35 ideas
| 10304 | Very few things in set theory remain valid in intuitionist mathematics [Bernays] |
| Full Idea: Very few things in set theory remain valid in intuitionist mathematics. | |
| From: Paul Bernays (On Platonism in Mathematics [1934]) |
| 10303 | Restricted Platonism is just an ideal projection of a domain of thought [Bernays] |
| Full Idea: A restricted Platonism does not claim to be more than, so to speak, an ideal projection of a domain of thought. | |
| From: Paul Bernays (On Platonism in Mathematics [1934], p.261) | |
| A reaction: I have always found Platonism to be congenial when it talks of 'ideals', and ridiculous when it talks of a special form of 'existence'. Ideals only 'exist' because we idealise things. I may declare myself, after all, to be a Restricted Platonist. |
| 10306 | Mathematical abstraction just goes in a different direction from logic [Bernays] |
| Full Idea: Mathematical abstraction does not have a lesser degree than logical abstraction, but rather another direction. | |
| From: Paul Bernays (On Platonism in Mathematics [1934], p.268) | |
| A reaction: His point is that the logicists seem to think that if you increasingly abstract from mathematics, you end up with pure logic. |
| 21202 | The strong force has a considerably greater range than the weak force [Martin,BR] |
| Full Idea: The strong nuclear force has a range of 10^-15 m, considerably larger than the range of the weak force. | |
| From: Brian R. Martin (Particle Physics [2011], 01) | |
| A reaction: This is because the bosons transmitting the weak force (W+, W-, W°) are much heavier than the gluons of the strong force. |
| 20624 | Work degrades into heat, but not vice versa [Close] |
| Full Idea: William Thomson, Lord Kelvin, declared (in 1865) the second law of thermodynamics: mechanical work inevitably tends to degrade into heat, but not vice versa. | |
| From: Frank Close (Theories of Everything [2017], 3 'Perpetual') | |
| A reaction: The basis of entropy, which makes time an essential part of physics. Might this be the single most important fact about the physical world? |
| 21211 | If an expected reaction does not occur, that implies a conservation law [Martin,BR] |
| Full Idea: If some reaction is not observed when there is apparently nothing to prevent it occurring, it is an indication that a conservation law is in operation. | |
| From: Brian R. Martin (Particle Physics [2011], 07) |
| 20623 | First Law: energy can change form, but is conserved overall [Close] |
| Full Idea: The first law of thermodynamics : energy can be changed from one form to another, but is always conserved overall. | |
| From: Frank Close (Theories of Everything [2017], 3 'Perpetual') | |
| A reaction: So we have no idea what energy is, but we know it's conserved. (Daniel Bernoulli showed the greater the mean energy, the higher the temperature. James Joule showed the quantitative equivalence of heat and work p.26-7) |
| 20625 | Third Law: total order and minimum entropy only occurs at absolute zero [Close] |
| Full Idea: The third law of thermodynamics says that a hypothetical state of total order and minimum entropy can be attained only at the absolute zero temperature, minus 273 degrees Celsius. | |
| From: Frank Close (Theories of Everything [2017], 3 'Arrow') | |
| A reaction: If temperature is energetic movement of atoms (or whatever), then obviously zero movement is the coldest it can get. So is absolute zero an energy state, or an absence of energy? I have no idea what 'total order' means. |
| 20622 | All motions are relative and ambiguous, but acceleration is the same in all inertial frames [Close] |
| Full Idea: There is no absolute state of rest; only relative motions are unambiguous. Contrast this with acceleration, however, which has the same magnitude in all inertial frames. | |
| From: Frank Close (Theories of Everything [2017], 3 'Newton's') | |
| A reaction: It seems important to remember this, before we start trumpeting about the whole of physics being relative. ....But see Idea 20634! |
| 20628 | The electric and magnetic are tightly linked, and viewed according to your own motion [Close] |
| Full Idea: Electric and magnetic phenomena are profoundly intertwined; what you interpret as electric or magnetic thus depends on your own motion. | |
| From: Frank Close (Theories of Everything [2017], 3 'Light!') | |
| A reaction: This sounds like an earlier version of special relativity. |
| 20635 | The general relativity equations relate curvature in space-time to density of energy-momentum [Close] |
| Full Idea: The essence of general relativity relates 'curvature in space-time' on one side of the equation to the 'density of momentum and energy' on the other. ...In full, Einstein required ten equations of this type. | |
| From: Frank Close (Theories of Everything [2017], 5 'Gravity') | |
| A reaction: Momentum involves mass, and energy is equivalent to mass (e=mc^2). |
| 20642 | Photon exchange drives the electro-magnetic force [Close] |
| Full Idea: The exchange of photons drives the electro-magnetic force. | |
| From: Frank Close (Theories of Everything [2017], 6 'Superstrings') | |
| A reaction: So light, which we just think of as what is visible, is a mere side-effect of the engine room of nature - the core mechanism of the whole electro-magnetic field. |
| 21209 | Electron emit and reabsorb photons, which create and reabsorb virtual electrons and positrons [Martin,BR] |
| Full Idea: In QED an electron constantly emits and reabsorbs virtual photons and these photons constantly create and reabsorb pairs of virtual electrons and positrons, and so on. | |
| From: Brian R. Martin (Particle Physics [2011], 06) | |
| A reaction: 'And so on'! These virtual particles have energy, and hence mass. |
| 20627 | Electric fields have four basic laws (two by Gauss, one by Ampère, one by Faraday) [Close] |
| Full Idea: Four basic laws of electric and magnetic fields: Gauss's Law (about the flux produced by a field), Gauss's law of magnets (there can be no monopoles), Ampère's Law (fields on surfaces), and Farday's Law (accelerated magnets produce fields). | |
| From: Frank Close (Theories of Everything [2017], 3 'Light!') | |
| A reaction: [Highly compressed, for an overview. Close explains them] |
| 20630 | Light isn't just emitted in quanta called photons - light is photons [Close] |
| Full Idea: Planck had assumed that light is emitted in quanta called photons. Einstein went further - light is photons. | |
| From: Frank Close (Theories of Everything [2017], 3 'Light!') | |
| A reaction: The point is that light travels as entities which are photons, rather than the emissions being quantized packets of some other stuff. |
| 20637 | In general relativity the energy and momentum of photons subjects them to gravity [Close] |
| Full Idea: In Einstein's general theory, gravity acts also on energy and momentum, not simply on mass. For example, massless photons of light feel the gravitational attraction of the Sun and can be deflected. | |
| From: Frank Close (Theories of Everything [2017], 5 'Planck') | |
| A reaction: Ah, a puzzle solved. How come massless photons are bent by gravity? |
| 20629 | Electro-magnetic waves travel at light speed - so light is electromagnetism! [Close] |
| Full Idea: Faradays' measurements predicted the speed of electro-magnetic waves, which happened to be the speed of light, so Maxwell made an inspired leap: light is an electromagnetic wave! | |
| From: Frank Close (Theories of Everything [2017], 3 'Light!') | |
| A reaction: Put that way, it doesn't sound like an 'inspired' leap, because travelling at exactly the same speed seems a pretty good indication that they are the same sort of thing. (But I'm not denying that Maxwell was a special guy!) |
| 20632 | In QED, electro-magnetism exists in quantum states, emitting and absorbing electrons [Close] |
| Full Idea: Dirac created quantum electrodynamics (QED): the universal electro-magnetic field can exist in discreet states of energy (with photons appearing and disappearing by energy excitations. This combined classical ideas, quantum theory and special relativity. | |
| From: Frank Close (Theories of Everything [2017], 3 'Light!') | |
| A reaction: Close says this is the theory of everything in atomic structure, but not in nuclei (which needs QCD and QFD). So if there are lots of other 'fields' (e.g. gravitational, weak, strong, Higgs), how do they all fit together? Do they talk to one another? |
| 20639 | Quantum fields contain continual rapid creation and disappearance [Close] |
| Full Idea: Quantum field theory implies that the vacuum of space is filled with particles and antiparticles which bubble in and out of existence on faster and faster timescales over shorter and shorter distances. | |
| From: Frank Close (Theories of Everything [2017], 6 'Intro') | |
| A reaction: Ponder this sentence until you head aches. Existence, but not as we know it, Jim. Close says calculations in QED about the electron confirm this. |
| 21201 | A 'field' is just a region to which points can be assigned in space and time [Martin,BR] |
| Full Idea: The word 'field' is simply a shorthand way of saying that a physical property is assigned to the points of space and time in a region. | |
| From: Brian R. Martin (Particle Physics [2011], 01) | |
| A reaction: This is disappointing because I had begun to think that fields were foundational for modern ontology. Turns out they are operational abstractions (according to Martin). Note that a field extends over time. |
| 21212 | The Higgs field, unlike others, has a nozero value in a state without particles [Martin,BR] |
| Full Idea: The Higgs field has the property of having a nonzero value in a state without particles, the vacuum state. Other fields are assumed to have a value zero in a vacuum state. | |
| From: Brian R. Martin (Particle Physics [2011], 09) | |
| A reaction: This seems to make a big difference to our concept of a field, since it has a measurable reality even when there are no particles. So it isn't just a geometrical frame for locating particles. |
| 20641 | Electrons get their mass by interaction with the Higgs field [Close] |
| Full Idea: The electron gets its mass by interaction with the ubiquitous Higgs field. | |
| From: Frank Close (Theories of Everything [2017], 6 'Hierarchy') | |
| A reaction: I thought I understood mass until I read this. Is it just wrong to say the mass of a table is the 'amount of stuff' in it? |
| 21205 | Many physicists believe particles have further structure, if only we could see it [Martin,BR] |
| Full Idea: Although standard particles are assumed to be structureless, many physicists believe that if distances could be probed down to 10^-35 m structures would be discovered. | |
| From: Brian R. Martin (Particle Physics [2011], 01) | |
| A reaction: Such probing is said to be probably impossible. And does the division then come to a halt? Aristotle's meditations on this are not irrelevant. |
| 20631 | Dirac showed how electrons conform to special relativity [Close] |
| Full Idea: In 1928 Paul Dirac discovered the quantum equation that describes the electron and conforms to the requirements special relativity theory. | |
| From: Frank Close (Theories of Everything [2017], 3 'Light!') | |
| A reaction: This sounds like a major step in the unification of physics. Quantum theory and General relativity remain irreconcilable. |
| 21203 | Uncertainty allows very brief violations of energy conservation - even shorter with higher energies [Martin,BR] |
| Full Idea: The uncertainty principle states that energy conservation can be violated, but only for a limited period of time. As the energy violation increases, the time period within which 'borrowed' energy has to be 'paid back' decreases. | |
| From: Brian R. Martin (Particle Physics [2011], 01) | |
| A reaction: This is the only reason modern physicists ever seem to mention the uncertainty principle. You can ask why this debt must be paid, but it seems to be hidden where the laws of physics may not even apply. |
| 21207 | The Exclusion Principle says no two fermions occupy the same state, with the same numbers [Martin,BR] |
| Full Idea: The 'exclusion principle' initially stated that no two electrons in a system could simultaneously occupy the same quantum state and thus have the same set of quantum numbers. The principle actually applies to all fermions, but not to bosons. | |
| From: Brian R. Martin (Particle Physics [2011], 02) | |
| A reaction: This principle is said to be at the root of atomic structure, making each element unique. What exactly is a 'system'? Why does this principle hold? How do you ensure two women don't wear the same dress at a party? |
| 20626 | Modern theories of matter are grounded in heat, work and energy [Close] |
| Full Idea: The link between temperature, heat, work and energy is at the root of our historical ability to construct theories of matter, such as Newton's dynamics, while ignoring, and indeed being ignorant of - atomic dimensions. | |
| From: Frank Close (Theories of Everything [2017], 3 'Arrow') | |
| A reaction: That is, presumably, that even when you fill in the atoms, and the standard model of physics, these aspects of matter do the main explaiining (of the behaviour, rather than of the structure). |
| 21204 | The standard model combines theories of strong interaction, and electromagnetic and weak interaction [Martin,BR] |
| Full Idea: As presently formulated, the standard model is two theories. One operates in the sector of strong interaction, and the other in the sector of the electromagnetic and weak interactions. | |
| From: Brian R. Martin (Particle Physics [2011], 01) | |
| A reaction: The first is Quantum Chomodynamics (QCD). The second is Quantum Electrodynamics (QED). Interesting that the weak interaction is included in the latter, which (I take it) means there is an electro-weak union. Interactions are the heart of the model. |
| 21208 | Eletrons don't literally 'spin', because they are point-like [Martin,BR] |
| Full Idea: The picture of a particle spinning like a top is sometime useful, but it is not consistent with the idea of the electron being point-like. In fact there is no analogy for spin in non-quantum physics. | |
| From: Brian R. Martin (Particle Physics [2011], 02) | |
| A reaction: If we take this stuff literally then it blow traditional metaphysics to bits, because an electron has properties without being a substance. In what sense can an electron 'have' properties if it is a point? In interactions they cease to be points. Eh? |
| 21210 | Virtual particles surround any charged particle [Martin,BR] |
| Full Idea: A cloud of virtual particles always surrounds a charged particle. | |
| From: Brian R. Martin (Particle Physics [2011], 06) | |
| A reaction: Here's a nice fact for aspiring Buddhists to meditate on. |
| 21206 | The properties of a particle are determined by its quantum numbers and its mass [Martin,BR] |
| Full Idea: In quantum theory, the full set of quantum numbers defines the state of the particle and, along with its mass, determines its properties. | |
| From: Brian R. Martin (Particle Physics [2011], 02) |
| 20633 | The Higgs field is an electroweak plasma - but we don't know what stuff it consists of [Close] |
| Full Idea: In 2012 it was confirmed that we are immersed in an electroweak plasma - the Higgs field. We curently have no knowledge of what this stuff might consist of. | |
| From: Frank Close (Theories of Everything [2017], 4 'Higgs') | |
| A reaction: The second sentence has my full attention. So we don't understand a field properly until we understand the 'stuff' it is made of? So what are all the familiar fields made of? Tell me more! |
| 21213 | String theory only has one free parameter (tension) - unlike the standard model with 19 [Martin,BR] |
| Full Idea: Unlike the standard model, with its 19 free parameters (including the masses of quarks, coupling constants and mixing angles), string theories have a single free paramater: the string tension. | |
| From: Brian R. Martin (Particle Physics [2011], 10) | |
| A reaction: This must be one feature in favour of string theory, despite its problems. |
| 20640 | Space-time is indeterminate foam over short distances [Close] |
| Full Idea: At very short distances, space-time itself becomes some indeterminate foam. | |
| From: Frank Close (Theories of Everything [2017], 6 'Intro') | |
| A reaction: [see Close for a bit more detail of this weird idea] |
| 21200 | An 'element' is what cannot be decomposed by chemistry [Martin,BR] |
| Full Idea: In the modern sense 'element' means a substance that cannot be decomposed by the methods of chemistry. | |
| From: Brian R. Martin (Particle Physics [2011], 01) |