariance approximated by a periodic function exp(ipx) (eigenfunction of -id/dx) and that Newton’s running time is not needed in a quantum bound state equilibrium, one may wonder what one should do in the case of a particle bound in a V(x) potential. In Newtonian mechanics V(x) suggests non-spatial invariance and v(x) velocity changes with x as well in contrast with exp(ipx) which is periodically invariant. In fact Newtonian mechanics (and Lagrangian/Hamiltonian as well) focus on d/dt i.e x(t). We have argued above that time intervals 1/E are independent of 1/p spatial ones. It may be noticed, however, that different p values lead to different wavelengths and so even though there is a kind of spatial invariance for each, when compared to each other this invariance is broken and superpositions of exp(ipx) may create local x probability densities. At the same they create spatial momentum densities because -d/dx (d/dx) 1/2m yields a kind of average kinetic energy when normalized. This seems to describe the x-p uncertainty relationship. In order to create spatial resolution (other than the built-in one in the wavelength) one needs to superpose different momenta, each of which are spatially invariant according to their periodic scheme exp(ipx). Thus one may create an average 1/2m <pp> and obtain a vrms. This may be described in terms of Newtonian external running x and t variables which have infinite resolution, but this vrms does not map to a physical state i.e to exp(i (mvrms) x) localized at x. Rather the various exp(ipx)’s which create vrms are the physical entities as may be seen by knocking a particle out of a bound state. The physical exp(ipx) momenta states have spatial invariance and so cannot be associated with a specific position in space. Only their superposition creates the notion of specific position in space, but then there is a distribution of p. This seems to be the basis for the x-p uncertainty principle. Thus we suggest that the particle of particle-wave duality is created through a mapping of a physical wave scenario to a continuous (infinite resolution) x-t scheme which in reality is an abstraction because each p,E free particle state has it sown internal clock-ruler i.e. 1/E and 1/p time and space units. Given that 1/E and 1/p have finite values the idea of dt and dx tending to 0 only makes sense as an abstraction which only holds in certain situations.
It’s di cult to gauge where popular opinion stands among physicists on the question of interpretation. My personal view is that the majority of professional working physicists (engaged in academic or industrial research of one form or another) probably think in terms of the Copenhagen interpretation they were taught at university, if they worry about interpretations at all. e chances are that they spend their time calculating amplitudes and probabilities and rarely li their heads from the computer monitor to ask what all of it means.
The 1935 paper by Einstein, Podolski and Rosen represented the culmination of a long debate that had begun soon after quantum theory was developed in the 1920s. One of the main protagonists in this discussion was Niels Bohr, a Danish physicist who worked in Copenhagen until, like so many other European scientists of his time, he became a refugee in the face of the German invasion during the Second World War. As we shall see, Bohr's views differed strongly from those of Einstein and his co-workers on a number of fundamental issues, but it was his approach to the fundamental problems of quantum physics that eventually gained general, though not universal, acceptance. Because much of Bohr's work was done in that city, his ideas and those developed from them have become known as the ‘Copenhagen interpretation’. In this chapter we shall discuss the main ideas of this approach. We shall try to appreciate its strengths as well as attempting to understand why some believe that there are important questions left unanswered. When Einstein said that ‘God does not play dice’, Bohr is said to have replied ‘Don't tell God what to do!’ The historical accuracy of this exchange may be in doubt, but it encapsulates the differences in approach of the two men. Whereas Einstein approached quantum physics with doubts, and sought to reveal its incompleteness by demonstrating its lack of consistency with our everyday ways of thinking about the physical universe, Bohr's approach was to accept the quantum ideas and to explore their consequences for our everyday ways of thinking.