Invariance of the laws of physics

[Delta2]

The invariance of the laws of physics in space-time is a corner stone of physics and all science.
A.Is this an axiom or can be derived from other more fundamental axioms?
B. Are there any books that discuss how science could be if the laws of physics could be changed (for example if we could make a simple experiment somewhere where two electrons repel, and then make the same experiment in some other place or some other time and found that two electrons attract?)

 

[anorlunda]

Imagine our forefathers who could not envision space travel or skydiving. They would have thought a pound is a pound the world around. Weight and mass would be the same thing.

At some later time, the possibility of free fall must have become apparent. They had to revise their thinking to distinguish the difference between weight and mass. Some ancients might have described that as changing the laws of physics, but others might describe it as applying the laws to previously unknown circumstances.

Isn't the whole point of astronomy to look and see how things elsewhere may be different than here? If things were the same everywhere, there would be no point in looking. When something different is found, we have to reconcile it with our current theories and models. That's the scientific method. Make theories. Gather evidence. Then see if the evidence confirms or refutes the theory. If you Google "scientific method" you should find lots of books.

 

[PeroK]

The invariance of the laws of physics in space-time is a corner stone of physics and all science.
A.Is this an axiom or can be derived from other more fundamental axioms?
B. Are there any books that discuss how science could be if the laws of physics could be changed (for example if we could make a simple experiment somewhere where two electrons repel, and then make the same experiment in some other place or some other time and found that two electrons attract?)

I think you are confusing different ideas in this post. You can loosely talk about invariance but at some point you have to be more precise about what you mean.

For example, in SR invariance is generally between inertial reference frames. Two identical experiments in two inertial reference frames should give the same result. Most importantly, a measurement of the speed of light.

There is also "invariance" across space and time, in the sense that the universe is homogenous and things don't change simply by displacing them in space or time.

The law that like charges repel (according to an inverse square law) is something different again. I'm not sure how you could construct a viable situation where, either with motion or in time, the electrons changed their behaviour: do they suddenly reach a spatial barrier, on the far side of which they attract?

 

[tech99]

I wondered if it was possible to make a computer game depicting a world where the laws of physics were different. But I have concluded that it is not possible to do this except for a limited portrayal, small area etc.

 

[Dale]

Are there any books that discuss how science could be if the laws of physics could be changed (for example if we could make a simple experiment somewhere where two electrons repel, and then make the same experiment in some other place or some other time and found that two electrons attract?)

From Noether’s theorem we know that such a universe would lose conservation of energy and conservation of linear momentum.

 

[Delta2]

I wondered if it was possible to make a computer game depicting a world where the laws of physics were different. But I have concluded that it is not possible to do this except for a limited portrayal, small area etc.

Actually you kind of read my mind. I was thinking that "what if" our physical reality which is very real to us, is kind of virtual for an entity (which we can call master programmer or God) and which can change the laws of physics by his own will, pretty much like a programmer in this world that has made a simulation of a phenomenon can change the laws of physics of the simulation by simply changing lines of codes in his program.

From Noether’s theorem we know that such a universe would lose conservation of energy and conservation of linear momentum.

And how do we know that those 2 laws of conservation are not violated from place to place and from time to time, or in other words that those two conservation laws have their own space-time invariance?

 

[Drakkith]

And how do we know that those 2 laws of conservation are not violated from place to place and from time to time, or in other words that those two conservation laws have their own space-time invariance?

We don't. We only know that they haven't been violated to a degree serious enough to be detectable to us at this time.

 

[hilbert2]

B. Are there any books that discuss how science could be if the laws of physics could be changed (for example if we could make a simple experiment somewhere where two electrons repel, and then make the same experiment in some other place or some other time and found that two electrons attract?)

As the spectrum of radiation from distant stars contains the same familiar hydrogen spectral lines (with easily explainable Doppler redshift) as our Sun, it's not likely that things like Planck's constant or elementary charge would have different values in some other part of the universe. Discontinuous changes, like the electron-electron force suddenly becoming attractive after crossing some invisible "border" somewhere, would be quite incompatible with the mathematical structure of the known physical laws.

 

[PeroK]

And how do we know that those 2 laws of conservation are not violated from place to place and from time to time, or in other words that those two conservation laws have their own space-time invariance?

We don't. But, to study something, you need to have some justification for thinking that it might be the case. As previous posts point out, there is justification for working on the basis that things don't change arbitrarily.

Moreover, what would you study instead? Electrons attracting? Electrons losing their repulsion slowly? Electrons gaining mass slowly? There are an unlimited number of "what ifs". As ever, Feynman has something to say about this here, which might be worth your watching:

http://www.cornell.edu/video/richard-feynman-messenger-lecture-7-seeking-new-laws

 

[Dale]

And how do we know that those 2 laws of conservation are not violated from place to place and from time to time, or in other words that those two conservation laws have their own space-time invariance?

You are putting one too many invariances in there. In Noether’s Theorem the laws of physics are written as a Lagrangian. If that Lagrangian is invariant wrt spacetime translations then energy and momentum are conserved. The conservation laws, in this approach, are not themselves separate laws of physics but are conserved quantities given by symmetries of the Lagrangian which is the laws of physics.

However, to your question about how we know: by experiment. With the exception of cosmology, our most predictive models are the ones where the Lagrangian is invariant with respect to spacetime translations. When you add a free parameter to a model you inherently reduce its predictive power.

Cosmology is an interesting case, because it is one where energy is not conserved. Because the data was not consistent with the simpler models, a model with additional free parameters was introduced. These additional parameters make the model more flexible but less predictive. So they are only used because the flexibility is required by the data.