Mass and Energy-Momentum

[geordief]

I note that both these seem to give rise to spacetime  curvature 

 

What might be  the apparent connection between  them?

 

Is mass a measure of some sort of concentration of the various fields?

(If that means anything )

[MigL]

Mass and energy are equivalent ( from E=mc² ).
As is momentum and energy ( from the same equation expanded to include massless particles )

[geordief]

2 hours ago, MigL said:

Mass and energy are equivalent ( from E=mc² ).
As is momentum and energy ( from the same equation expanded to include massless particles )

OK ,so  if we can substitute "energy " for "mass"(with the conversion factor,c^2) is there an intuitive way to understand why this energy  causes a more or less proportional  resistance to acceleration ?

If we just consider a massive object like a proton  would the energy be bound up in the  constituent particles and the forces holding them together (the bonds)? -and so would also describe the "mass"...

 

Maybe your last bit about expanding the equation to include massless particles  would need its own thread?

[swansont]

The full equation is E^2 = p^2c^2 + m^2c^4

The total energy depends on mass and momentum (related to kinetic energy)

[Tutoroot]

While normally we don't define a velocity for time, there is no reason we can't. Velocity is just distance over time. While it is quite common to express distances in units of time (i.e. light year), it is less common to express time in units of distance. However, if you do so, the definition for time velocity follows. To express time as a unit of distance, simply multiply by the speed of light. Velocities are always relative, so we need a second reference frame to use to measure the time velocity. 

[Bufofrog]

8 hours ago, Tutoroot said:

the definition for time velocity follows. To express time as a unit of distance, simply multiply by the speed of light

Then you are expressing a distance, not a velocity.  In other words you are saying that the velocity of time could equal 1 km, which makes no sense.

[geordief]

44 minutes ago, Bufofrog said:

Then you are expressing a distance, not a velocity.  In other words you are saying that the velocity of time could equal 1 km, which makes no sense.

Is there any point to comparing the passage of times between different frames of reference?

 

That would give numbers varying from zero to infinity. 

 

Could that represent a "speed  of time"?

 

I don't think (as per what I have heard) that space and time are equivalent  but they do seem very close  (and the signs in the spacetime interval  could be reversed)

[Bufofrog]

1 hour ago, geordief said:

Is there any point to comparing the passage of times between different frames of reference?

Sure.

1 hour ago, geordief said:

That would give numbers varying from zero to infinity.

Comparing passage of time for 2 reference frames will never give an answer of zero, unless you add in gravitation time dilation, I suppose.

1 hour ago, geordief said:

Could that represent a "speed  of time"?

I don't see how different reference frame could represent the 'speed of time', to be fair I don't know what the 'speed of time' is supposed to be exactly.  To me it seems like asking what is the speed of length.

[geordief]

2 minutes ago, Bufofrog said:

 

I don't see how different reference frame could represent the 'speed of time', to be fair I don't know what the 'speed of time' is supposed to be exactly.  To me it seems like asking what is the speed of length.

I agree .What about a property  of time  that changes with time? 

(Ps you said there might be a point in this measurement.What might that point be?Just academic or could there be any utility?)

[Bufofrog]

30 minutes ago, geordief said:

I agree .What about a property  of time  that changes with time?

I'm not sure what you mean.

30 minutes ago, geordief said:

(Ps you said there might be a point in this measurement.What might that point be?Just academic or could there be any utility?)

The difference in the passage of time between reference frame is important for things like GPS.  Not taking time dilation into account will make GPS inaccurate.

[geordief]

7 minutes ago, Bufofrog said:

I'm not sure what you mean.

The difference in the passage of time between reference frame is important for things like GPS.  Not taking time dilation into account will make GPS inaccurate.

The ratio of the passage through time  btw frames changes as  the relative motion btw the frames changes (if i does)

That is the measurement I am wondering if it is academic or of some practical consequence.

[swansont]

10 hours ago, geordief said:

Is there any point to comparing the passage of times between different frames of reference

Like in the Hafele-Keating experiment? I’d say there was a point in doing that.

[geordief]

23 minutes ago, swansont said:

Like in the Hafele-Keating experiment? I’d say there was a point in doing that.

What if the frames relative  motion varies between zero and c?(so not  a Hafele-Keating experiment)

Would there be any particular interpretation to the results of such an experiment?

(I  mean ,we know what those measurements would be,I think and there would be no need to perform the experiment but would that flesh out our understanding of how time works at all?)

[Genady]

8 hours ago, geordief said:

The ratio of the passage through time  btw frames changes as  the relative motion btw the frames changes (if i does)

That is the measurement I am wondering if it is academic or of some practical consequence.

It does in particle accelerators. I guess it is of a practical consequence.

[geordief]

5 minutes ago, Genady said:

It does in particle accelerators. I guess it is of a practical consequence.

Ah yes,maybe more mundane than I thought.

[Awatso]

On 2/3/2023 at 2:17 PM, geordief said:

Is there any point to comparing the passage of times between different frames of reference?

 

 

There is for optics and electromagnetism, which was the problem that was causing problems around the turn of the 20thC.   Classic mechanics was failing with various experiments and it was the new idea of time not being independant of location that linked it together so both sets of results could be explained. 

The Lorantz transformations are used between different co-ordinate systems that have relative velocity to work out the relative time component.

Especially with trains and embankments !  ( joke ).

I hope I have got that right, obviously corrections will be welcome. 

 

 

[studiot]

1 hour ago, Awatso said:

 

There is for optics and electromagnetism, which was the problem that was causing problems around the turn of the 20thC.   Classic mechanics was failing with various experiments and it was the new idea of time not being independant of location that linked it together so both sets of results could be explained. 

The Lorantz transformations are used between different co-ordinate systems that have relative velocity to work out the relative time component.

Especially with trains and embankments !  ( joke ).

I hope I have got that right, obviously corrections will be welcome. 

 

 

Please note

1. That all velocity is 'relative'. 'Velocity' without a reference point is meaningless.
    
2. Trains were the fastest transport known in Einstein's day.
    
3. Maxwell's EM theory actually obeyed the 'principle of relativity'. It was Newtonian mechanics as embodied in the usual statements of his three laws that did not.